{ "cells": [ { "cell_type": "markdown", "id": "ch21-cell00", "metadata": {}, "source": [ "# Scientific Computing: Precision, Performance, and Reproducibility\n", "\n", "*Mathematical Rules of Thumb · Jason Karpeles · Chapter 21*\n", "\n", "Precision, Performance, and Reproducibility\n", "\n", "Open [the interactive reader](reader.html) to explore the supported parameter choices without running code. Saved figures and calculations below can be read as they are. All example inputs are constructed.\n", "\n", "Optional reproduction requires Python, NumPy, Matplotlib and IPython. Code is marked collapsed, although viewer support varies. All mathematical functions and inputs are included here; no author-machine paths or other notebooks are required." ] }, { "cell_type": "code", "execution_count": 1, "id": "ch21-cell01", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:58:20.781574Z", "iopub.status.busy": "2026-10-03T00:58:20.781482Z", "iopub.status.idle": "2026-10-03T00:58:20.827479Z", "shell.execute_reply": "2026-10-03T00:58:20.827413Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustrated-setup" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Calculation definitions loaded; all inputs are constructed.\n" ] } ], "source": [ "import io\n", "import matplotlib\n", "matplotlib.use('Agg')\n", "from IPython.display import Image, Markdown, display\n", "from cycler import cycler\n", "\"\"\"Constructed teaching calculations shared by readers and portable notebooks.\n", "\n", "Requires NumPy and Matplotlib. No measurements, online data or trained models.\n", "All stochastic illustrations use stated, fixed seeds.\n", "\"\"\"\n", "import math\n", "import itertools\n", "from collections import deque\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "def canvas(xlabel, ylabel, title, two=False):\n", " fig, axes = plt.subplots(1, 2 if two else 1, figsize=(10, 4.4), layout='constrained')\n", " for ax in np.atleast_1d(axes):\n", " ax.grid(alpha=.18)\n", " ax.set(xlabel=xlabel, ylabel=ylabel)\n", " np.atleast_1d(axes)[0].set_title(title)\n", " return fig, axes\n", "\n", "\n", "def integer_ticks(ax, axis='x'):\n", " from matplotlib.ticker import MaxNLocator\n", " (ax.xaxis if axis=='x' else ax.yaxis).set_major_locator(MaxNLocator(integer=True))\n", "\n", "\n", "def bits(x):\n", " return f'{x:.6g} bit'+('' if x==1 else 's')\n", "\n", "\n", "def result(fig, ax, metrics, text):\n", " for a in np.atleast_1d(ax):\n", " if a.get_legend_handles_labels()[0]:\n", " old=a.get_legend()\n", " a.legend(fontsize=9,loc=old._loc if old is not None else 'best')\n", " return fig, metrics, text\n", "\n", "\n", "def illustrate(chapter, demo, p):\n", " \"\"\"Return an executed figure, metrics and interpretation for one example.\"\"\"\n", " fig,metrics,text=globals()[f'chapter_{chapter:02d}'](demo, p)\n", " # Mark a selected point on comparisons whose full curve stays fixed.\n", " if (chapter,demo) in {(9,1),(11,1),(11,3),(13,2),(15,1),(15,2),(15,3),\n", " (16,1),(17,2),(17,3),(18,3),(19,3),(20,3),(22,2),(23,3)}:\n", " ax=fig.axes[0];ax.axvline(p,color='#a26913',linestyle=':',label='Selected input')\n", " ax.legend(fontsize=9)\n", " return fig,metrics,text\n", "\n", "\n", "def chapter_01(d, p):\n", " if d == 1:\n", " x=np.linspace(0,.2,201); exact=(1+x)**5; linear=1+5*x\n", " fig,ax=canvas('Fractional input increase', 'Response multiplier', 'Where linearization bends')\n", " ax.plot(x,exact,label='Exact fifth power');ax.plot(x,linear,'--',label='Linear estimate');ax.axvline(p,color='#a26913',linestyle=':',label='Selected input')\n", " a=(1+p)**5;b=1+5*p;m={'Exact multiplier':a,'Linear estimate':b,'Absolute error':abs(a-b)}\n", " t=f'An input increase of {100*p:g}% gives {a:.6g}, versus {b:.6g} from linearization. Judge the {abs(a-b):.6g} error against your tolerance.'\n", " elif d == 2:\n", " k=np.arange(1,21);tails=p**k/(1-p)\n", " fig,ax=canvas('First omitted exponent k','Infinite tail','Tail = first omitted term × 1/(1−r)')\n", " ax.semilogy(k,tails,label='Exact tail');ax.semilogy(k,p**k,'--',label='First omitted term');ax.scatter([5],[p**5/(1-p)],color='#a26913',zorder=3,label='Tail after exponent 4 (k=5)');integer_ticks(ax)\n", " m={'Ratio r':p,'Tail from r^5 onward':p**5/(1-p),'Tail / first term':1/(1-p)}\n", " t=f'The tail starting at r^5 equals r^5/(1-r). At r={p:g}, its multiplier over the first omitted term is {1/(1-p):.6g}; a ratio near one makes the tail much larger.'\n", " elif d==3:\n", " x=np.linspace(-3,3,301);y=x*x+p*x+1\n", " fig,ax=canvas('x','x² + b x + 1','Roots change at the discriminant boundary')\n", " ax.plot(x,y,label=f'b={p:g}');ax.axhline(0,color='gray');disc=p*p-4\n", " m={'Discriminant':disc,'Real root count':2 if disc>0 else 1 if disc==0 else 0,'Vertex x':-p/2}\n", " t=f'The discriminant b²-4 is {disc:g}. This gives '+('two distinct real roots.' if disc>0 else 'one repeated real root.' if disc==0 else 'no real roots; the two roots are complex conjugates.')\n", " elif d==4:\n", " r=np.linspace(.005,.25,250);fig,ax=canvas('Growth rate per period (%)','Rule-of-70 error (% of exact time)','How far the rule of 70 drifts as the rate grows')\n", " ax.plot(100*r,100*(.7/r-np.log(2)/np.log1p(r))/(np.log(2)/np.log1p(r)),label='(70/rate% − exact) / exact');ax.axhline(0,color='gray');ax.axvline(100*p,color='#a26913',linestyle=':',label='Selected rate')\n", " ex=math.log(2)/math.log1p(p);est=70/(100*p);m={'Rate per period (%)':100*p,'Exact doubling time (periods)':ex,'Rule-of-70 estimate (periods)':est,'Estimate error (periods)':est-ex}\n", " t=f'At {100*p:g}% per period the exact doubling time is {ex:.4g} periods; the rule of 70 says {est:.4g}. '+('Good enough for mental arithmetic.' if abs(est-ex)/ex<.03 else f'The shortcut is {100*abs(est-ex)/ex:.2g}% too short at this high rate, because 70 matches continuous growth and ln(1+r) falls below r as r grows.')\n", " elif d==5:\n", " x=np.linspace(-4,8,1201);x=x[np.abs(x-3)>.05];y=(x+1)/(x-3)\n", " fig,ax=canvas('x','(x+1)/(x-3)','Multiplying by x−3 flips the inequality when x<3')\n", " ax.plot(x[x<3],y[x<3],color='#136f75',label='(x+1)/(x-3)');ax.plot(x[x>3],y[x>3],color='#136f75');ax.axhline(0,color='gray');ax.axvline(3,color='gray',linestyle='dashed',label='Excluded x=3')\n", " ax.axvspan(-1,3,color='#136f75',alpha=.12,label='True solution [-1, 3)');ax.plot([-4,-1],[-9.5,-9.5],lw=5,color='#a26913',label='Naive answer x ≤ -1');ax.set(ylim=(-10,10))\n", " v=(p+1)/(p-3);true=v<=0;naive=p+1<=0;ax.scatter([p],[v],color='black',zorder=3,label=f'Test x={p:g}')\n", " m={'Test x':p,'(x+1)/(x-3)':v,'Truly satisfies':'yes' if true else 'no','Naive x ≤ -1 says':'yes' if naive else 'no'}\n", " t=f'At x={p:g} the fraction equals {v:.4g}, so the inequality is '+('true' if true else 'false')+'. Cross-multiplying without a sign check gives x+1 ≤ 0, which says '+('true' if naive else 'false')+'. '+('The two agree here only because x>3 keeps the denominator positive.' if true==naive else 'They disagree because x<3 makes the denominator negative, which reverses the inequality.')\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_02(d,p):\n", " if d==1:\n", " x=np.linspace(.5,3,151);fig,ax=canvas('Linear scale factor','Relative size','Similar shapes scale by different powers')\n", " ax.plot(x,x**2,label='Area');ax.plot(x,x**3,label='Volume');ax.axvline(p,color='#a26913',linestyle=':',label='Selected input')\n", " m={'Area factor':p*p,'Volume factor':p**3,'Boundary / area factor':1/p};t=f'A similar shape scaled by {p:g} has area multiplied by {p*p:g}, volume by {p**3:g}, and boundary-to-area ratio by {1/p:.6g}. These multipliers hold only when every length scales by the same factor.'\n", " elif d==2:\n", " radius=10.;x=np.linspace(0,12,151);exact=radius-np.sqrt(radius**2-(x/2)**2);estimate=x*x/(8*radius)\n", " fig,ax=canvas('Chord length','Sagitta (same length units)','Shallow arcs and their approximation');ax.plot(x,exact,label='Exact');ax.plot(x,estimate,'--',label='c²/(8R)');ax.axvline(p,color='#a26913',linestyle=':',label='Selected input')\n", " a=radius-math.sqrt(radius**2-(p/2)**2);b=p*p/(8*radius);m={'Radius':radius,'Exact sagitta':a,'Approximate sagitta':b,'Relative error (vs exact sagitta)':abs(a-b)/a};t=f'With radius 10 and chord {p:g}, sagitta is {a:.6g}. The shallow-arc estimate is {b:.6g}; its relative error grows as the chord becomes less shallow.'\n", " elif d==3:\n", " n=np.arange(3,81);ratio=n*np.sin(2*np.pi/n)/(2*np.pi)\n", " fig,ax=canvas('Polygon side count','Fractional missing area','Inscribed polygons approach a circle');ax.loglog(n,1-ratio,label='Exact missing fraction');ax.loglog(n,2*np.pi**2/(3*n*n),'--',label='Leading n⁻² scale');ax.axvline(p,color='#a26913',linestyle=':',label='Selected input');ax.set_xticks([3,5,10,20,40,80]);ax.set_xticklabels(['3','5','10','20','40','80']);ax.minorticks_off()\n", " err=1-p*math.sin(2*math.pi/p)/(2*math.pi);m={'Sides':p,'Circle area fraction missing':err};t=f'The regular {p:g}-gon misses {100*err:.6g}% of its unit-circle area. The n⁻² curve is an asymptotic comparison, not an exact formula for small polygons.'\n", " elif d==4:\n", " a,b=3.,4.;fig,ax=canvas('x (length units)','y (length units)','Can sides 3, 4 and c close into a triangle?')\n", " lo,hi=b-a,a+b;ok=lo1e-9 else ''\n", " t=f'The vector and its opposite share the component ratio y/x. Here atan2 gives {correct:.6g}°.{wrap} '+('Plain atan also gives '+f'{wrong:.6g}°, because x>0 places this vector in the half-plane plain atan covers.' if same else f'Plain atan gives {wrong:.6g}°, which points along the opposite vector.')\n", " elif d==3:\n", " x=np.logspace(-12,-1,120);direct=1-np.cos(x);stable=2*np.sin(x/2)**2\n", " fig,ax=canvas('Angle (radians)','Relative difference from stable identity','Subtraction can erase a small quantity');ax.loglog(x,np.maximum(abs(direct-stable)/stable,1e-18),label='Direct subtraction error');ax.axvline(p,color='#a26913');a=1-math.cos(p);b=2*math.sin(p/2)**2\n", " rel=abs(a-b)/b;m={'Direct 1 − cos(x)':a,'Half-angle identity':b,'Relative difference':rel};t=f'At x={p:g}, direct subtraction gives {a:.10g}, while the equivalent half-angle expression gives {b:.10g}. '+('Binary64 rounding made cos(x) exactly 1, so the direct result was erased.' if a==0 else f'The direct result survives but has lost digits: its relative difference is {rel:.2g}.')\n", " elif d==4:\n", " A=math.radians(30);b=10.;h=b*math.sin(A);fig,ax=canvas('x (length units)','y (length units)','Side a swings from C; how many places meet the base?')\n", " C=(b*math.cos(A),h);ax.plot([0,22],[0,0],color='gray',label='Base line from A');ax.plot([0,C[0]],[0,C[1]],lw=3,label='Side b=10');th=np.linspace(0,2*np.pi,300);ax.plot(C[0]+p*np.cos(th),C[1]+p*np.sin(th),':',color='#a26913',label=f'Reach of side a={p:g}')\n", " xs=[] if p1e-9]\n", " for x in xs: ax.plot([C[0],x],[C[1],0],lw=2,color='#136f75')\n", " ax.scatter(xs,[0]*len(xs),color='#136f75',zorder=3,label='Valid vertex B' if xs else None);ax.set(xlim=(-3,22),ylim=(-8,14));ax.set_aspect('equal')\n", " m={'Height b·sin A':h,'Side a':p,'Number of triangles':len(xs)}\n", " t={0:f'a={p:g} is shorter than the height {h:g}, so side a cannot reach the base: no triangle. Arcsin would fail with sin B>1.',2:f'a={p:g} is between the height {h:g} and b=10, so it meets the base twice: two valid triangles. Arcsin returns only the acute B; the obtuse angle 180° minus B is also valid.',1:f'a={p:g} is at least b=10, so only one meeting point lies on the correct side of A: one triangle.'}[len(xs)]\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_04(d,p):\n", " if d==1:\n", " x=np.linspace(80,120,201);fig,ax=canvas('x','Square root','Tangent estimates need an error budget');ax.plot(x,np.sqrt(x),label='Exact');ax.plot(x,10+(x-100)/20,'--',label='Tangent at 100');ax.axvline(100+p,color='#a26913',linestyle=':',label='Selected input');a=math.sqrt(100+p);b=10+p/20;bound=p*p/(8*min(100,100+p)**1.5)\n", " m={'Exact':a,'Linear estimate':b,'Actual error':abs(a-b),'Remainder bound':bound};t=f'For x=100+{p:g}, the linear estimate differs by {abs(a-b):.6g}. Bounding the second derivative on the intervening interval certifies error at most {bound:.6g}.'\n", " elif d==2:\n", " step=(p+2/p)/2;x=np.linspace(.1,max(3,step+.5),301);fig,ax=canvas('x','x² − 2','Newton follows a tangent');ax.plot(x,x*x-2,label='Function');ax.plot(x,p*p-2+2*p*(x-p),'--',label='Tangent');ax.axhline(0,color='gray');ax.scatter([p,step],[p*p-2,0],color='#a26913',zorder=3,label='Start and next x')\n", " m={'Starting x':p,'Next x':step,'Next residual':step*step-2};t=f'The tangent from x={p:g} crosses zero at {step:.6g}. '+(f'The step overshot: the residual grew from {abs(p*p-2):.6g} to {abs(step*step-2):.6g}. Newton is reliable only near the root, so bracket first.' if abs(step*step-2)>abs(p*p-2) else f'The residual shrank from {abs(p*p-2):.6g} to {abs(step*step-2):.6g}, so this step helped.')\n", " elif d==3:\n", " x=np.arange(1,101);a=x.astype(float)**(-p);partial=np.cumsum(a);fig,ax=canvas('Terms retained','Partial sum','A p-series threshold is about the infinite tail');ax.plot(x,partial,label=f'p={p:g}');tail=100**(1-p)/(p-1) if p>1 else 'No finite tail bound'\n", " m={'Exponent p':p,'100-term sum':partial[-1],'Integral upper bound on tail':tail};t='Adding n⁻ᵖ forever gives a finite total only when p>1. '+(f'At p={p:g}, the tail after 100 is at most {tail:.6g}.' if p>1 else 'A finite partial sum does not establish convergence; this selected series diverges.')\n", " elif d==4:\n", " x=1.;k=np.arange(0,11);part=np.cumsum([x**j/math.factorial(j) for j in k]);err=abs(math.e-part);nxt=np.array([x**(j+1)/math.factorial(j+1) for j in k])\n", " fig,ax=canvas('Polynomial degree n','Error at x=1','Taylor error for eˣ tracks the first omitted term');ax.semilogy(k,err,'o-',label=r'Actual error $|e-T_n(1)|$');ax.semilogy(k,nxt,'s',linestyle='dashed',label='First omitted term 1/(n+1)!');ax.axvline(p,color='#a26913',linestyle=':',label='Selected degree');integer_ticks(ax)\n", " e=err[p];s=nxt[p];m={'Degree n':p,'Actual error':e,'First omitted term':s,'Actual / omitted':e/s}\n", " t=f'Stopping at degree {p} leaves error {e:.3g}. The first omitted term {s:.3g} predicts it within a factor {e/s:.3g}, so you can read the error budget before computing e. '+('At this low degree the later terms still add a noticeable share.' if e/s>1.2 else 'Higher degrees make the first omitted term almost the whole story.')\n", " elif d==5:\n", " x=np.linspace(-.5,.5,1001);x=x[np.abs(x)>.004];y=(np.sin(x)+p)/x\n", " fig,ax=canvas('x','(sin x + a) / x','L\\'Hôpital needs 0/0 first');ax.plot(x[x<0],y[x<0],color='#136f75',label=f'a={p:g}');ax.plot(x[x>0],y[x>0],color='#136f75');ax.axhline(1,color='#a26913',linestyle='dashed',label='Blind L\\'Hôpital: cos 0 / 1 = 1');ax.set(ylim=(-6,6))\n", " r=(math.sin(.01)+p)/.01;m={'Numerator at x=0':p,'Form at x=0':'0/0' if p==0 else 'nonzero/0','Ratio at x=0.01':r,'Blind L\\'Hôpital answer':1}\n", " t=(f'With a=0 the form is 0/0, so L\\'Hôpital applies and the limit really is 1; the ratio at x=0.01 is {r:.6g}.' if p==0 else f'With a={p:g} the numerator tends to {p:g} while the denominator tends to 0, so the ratio blows up (it is {r:.4g} at x=0.01) and has no finite limit. Differentiating anyway still returns 1, a wrong answer.')\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_05(d,p):\n", " if d==1:\n", " n=np.arange(max(21,math.ceil(math.log(.01)/math.log(p))+4));x=1-p**n;error=p**n;certificate=p**n/(1-p)*(1-p)\n", " fig,ax=canvas('Iteration','Absolute error','A contraction supplies a certificate');ax.semilogy(n,error,lw=4,alpha=.45,label='Exact error to fixed point 1');ax.semilogy(n,certificate,'--',label='Contraction bound (coincides here)');ax.axhline(.01,color='gray',linestyle=':',label='Target .01');ax.axvline(math.ceil(math.log(.01)/math.log(p)),color='#a26913',label='Steps needed');m={'Contraction q':p,'Error after 10 steps':p**10,'Steps for error ≤ .01':math.ceil(math.log(.01)/math.log(p))};t=f'T(x)=q x+(1-q), starting at zero, has error qⁿ. At q={p:g}, {m[\"Steps for error ≤ .01\"]} steps suffice for .01 error. In this affine example the bound equals the exact error, so the two curves coincide. q must be strictly below one.'\n", " elif d==2:\n", " x=np.linspace(0,1,501);fig,ax=canvas('x in [0,1]','xⁿ','Pointwise convergence is not uniform');ax.plot(x,x**p,label=f'n={p:g}');ax.scatter([1],[1],label='Endpoint remains 1');m={'Value at x=.9':.9**p,'Value at x=1':1,'Supremum error to pointwise limit':1};t=f'Increasing n suppresses xⁿ at every fixed x<1, but a boundary layer remains near one. The supremum difference from the discontinuous pointwise limit is 1 for every n; this is not uniform convergence.'\n", " elif d==3:\n", " n=np.arange(1,31);tail=p**(n+1)/(1-p);fig,ax=canvas('Last retained exponent n','Uniform remainder ceiling','A geometric majorant controls every x');ax.semilogy(n,tail,label='Geometric bound on the tail');ax.yaxis.set_major_formatter(__import__('matplotlib').ticker.LogFormatterSciNotation(labelOnlyBase=False));m={'Uniform |x| ceiling q':p,'Remainder after exponent 10':p**11/(1-p)};t=f'For |x|≤{p:g}<1, the series sum xⁿ is uniformly controlled by sum qⁿ. Its tail after exponent 10 is at most {m[\"Remainder after exponent 10\"]:.6g}; the bound deteriorates as q approaches one.'\n", " elif d==4:\n", " pos=iter(1/np.arange(1,10**6,2));neg=iter(-1/np.arange(2,10**6,2));s=0.;path=[]\n", " for _ in range(3000): s+=next(pos) if s<=p else next(neg);path.append(s)\n", " fig,ax=canvas('Terms used','Running sum','Same terms ±1/n, new order, new sum');ax.semilogx(range(1,3001),path,label='Rearranged sum');ax.axhline(math.log(2),color='gray',linestyle='dashed',label='Usual order: ln 2 ≈ 0.693');ax.axhline(p,color='#a26913',linestyle=':',label=f'Target {p:g}')\n", " m={'Target':p,'Sum after 3000 terms':path[-1],'Usual-order sum ln 2':math.log(2)}\n", " t=f'Adding positives while at or below {p:g} and negatives while above steers the running sum to {path[-1]:.4g}. '+'The terms are exactly those of the ln 2 series; only the order changed. Because the sum of |terms| diverges, order is part of the answer.'\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_06(d,p):\n", " if d==1:\n", " theta=np.linspace(0,2*np.pi,361);z=np.exp(1j*theta);fig,ax=canvas('Real part','Imaginary part','A power multiplies the argument');ax.plot(z.real,z.imag,'--',color='#9aa3a8',label='Unit circle');ang=np.linspace(0,np.radians(135*p),400);rad=.25+.12*ang/(2*np.pi);ax.plot(rad*np.cos(ang),rad*np.sin(ang),color='#a26913',label='Unwrapped angle path');point=np.exp(1j*np.radians(135));out=point**p;ax.quiver(0,0,point.real,point.imag,angles='xy',scale_units='xy',scale=1,color='#9aa3a8',label='Input z (135°)');ax.quiver(0,0,out.real,out.imag,angles='xy',scale_units='xy',scale=1,color='#136f75',label=f'Output z^{p:g}');ax.set(xlim=(-1.3,1.3),ylim=(-1.3,1.3));ax.set_aspect('equal');unwrapped=135*p;principal=math.degrees(np.angle(out));turns=round((unwrapped-principal)/360);m={'Input argument (degrees)':135,'Unwrapped output argument':unwrapped,'Principal output argument':principal,'Full turns lost by principal value':turns};t=f'Integer power {p:g} multiplies the argument: 135°×{p:g}={unwrapped:g}°. '+(f'The principal argument wraps this to {principal:.6g}°, dropping {turns} full turn{\"s\" if turns!=1 else \"\"}; only the unwrapped angle records them.' if turns else f'Here {unwrapped:g}° already lies in (−180°,180°], so no wrap occurs.')\n", " elif d==2:\n", " k=np.arange(0,7);fig,ax=canvas('Derivative order k','Cauchy upper bound','A larger analytic disk gives stronger bounds')\n", " for R in (1,2,4):\n", " b=np.array([math.factorial(int(n))*3/R**n for n in k]);ax.semilogy(k,b,'o-',lw=2.5 if R==p else 1,alpha=1 if R==p else .35,label=f'k! M / Rᵏ, R={R}'+(' (selected)' if R==p else ''))\n", " integer_ticks(ax);m={'Disk radius R':p,'Boundary bound M':3,'Second derivative ceiling':6/p**2};t=f'If the function is analytic on and inside this disk and its boundary modulus is at most 3, |f″(0)|≤6/R²={6/p**2:.6g}. Doubling the radius cuts this ceiling by four. A function that stays tame across a wide disk cannot bend sharply at its center.'\n", " elif d==3:\n", " theta=np.linspace(0,2*np.pi,501);z=np.exp(1j*theta);w=z**3+p;fig,ax=canvas('Real part','Imaginary part','Boundary image and roots of z³ + a');ax.plot(w.real,w.imag,label='Mapped unit-circle boundary');ax.scatter([0],[0],color='#a26913',label='Origin');roots=np.roots([1,0,0,p]);ax.plot(np.cos(theta),np.sin(theta),':',color='#9aa3a8',label='Unit circle |z|=1');ax.scatter(roots.real,roots.imag,marker='x',s=70,color='#aa4e37',zorder=3,label='Roots of z³+a');ax.set(xlim=(-1.4,2.4),ylim=(-1.3,2.3));ax.set_aspect('equal');count=int(np.sum(abs(roots)<1-1e-10));m={'Constant a':p,'Strict domination |a| < 1':p<1,'Zeros strictly inside disk':count};t=f'For a={p:g}, '+('Rouché compares z³ with a on |z|=1 and gives three interior zeros.' if p<1 else 'strict boundary domination fails. At a=1 the zeros lie on the boundary; above one they lie outside. The failed theorem test must not be treated as a zero-count proof.')\n", " elif d==4:\n", " theta=np.linspace(0,2*np.pi,4001)[:-1];poles=np.array([.5,1.5]);res=np.array([-1.,1.]);z=p*np.exp(1j*theta);I=np.sum(1/((z-.5)*(z-1.5))*1j*z)*(2*np.pi/len(theta));inside=abs(poles)1e-16 else 'Below 1e-16 (rounding level)','Steps to reach 10⁻⁶':hit if hit else 'More than 60'};t=f'Matrix diag(1,{p:g},0.3), start (1,1,1)/√3. Each step multiplies the error by about {p:g}. '+(f'The error passes 10⁻⁶ in {hit} steps.' if hit else f'After 60 steps the error is still {err[-1]:.3g}. A ratio this close to one needs about {math.ceil(math.log(1e-6)/math.log(p))} steps, so use a shift or a different method.')\n", " elif d==5:\n", " rng=np.random.default_rng(705);U,_=np.linalg.qr(rng.standard_normal((50,2)));V,_=np.linalg.qr(rng.standard_normal((2,2)));A=U@np.diag([1.,1/p])@V.T;xt=np.array([1.,1.]);b=A@xt;Q,R=np.linalg.qr(A);xq=np.linalg.solve(R,Q.T@b);xn=np.linalg.solve(A.T@A,A.T@b);eq=np.linalg.norm(xq-xt)/np.linalg.norm(xt);en=np.linalg.norm(xn-xt)/np.linalg.norm(xt)\n", " ks=np.logspace(0,8,60);fig,ax=canvas('Condition number κ of A','Relative error in the solution','Normal equations square the condition number');ax.loglog(ks,np.maximum(ks*2.2e-16,1e-17),color='#136f75',label='QR scale: κ × 2.2×10⁻¹⁶');ax.loglog(ks,np.minimum(ks**2*2.2e-16,10),ls='dashed',color='#a26913',label='Normal equations scale: κ² × 2.2×10⁻¹⁶');ax.scatter([p],[max(eq,1e-17)],s=90,color='#136f75',zorder=3,label='Actual QR error');ax.scatter([p],[max(en,1e-17)],s=90,marker='s',color='#aa4e37',zorder=3,label='Actual normal-equations error');ax.set_ylim(1e-17,20)\n", " m={'Condition number of A':float(p),'Condition number of AᵀA':float(p)**2,'QR relative error':eq,'Normal-equations relative error':en};t=f'A is a constructed 50×2 matrix with κ={p:g} and an exact fit, so the true answer is (1,1). QR works with A directly and loses about log10 κ={math.log10(p):.0f} digits; its error is {eq:.2g}. The normal equations solve with AᵀA, whose condition number is κ²={p**2:.3g}. '+('At this mild conditioning both errors are tiny, so the difference does not matter yet.' if p**2<1e8 else f'Their error is {en:.2g}, about {en/max(eq,1e-16):.2g} times worse. Squaring κ doubles the digits lost.' if p**2<1e15 else f'κ² is past 1/2.2×10⁻¹⁶, so AᵀA is singular to working precision and the normal-equations answer is wrong in the leading digits (error {en:.2g}), while QR still has about {-math.log10(max(eq,1e-16)):.0f} correct digits.')\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_08(d,p):\n", " if d==1:\n", " a,b=43,p;trace=[]\n", " while b:trace.append(b);a,b=b,a%b\n", " fig,ax=canvas('Euclidean step','Value','Remainders reveal the gcd');ax.plot(range(len(trace)),trace,'o-',label='Input a, then nonzero remainders');ax.set_xlim(-.5,max(len(trace),3)-.5);integer_ticks(ax);g=math.gcd(p,43);inv=pow(p,-1,43) if g==1 else 'Does not exist';m={'gcd(a,43)':g,'Inverse modulo 43':inv};t=f'For a={p:g}, gcd(a,43)={g}. '+(f'The inverse is {inv}, checked by a×inverse mod43=1.' if g==1 else '43 ≡ 0 mod 43, so a has no inverse and you cannot divide by it modulo 43.')\n", " elif d==2:\n", " n=np.arange(0,60);selected=[k for k in n if k%3==2 and k%5==p];fig,ax=canvas('Integer candidate','Remainder','Two congruences select one class modulo 15');ax.scatter(n,n%3,s=10,label='mod 3');ax.scatter(n,n%5,s=10,label='mod 5');ax.scatter(selected,[2]*len(selected),s=100,facecolors='none',edgecolors='#a26913',label='Both conditions');ax.set_ylim(-.5,7.5);r=next(k for k in range(15) if k%3==2 and k%5==p);m={'Remainder modulo 3':2,'Remainder modulo 5':p,'Solution modulo 15':r};t=f'The simultaneous conditions x≡2 mod3 and x≡{p:g} mod5 select x≡{r} mod15. Because 3 and 5 share no factor, exactly one remainder out of 15 works, so the circled points repeat every 15.'\n", " elif d==3:\n", " prime=np.ones(p+1,dtype=bool);prime[:2]=False\n", " for k in range(2,math.isqrt(p)+1):\n", " if prime[k]:prime[k*k::k]=False\n", " x=np.arange(2,p+1);counts=np.cumsum(prime)[2:];fig,ax=canvas('Upper limit n','Prime count','An asymptotic estimate is not an exact count');ax.plot(x,counts,label='Sieve count');ax.plot(x,x/np.log(x),'--',label='n/log n');m={'Exact prime count':int(prime.sum()),'n/log n estimate':p/math.log(p)};t=f'The sieve finds {int(prime.sum())} primes through {p:g}. n/log n gives {p/math.log(p):.6g}; the true count is {int(prime.sum())/(p/math.log(p)):.3f} times the estimate. The formula promises only that this ratio tends to 1 as n grows. It gets there very slowly and not steadily: from n=100 to n=2000 it wanders between about 1.14 and 1.26.'\n", " elif d==4:\n", " k=np.arange(1,26);vals=np.array([pow(p,int(e),11) for e in k]);order=next(e for e in range(1,11) if pow(p,e,11)==1);fig,ax=canvas('Exponent k','aᵏ mod 11','Powers repeat with a fixed period');ax.plot(k,vals,'o-',color='#136f75',label=f'{p}ᵏ mod 11');ax.scatter(k[vals==1],vals[vals==1],s=123,facecolors='none',edgecolors='#aa4e37',zorder=3,label='Value 1: cycle restarts');ax.axvline(23,color='#a26913',ls=':',label='k=23');ax.set_ylim(0,14.5);integer_ticks(ax);integer_ticks(ax,'y');m={'Base a':p,'Period (order of a mod 11)':order,'23 mod period':23%order,f'{p}²³ mod 11':pow(p,23,11)};t=f'The powers of {p} repeat every {order} steps, so only the exponent mod {order} matters. 23 mod {order} = {23%order}, so {p}²³ ≡ {pow(p,23%order,11)} mod 11 without computing a 23-fold product. '+('Fermat\\'s period 10 always works mod 11; here it is the true period.' if order==10 else f'Fermat\\'s exponent 10 also works, because {order} divides 10, but the true period is shorter.')\n", " elif d==5:\n", " divs=[k for k in range(1,p+1) if p%k==0];r=math.sqrt(p);small=[k for k in divs if k<=r];tests=math.isqrt(p)-1\n", " fig,ax=canvas('Divisor d','Partner n/d',f'Divisors of {p} pair up across √n');ax.plot([0,p+1],[0,p+1],ls='dotted',color='#9aa3a8',label='d = n/d line');ax.scatter(small,[p//k for k in small],s=70,color='#136f75',zorder=3,label='Small partner d ≤ √n');big=[k for k in divs if k>r];ax.scatter(big,[p//k for k in big],s=70,marker='s',color='#a26913',zorder=3,label='Large partner d > √n');ax.axvline(r,color='#aa4e37',ls='dashed',label=f'√{p} ≈ {r:.3g}');ax.set_xscale('log');ax.set_yscale('log');ax.set(xlim=(.8,p*1.3),ylim=(.8,p*1.3))\n", " m={'n':p,'√n':r,'Divisors found':len(divs),'Trial divisors needed (2 to ⌊√n⌋)':tests,'Prime':len(divs)==2}\n", " t=f'Every divisor d of {p} comes with a partner {p}/d, and one of the two is at most √{p}≈{r:.4g}. '+(f'So testing 2 through {math.isqrt(p)} ({tests} trials) is enough: none divides {p}, so {p} is prime. Testing past √n would only find partners of divisors already ruled out.' if len(divs)==2 else f'The small divisors {\", \".join(map(str,small))} already reveal all {len(divs)} divisors; the large ones are their partners. '+(f'Here √{p} is a whole number, so {math.isqrt(p)} is its own partner and sits on the diagonal.' if math.isqrt(p)**2==p else f'{p} looks prime at a glance, but the trial divisor {small[1]} finds {p}={small[1]}×{p//small[1]} well before √n.'))\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_09(d,p):\n", " if d==1:\n", " k=np.arange(0,9);choose=[math.comb(8,int(i)) for i in k];ordered=[math.perm(8,int(i)) for i in k];fig,ax=canvas('Selected people k','Outcome count','Distinct jobs multiply committee counts');integer_ticks(ax);ax.semilogy(k,choose,'o-',label='Unordered committee');ax.semilogy(k,ordered,'o-',label='Distinct ordered jobs');m={'Committee count':math.comb(8,p),'Job assignments':math.perm(8,p),'Multiplicity k!':math.factorial(p)};t=f'For {p:g} of eight people, {math.comb(8,p)} committees become {math.perm(8,p)} assignments to distinct jobs. Each committee has exactly {math.factorial(p)} orderings.'\n", " elif d==2:\n", " counts=np.bincount([sum(bits) for bits in itertools.product([0,1],repeat=p)],minlength=p+1);fig,ax=canvas('Number of ones','Binary strings','Counting a small exhaustive space');ax.bar(range(p+1),counts,label='Exact exhaustive count');integer_ticks(ax);integer_ticks(ax,'y');m={'Total strings':2**p,'At least one 1':2**p-1,'Balanced count':math.comb(p,p//2)};t=f'Enumerating all {2**p} binary strings confirms the binomial counts. Excluding only the all-zero string leaves {2**p-1}. The tallest bar is in the middle: {math.comb(p,p//2)} strings have exactly {p//2} ones.'\n", " elif d==3:\n", " strings=list(itertools.product([0,1],repeat=p));orbits={min(s[i:]+s[:i] for i in range(p)) for s in strings};sizes={s:sum(min(t[i:]+t[:i] for i in range(p))==s for t in strings) for s in orbits};fig,ax=canvas('Rotation orbit size','Number of orbits','Uniform division fails for necklaces');vals=sorted(set(sizes.values()));ax.bar(vals,[list(sizes.values()).count(k) for k in vals]);ax.set_xticks(vals);integer_ticks(ax,'y');m={'Binary necklaces':len(orbits),'Naive 2ⁿ/n':2**p/p,'Distinct orbit sizes':', '.join(map(str,vals))};t=f'Rotation orbits do not all have size {p:g}. Constant strings have orbit size one, so dividing {2**p} by {p:g} does not count the {len(orbits)} distinct necklaces.'\n", " elif d==4:\n", " n=np.arange(1,11);D=[1,0]\n", " for i in range(2,11):D.append((i-1)*(D[-1]+D[-2]))\n", " D=np.array(D[1:]);fig,ax=canvas('Number of people n','Probability nobody gets own hat','The no-match chance settles near 1/e fast');ax.plot(n,D/np.array([math.factorial(int(i)) for i in n]),'o-',color='#136f75',label='Exact D(n)/n!');ax.axhline(1/math.e,color='#a26913',ls='dashed',label='1/e ≈ 0.3679');ax.scatter([p],[D[p-1]/math.factorial(p)],s=140,facecolors='none',edgecolors='#aa4e37',zorder=3,label=f'Selected n={p}');integer_ticks(ax);ax.set_ylim(0,.55);m={'People n':p,'Derangements D(n)':int(D[p-1]),'Arrangements n!':math.factorial(p),'Exact probability':D[p-1]/math.factorial(p),'n!/e rounded':round(math.factorial(p)/math.e)};t=f'With {p} people there are {math.factorial(p)} ways to hand back hats and {D[p-1]} leave nobody with their own. '+(f'That is {D[p-1]/math.factorial(p):.4g}, already within {abs(D[p-1]/math.factorial(p)-1/math.e):.2g} of 1/e. Rounding n!/e gives the exact count, so the shortcut is safe.' if p>=4 else f'That is {D[p-1]/math.factorial(p):.4g}, still visibly off 1/e. Even so, rounding n!/e={math.factorial(p)/math.e:.4g} gives the exact count {D[p-1]}.')\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_10(d,p):\n", " edges={'path':[(0,1),(1,2),(2,3)],'triangle-isolate':[(0,1),(1,2),(2,0)],'cycle':[(0,1),(1,2),(2,3),(3,0)]}\n", " if d==1:\n", " es=edges[p];adj={i:[] for i in range(4)}\n", " for a,b in es:adj[a].append(b);adj[b].append(a)\n", " seen={0};queue=deque([0])\n", " while queue:\n", " for j in adj[queue.popleft()]:\n", " if j not in seen:seen.add(j);queue.append(j)\n", " fig,ax=canvas('x (layout only)','y (layout only)','Edge count needs a structural condition');xy=np.array([[0,0],[1,0],[1,1],[0,1]])\n", " for a,b in es:ax.plot(xy[[a,b],0],xy[[a,b],1],color='#136f75')\n", " ax.scatter(xy[:,0],xy[:,1],s=150);[ax.annotate(str(i),xy[i]+np.array([.05,-.09])) for i in range(4)];ax.set(xlim=(-.2,1.25),ylim=(-.2,1.2));ax.set_aspect('equal');tree=len(seen)==4 and len(es)==3;m={'Vertices':4,'Edges':len(es),'Reachable from vertex 0':len(seen),'Tree':tree};t=f'This graph has {len(es)} edges and {len(seen)} reachable vertices. It '+('is a tree: connected with n−1 edges.' if tree else ('is not a tree. It has n−1=3 edges but is disconnected, so the edge count alone cannot replace connectivity.' if len(seen)<4 else 'is not a tree. It is connected but has 4 edges, one more than n−1=3, so it contains a cycle.'))\n", " elif d==2:\n", " theta=2*np.pi*np.arange(p)/p;xy=np.column_stack([np.cos(theta),np.sin(theta)]);fig,ax=canvas('x (layout only)','y (layout only)','Odd cycles obstruct two-coloring' if p%2 else 'Even cycles two-color consistently');ax.plot(xy[:,0],xy[:,1],color='#136f75');ax.plot(xy[[-1,0],0],xy[[-1,0],1],color='#aa4e37' if p%2 else '#136f75',lw=3,label='Closing edge: same colors (conflict)' if p%2 else 'Closing edge: colors differ');ax.scatter(xy[:,0],xy[:,1],c=['#136f75' if i%2==0 else '#b77518' for i in range(p)],s=130);ax.set_aspect('equal');m={'Cycle length':p,'Bipartite':p%2==0};t=f'An alternating two-coloring '+('closes consistently on this even cycle.' if p%2==0 else 'conflicts at the closing edge on this odd cycle. One odd cycle rules out bipartiteness.')\n", " elif d==3:\n", " es=edges[p];degrees=[sum(i in e for e in es) for i in range(4)];odd=sum(v%2 for v in degrees);fig,ax=canvas('Vertex','Degree','Euler trails use every edge');ax.bar(range(4),degrees);integer_ticks(ax);integer_ticks(ax,'y');m={'Odd-degree vertices':odd,'Euler trail possible on edge component':odd in (0,2)};t=f'There are {odd} odd-degree vertices. '+('Zero odd vertices: you can walk every edge once and end where you started.' if odd==0 else 'Two odd vertices: you can walk every edge once, but you must start at one odd vertex and finish at the other.' if odd==2 else 'More than two odd vertices: no walk covers every edge exactly once.')+(' Vertex 3 has no edges and is ignored, since the walk only has to cover edges.' if 0 in degrees else '')\n", " elif d==4:\n", " import heapq;E={'S':[('A',2),('B',3)],'B':[('A',p)],'A':[('T',1)],'T':[]};V=['S','A','B','T'];dist={v:math.inf for v in V};dist['S']=0;done=set();h=[(0,'S')]\n", " while h:\n", " d0,u=heapq.heappop(h)\n", " if u in done:continue\n", " done.add(u)\n", " for v,w in E[u]:\n", " if v not in done and d0+w',shrinkA=11,shrinkB=11,lw=2.5 if (u,v)==('B','A') else 1.2,color='#aa4e37' if (u,v)==('B','A') and p<0 else '#136f75'));ax[0].annotate(f'{w:g}',((xy[u][0]+xy[v][0])/2+.04,(xy[u][1]+xy[v][1])/2+.04))\n", " ax[0].scatter(*zip(*xy.values()),s=300,color='#dbe7e8',zorder=3);[ax[0].annotate(v,xy[v],ha='center',va='center',zorder=4) for v in V];ax[0].set(xlim=(-.3,2.3),ylim=(-1,1),xticks=[],yticks=[]);i=np.arange(4);ax[1].bar(i-.2,[dist[v] for v in V],.4,label='Dijkstra answer');ax[1].bar(i+.2,[true[v] for v in V],.4,label='True shortest (Bellman-Ford)');ax[1].set(xticks=i,xticklabels=V,xlabel='Vertex',ylabel='Path length from S',title=f'Edge B to A weight {p:g}');integer_ticks(ax[1],'y');wrong=[v for v in V if dist[v]!=true[v]];m={'Weight on B→A':p,'Dijkstra distance to T':dist['T'],'True distance to T':true['T'],'Vertices Dijkstra gets wrong':', '.join(wrong) if wrong else 'None'};t=f'Dijkstra settles A at length 2 before it looks at B. '+('All weights are nonnegative, so no later path can undercut a settled vertex. Every answer is correct.' if p>=0 else (f'The detour S→B→A costs 3{p:+g}={3+p:g}, still longer than 2, so Dijkstra happens to be right. A negative edge removes the guarantee, not every correct answer.' if 3+p>=2 else f'The detour S→B→A costs 3{p:+g}={3+p:g}, shorter than 2. Dijkstra already locked A, so it reports {\", \".join(wrong)} too long. Use Bellman-Ford when any weight is negative.'))\n", " elif d==5:\n", " G={'K4':(4,6,False,True),'K5':(5,10,False,False),'K3,3':(6,9,True,False)};n,e,bip,planar=G[p];b=3*n-6\n", " fig,ax=canvas('Graph','Number of edges',f'{p}: the 3n−6 screen can only rule planarity out');names=list(G);x=np.arange(3)\n", " ax.bar(x-.2,[G[g][1] for g in names],.4,color=['#aa4e37' if g==p else '#9fc2c4' for g in names],label='Edges m');ax.bar(x+.2,[3*G[g][0]-6 for g in names],.4,color='#d8b47a',label='Planar ceiling 3n−6');ax.set(xticks=x,xticklabels=names);integer_ticks(ax,'y')\n", " m={'Vertices n':n,'Edges m':e,'Ceiling 3n−6':b,'Screen rejects planarity':e>b,'Actually planar':planar}\n", " t=f'{p} has n={n} and m={e}, against the ceiling 3n−6={b}. '+({'K4':'It passes the screen and is planar: draw one vertex inside the triangle of the other three.','K5':'Ten edges exceed nine, so the screen proves K5 is not planar without any drawing.','K3,3':'Nine edges are under twelve, so the screen passes, yet K3,3 is not planar. Passing proves nothing. For a graph with no triangles the sharper ceiling 2n−4=8 does catch it.'}[p])\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_11(d,p):\n", " if d==1:\n", " n=np.arange(1,51);exact=np.array([math.lgamma(int(k)+1) for k in n]);base=.5*np.log(2*np.pi*n)+n*np.log(n)-n;fig,ax=canvas('n','Relative factorial error','The first Stirling correction helps');ax.semilogy(n,abs(np.expm1(base-exact)),label='Leading formula');ax.semilogy(n,abs(np.expm1(base+1/(12*n)-exact)),label='Log correction');m={'n':p,'Leading relative error':abs(math.expm1(.5*math.log(2*math.pi*p)+p*math.log(p)-p-math.lgamma(p+1))),'Corrected relative error':abs(math.expm1(.5*math.log(2*math.pi*p)+p*math.log(p)-p+1/(12*p)-math.lgamma(p+1)))};t=f'At n={p}, the leading Stirling formula misses n! by {100*m[\"Leading relative error\"]:.3g}%. Adding 1/(12n) to the log cuts the miss to about 1 part in {1/m[\"Corrected relative error\"]:,.0f}. Working with log n! keeps huge factorials from overflowing. A few checked values do not prove the correction always works this well.'\n", " elif d==2:\n", " x=np.logspace(0,5,200);fig,ax=canvas('x','Term magnitude','Dominant balance locates a transition');ax.loglog(x,x,label='x');ax.loglog(x,p/x,label='a/x');ax.axvline(math.sqrt(p),color='#a26913',linestyle=':',label='Balance scale √a');m={'Parameter a':p,'Balance scale x':math.sqrt(p)};t=f'The competing terms x and a/x are equal at x=√a={math.sqrt(p):.6g}. For x below {math.sqrt(p):.6g}, a/x is the bigger term; above it, x is. Near the crossing neither term can be dropped.'\n", " elif d==3:\n", " x=np.logspace(0,7,100);exact=x/(np.sqrt(x*x+x)+x);leading=np.full_like(x,.5);fig,ax=canvas('x','Difference','Equivalent leading terms can cancel');ax.semilogx(x,exact,label='Rationalized exact difference');ax.semilogx(x,leading,'--',label='Limit 1/2');value=p/(math.sqrt(p*p+p)+p);m={'Exact difference':value,'Gap to limit 1/2':.5-value,'Naively subtract leading equivalents':0,'Correct limiting value':.5};t=f'√(x²+x)−x is {value:.10g} at x={p:,} and tends to 1/2. Replacing each large term by x and subtracting would incorrectly give zero.'\n", " elif d==4:\n", " n=np.arange(2,81);fig,ax=canvas('n','Value (log scale)','Exponential growth eventually beats any power');ax.semilogy(n,np.log(n),label='log n');ax.semilogy(n,n.astype(float)**p,label=f'n^{p}');ax.semilogy(n,2.0**n,label='2^n');ax.set_ylim(.5,1e24);cross=next(int(k) for k in range(2,1000) if 2.0**k>float(k)**p);ax.axvline(cross,color='#a26913',linestyle=':',label=f'2^n passes n^{p} at n={cross}');integer_ticks(ax);m={'Power k':p,'Last n where n^k ≥ 2^n':cross-1,'First n where 2^n > n^k':cross,'n^k at n=100':float(100**p),'2^n at n=100':2.0**100};t=f'With k={p}, the power n^{p} matches or beats 2^n up to n={cross-1}; from n={cross} on, 2^n wins and the gap grows without limit. '+('Even a small power leads for a few steps, so short tests can mislead.' if p==2 else ('A bigger power only delays the takeover; it never prevents it.' if p==5 else f'Even n^10 loses, but only after n={cross-1}. Below that, the exponential looks like the slower function.'))\n", " elif d==5:\n", " tq,wq=np.polynomial.laguerre.laggauss(150);exact=float(np.sum(wq/(1+p*tq)));K=np.arange(1,31);terms=np.array([(-1)**k*math.factorial(k)*p**k for k in range(30)]);err=np.abs(np.cumsum(terms)-exact);best=int(K[np.argmin(err)]);fig,ax=canvas('Terms kept K','Absolute error (log scale)','More terms help, then hurt');ax.semilogy(K,err,'o-',ms=4,label='|partial sum − exact|');ax.axvline(best,color='#a26913',linestyle=':',label=f'Smallest error at K={best}');integer_ticks(ax);m={'Small parameter x':p,'Exact integral':exact,'Best number of terms':best,'Smallest error':float(err.min()),'Error with 30 terms':float(err[-1])};t=f'The series 1 − 1!x + 2!x² − … for ∫e^(−t)/(1+xt)dt diverges for every x>0, yet at x={p:g} keeping {best} terms gives error {err.min():.2g}. Terms shrink until k is near 1/x={1/p:g}, then grow. '+(f'With 30 terms the error explodes to {err[-1]:.2g}: adding terms past the smallest one makes things worse.' if err[-1]>1 else f'Thirty terms already overshoot: the error is back up to {err[-1]:.2g}, worse than the best truncation.')+' Stop near the smallest term.'\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_12(d,p):\n", " if d==1:\n", " n=np.arange(1,1001);exact=-np.expm1(n*np.log1p(-p));approx=-np.expm1(-n*p);fig,ax=canvas('Independent opportunities n','At least one event probability','Rare events accumulate');ax.plot(n,exact,label='Exact independent model');ax.plot(n,approx,'--',label='Poisson approximation');ax.plot(n,np.minimum(1,n*p),':',label='Union bound');ax.axvline(100,color='#a26913',linestyle=':',label='n=100 (reported)');m={'Per-opportunity probability':p,'Exact risk at n=100':-math.expm1(100*math.log1p(-p)),'Union ceiling at n=100':min(1,100*p)};t=f'Over 100 opportunities at p={p:g}, the chance of at least one event is {-math.expm1(100*math.log1p(-p)):.4g} if they are independent. The union bound n·p={min(1,100*p):.4g} is a ceiling that holds even without independence. '+('Here it caps at 1, which tells you nothing; use the exact formula if independence is credible.' if 100*p>=1 else 'For rare events the two nearly agree, so n·p is a safe quick estimate.')+' A shared cause (one storm, one bad batch) breaks the independent formula.'\n", " elif d==2:\n", " prevalence=np.logspace(-4,-.3,200);sens=.95;fpr=.05;posterior=sens*prevalence/(sens*prevalence+fpr*(1-prevalence));fig,ax=canvas('Prior prevalence','Probability after a positive result','Base rates change positive-result meaning');ax.semilogx(prevalence,posterior);a=sens*p/(sens*p+fpr*(1-p));ax.scatter([p],[a]);m={'Sensitivity':sens,'False-positive rate':fpr,'Prior probability':p,'Posterior probability':a};t=f'Under the stipulated .95 sensitivity and .05 false-positive rate, prior probability {p:g} becomes {a:.6g} after a positive result. Picture 100,000 people: {95000*p:,.0f} true positives against {5000*(1-p):,.0f} false positives. '+('False alarms swamp the real cases, so a positive is still probably wrong.' if a<.5 else 'Cases are common enough that a positive is now probably right.')+' Inputs are made up for illustration.'\n", " elif d==3:\n", " n=np.logspace(2,6,100);se=np.sqrt(.3*.7/n);fig,ax=canvas('Independent simulations n','Monte Carlo standard error','More trials improve precision slowly');ax.loglog(n,se,label='√(.3×.7/n)');ax.scatter([p],[math.sqrt(.21/p)],label='Model SE at selected n');rng=np.random.default_rng(1203);estimate=float(np.mean(rng.random(p)<.3));ax.scatter([p],[max(abs(estimate-.3),1e-6)],marker='x',s=70,color='#aa4e37',label='This run: distance of estimate from .3');m={'Seed':1203,'Trials':p,'Simulated estimate':estimate,'Model standard error':math.sqrt(.21/p),'True constructed probability':.3};t=f'Seed 1203 gives estimate {estimate:.6g} from {p:g} independent Bernoulli trials, missing the true .3 by {abs(estimate-.3):.3g}, about {abs(estimate-.3)/math.sqrt(.21/p):.2g} model standard errors. Quadrupling the simulation budget halves the model standard error; it does not fix an incorrect probability model.'\n", " elif d==4:\n", " k=np.arange(1,int(4*math.sqrt(p))+2);prob=-np.expm1(np.cumsum(np.log1p(-(k-1)/p)));fig,ax=canvas('Number of items drawn k','Probability of at least one repeat','Collisions arrive near the square root');ax.plot(k,prob,label='Exact: 1 − ∏(1 − i/N)');ax.plot(k,-np.expm1(-k*(k-1)/(2*p)),linestyle='dashed',label='Approx: 1 − exp(−k(k−1)/(2N))');half=int(k[np.argmax(prob>=.5)]);ax.axvline(half,color='#a26913',linestyle=':',label=f'50% reached at k={half}');ax.axhline(.5,color='gray',linestyle=':');integer_ticks(ax);m={'Equally likely values N':p,'Items for 50% repeat chance':half,'1.1774·√N':1.1774*math.sqrt(p),'Items as share of N':half/p};t=f'With {p:,} equally likely values, a repeat becomes more likely than not after only {half} draws, about 1.18√N. That is {100*half/p:.3g}% of the possible values. '+('This is the classic birthday surprise: 23 people suffice.' if p==365 else ('Growing N by a factor of 100 grows the threshold only about tenfold (119 here, 1,178 at N=1,000,000).' if p<10**6 else 'Even a million IDs collide after about 1,178 draws, so random IDs need far more room than their count suggests.'))\n", " elif d==5:\n", " i=np.arange(1,p+1);wait=p/(p-i+1);cum=np.cumsum(wait);total=float(cum[-1]);fig,ax=canvas('New coupons collected','Expected draws so far','The last few coupons cost the most');ax.plot(i,cum,label='Expected total draws, N·Σ1/k');ax.plot(i,i,color='gray',linestyle='dashed',label='One draw per new coupon');half=int(i[np.argmax(cum>=total/2)]);ax.axvline(half,color='#a26913',linestyle=':',label=f'Half of all draws spent by coupon {half}');integer_ticks(ax);tail=int(math.ceil(.1*p));lastshare=float((cum[-1]-cum[-tail-1])/total);m={'Distinct coupons N':p,'Expected draws for all':total,'N ln N + 0.5772N':p*math.log(p)+.5772*p,'Draws per coupon':total/p,'Share spent on last 10%':lastshare};t=f'Collecting all {p} equally likely coupons takes {total:.4g} draws on average, about N ln N + 0.577N = {p*math.log(p)+.5772*p:.4g}, or {total/p:.3g} draws per coupon. Half of those draws are already spent by coupon {half} of {p}, and '+('the last coupon' if tail==1 else f'the last {tail} coupons')+f' alone take'+('s' if tail==1 else '')+f' {100*lastshare:.3g}% of the effort. '+('Even with only 10 types, the final one takes on average 10 draws by itself.' if p==10 else 'Finishing a set is dominated by hunting for the rare missing pieces, so budgets based on N draws fail badly.')\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def wilson(k,n,z=1.96):\n", " q=k/n;den=1+z*z/n;center=(q+z*z/(2*n))/den;half=z*math.sqrt(q*(1-q)/n+z*z/(4*n*n))/den\n", " return center-half,center+half\n", "\n", "\n", "def chapter_13(d,p):\n", " if d==1:\n", " n=np.arange(10,501);fig,ax=canvas('Total observations n','95% planning half-width','Precision depends on independent information');ax.plot(n,1.96*12/np.sqrt(n),label='Independent observations, σ=12');deff=1+4*p;ax.plot(n,1.96*12*np.sqrt(deff/n),'--',label=f'Clusters of 5, within-cluster correlation ρ={p:g}');ax.axhline(3,color='gray',linestyle=':',label='Target half-width 3');target=(1.96*12/3)**2;need=5*math.ceil(target*deff/5);ax.axvline(need,color='#a26913',linestyle=':',label=f'Needed: {need}');m={'Design effect':deff,'Independent target n (unrounded)':target,'Target × design effect':target*deff,'Clustered observations needed':need};t=f'With clusters of five and within-cluster correlation ρ={p:g}, the design effect (how much clustering inflates variance) is {deff:g}. The unrounded target {target:.6g} times {deff:g} is {target*deff:.6g}, rounded up to whole clusters of five: {need}. The displayed planning formula assumes equal clusters and a specified variance; repeated measurements do not automatically count as independent observations.'\n", " elif d==2:\n", " n=np.arange(10,1001);exact=-np.expm1(math.log(.05)/n);fig,ax=canvas('Independent zero-event trials n','One-sided 95% upper bound','No observed failures does not mean zero risk');ax.plot(n,exact,label='Exact binomial upper bound');ax.plot(n,3/n,'--',label='Rule of three');m={'Zero-event trials':p,'Exact upper bound':-math.expm1(math.log(.05)/p),'Rule-of-three bound':3/p};t=f'With zero events in {p:g} independent identical trials, the exact one-sided 95% upper bound is {m[\"Exact upper bound\"]:.6g}. Rule 3/n is a close approximation, not a probability of safety.'\n", " elif d==3:\n", " n=20;k=np.arange(n+1);intervals=np.array([wilson(int(a),n) for a in k]);wald=k/n+np.array([-1,1])[:,None]*1.96*np.sqrt((k/n)*(1-k/n)/n);fig,ax=canvas('Observed successes k (n=20)','Interval endpoint','Wilson remains informative at the extremes');ax.plot(k,intervals[:,0],label='Wilson lower');ax.plot(k,intervals[:,1],label='Wilson upper');ax.plot(k,wald[0],'--',label='Wald lower');ax.plot(k,wald[1],'--',label='Wald upper');ax.axvline(p,color='#a26913',linestyle=':',label='Selected k');integer_ticks(ax);lo,hi=wilson(p,n);lo=max(0.,lo) if abs(lo)<1e-12 else lo;hi=min(1.,hi) if abs(hi-1)<1e-12 else hi;m={'Successes':p,'Trials':n,'Wilson lower':lo,'Wilson upper':hi};t=f'For {p:g}/20 successes, Wilson gives [{lo:.6g},{hi:.6g}]. '+('Wald gives [0,0] here, claiming certainty from 20 trials. Wilson does not.' if p==0 else ('Wald gives [{:.3g},{:.3g}], with an impossible negative lower end.'.format(.1-1.96*math.sqrt(.09/20),.1+1.96*math.sqrt(.09/20)) if p==2 else 'Near the middle, Wald and Wilson nearly agree; the difference matters at the extremes.'))\n", " elif d==4:\n", " rng=np.random.default_rng(1333);sims,nmax=4000,1000;z=np.cumsum(rng.standard_normal((sims,nmax)),axis=1)/np.sqrt(np.arange(1,nmax+1));looks=np.linspace(nmax/p,nmax,p).astype(int)-1;hit=(np.abs(z[:,looks])>1.96).any(axis=1);fig,ax=canvas('Planned looks at the data','False-positive rate (no real effect)','Peeking and stopping on p<.05 inflates errors');allk=[1,2,5,10,20,50];rates=[float((np.abs(z[:,np.linspace(nmax/j,nmax,j).astype(int)-1])>1.96).any(axis=1).mean()) for j in allk];ax.plot(allk,rates,'o-',label='Simulated: stop at first p<.05');ax.axhline(.05,color='gray',linestyle='dashed',label='Promised 5%');ax.scatter([p],[hit.mean()],s=90,color='#a26913',zorder=3,label=f'Selected: {p} look'+('' if p==1 else 's'));ax.set_xscale('log');ax.set_xticks(allk,[str(j) for j in allk]);m={'Looks':p,'Simulated false-positive rate':float(hit.mean()),'Nominal rate':.05,'Simulated null experiments':sims,'Seed':1333};t=f'With no true effect and '+('a single look at the end,' if p==1 else f'{p} equally spaced looks,')+f' stopping at the first p<.05 declares a false discovery in {100*hit.mean():.3g}% of {sims} simulated experiments. '+('One planned look keeps the promised 5%, up to simulation noise.' if p==1 else f'That is about {hit.mean()/.05:.2g} times the promised 5%. Each extra look is another chance for noise to cross the line. Fix the look schedule in advance or use a sequential correction.')\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_14(d,p):\n", " if d==1:\n", " arrival=np.linspace(.1,9.9,201);fig,ax=canvas('Arrival rate λ (per hour)','Mean system time (hours)','Queues become fragile near capacity');ax.plot(arrival,1/(10-arrival),label='Stable M/M/1');ax.axvline(p,color='#a26913',label=f'Selected λ={p:g}');stable=p<10\n", " if not stable:ax.text(p-.15,ax.get_ylim()[1]*.6,'λ ≥ μ: unstable,\\nno stationary mean',ha='right',color='#aa4e37')\n", " m={'Utilization':p/10,'Mean system time':1/(10-p) if stable else 'No stationary mean','Mean customers in system':p/(10-p) if stable else 'Unstable'};t=f'At service rate 10/hour and arrivals {p:g}/hour, '+(f'mean system time is {1/(10-p):.6g} hours under the M/M/1 assumptions.' if stable else 'the stationary formula is inapplicable: demand meets or exceeds service capacity.')\n", " elif d==2:\n", " n=np.arange(51);fig,ax=canvas('Steps after shock','Remaining shock fraction','AR(1) dependence persists');hl=math.log(.5)/math.log(p);ax.plot(n,p**n,label='Remaining fraction φⁿ');ax.axhline(.5,color='gray',linestyle=':',label='Half remaining');ax.axvline(hl,color='#a26913',linestyle=':',label=f'Half-life {hl:.3g} steps');m={'AR coefficient':p,'Half-life in steps':math.log(.5)/math.log(p),'Long-run variance factor':(1+p)/(1-p)};t=f'A shock is multiplied by φ={p:g} each step (it keeps {100*p:g}% per step), with half-life {math.log(.5)/math.log(p):.3g} steps. A long average is {(1+p)/(1-p):.3g} times as noisy (in variance) as an average of the same number of independent readings. '+('Even this weak persistence costs some precision, though half of a shock is gone within one step.' if p<.5 else 'Lingering shocks make neighboring readings repeat each other, so persistence costs precision.')\n", " elif d==3:\n", " count=np.arange(0,31);pmf=np.array([math.exp(-p)*p**int(k)/math.factorial(int(k)) for k in count]);fig,ax=canvas('Arrival count in one hour','Probability','Rate times exposure determines the Poisson count');ax.bar(count,pmf);m={'Hourly arrival rate':p,'Mean count in one hour':p,'Probability of any arrival':-math.expm1(-p),'Mean wait (hours)':1/p};t=f'A constant Poisson rate {p:g}/hour gives mean count {p:g} in one hour and mean exponential wait {1/p:.6g} hour{\"\" if p==1 else \"s\"}. Changing or dependent arrival rates need a different model.'\n", " elif d==4:\n", " rng=np.random.default_rng(1421);steps=rng.choice([-1,1],size=(2000,p));walk=np.cumsum(steps,axis=1);n=np.arange(1,p+1);fig,ax=canvas('Steps taken n','Position (steps from start)','Random-walk spread grows like √n');[ax.plot(n,walk[i],lw=.7,alpha=.6,label='Five sample walks' if i==0 else None) for i in range(5)];ax.plot(n,np.sqrt(n),color='k',linestyle='dashed',label='±√n');ax.plot(n,-np.sqrt(n),color='k',linestyle='dashed');ax.plot(n,np.sqrt((walk**2).mean(axis=0)),color='#a26913',label='Simulated RMS distance (2000 walks)');integer_ticks(ax);rms=float(np.sqrt((walk[:,-1]**2).mean()));m={'Steps':p,'Theory √n':math.sqrt(p),'Simulated RMS distance':rms,'Typical distance / steps':rms/p,'Seed':1421};t=f'After {p:,} fair ±1 steps, the typical distance from start is about √{p:,}={math.sqrt(p):.4g} steps (simulation: {rms:.4g}). That is only {100*rms/p:.2g}% of the steps taken. '+('Ten times more steps would move the walker only about 3.16 times farther.' if p<10000 else 'A hundredfold increase in steps from 100 to 10,000 only multiplied the typical distance by ten.')\n", " elif d==5:\n", " t=np.linspace(0,30,301);mean=10;scale=mean/math.gamma(1.5);expo=np.exp(-t/mean);weib=np.exp(-((p+t)/scale)**2+(p/scale)**2);fig,ax=canvas('Extra minutes of waiting t','P(still waiting after t more)','Exponential waits do not age');ax.plot(t,expo,label='Exponential (memoryless), mean 10');ax.plot(t,weib,linestyle='dashed',label='Aging wait, mean 10, '+('no time waited yet' if p==0 else f'after {p:g} min already'));m={'Minutes already waited':p,'Exponential: expected extra wait':mean,'Aging model: expected extra wait':float(np.trapezoid(np.exp(-((p+np.linspace(0,200,200001))/scale)**2+(p/scale)**2),np.linspace(0,200,200001))),'Exponential: P(over 10 more)':math.exp(-1),'Aging model: P(over 10 more)':math.exp(-((p+10)/scale)**2+(p/scale)**2)};t=('Before any waiting, a memoryless (exponential) wait has mean' if p==0 else f'After {p:g} minutes already waited, a memoryless (exponential) wait still has mean')+f' {mean} more minutes and a {100*math.exp(-1):.3g}% chance of lasting 10 more'+('. ' if p==0 else ': the past wait is forgotten. ')+('At time zero the two models are just two different shapes with the same 10-minute mean.' if p==0 else f'An aging wait with the same 10-minute mean (Weibull shape 2) now expects only {m[\"Aging model: expected extra wait\"]:.3g} more minutes. ')+('' if p==0 else ('\"Overdue\" reasoning is valid only for aging processes, never for exponential ones.' if p>=15 else 'Whether waiting longer makes the end nearer depends on the model, not on intuition.'))\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def entropy(p):\n", " p=np.asarray(p);return float(-np.sum(p[p>0]*np.log2(p[p>0])))\n", "\n", "\n", "def chapter_15(d,p):\n", " if d==1:\n", " x=np.linspace(0,1,201);h=[entropy([a,1-a]) for a in x];fig,ax=canvas('Bernoulli probability p','Entropy (bits)','Uncertainty peaks at equal probabilities');ax.plot(x,h);m={'Entropy in bits':entropy([p,1-p]),'Effective alphabet size':2**entropy([p,1-p])};t=f'At p={p:g}, entropy is {bits(m[\"Entropy in bits\"])}. '+(f'The rare outcome carries {bits(-math.log2(p))} of surprisal when it happens. ' if p<.5 else '')+('A rare event has high surprisal when it occurs, but low average entropy because it is rare.' if p<.1 else ('Neither outcome is rare here; equal probabilities give the maximum 1 bit.' if p==.5 else 'As p moves away from .5 toward zero, entropy falls because outcomes become more predictable.'))\n", " elif d==2:\n", " truth=np.array([.8,.2]);x=np.linspace(.01,.99,201);cross=-.8*np.log2(x)-.2*np.log2(1-x);fig,ax=canvas('Model probability q for outcome 1','Bits per outcome','A mismatched model costs extra information');ax.plot(x,cross,label='Cross-entropy');ax.axhline(entropy(truth),color='gray',linestyle='dashed',label='True entropy');ce=-.8*math.log2(p)-.2*math.log2(1-p);m={'True entropy':entropy(truth),'Cross-entropy':ce,'Perplexity':2**ce,'KL divergence (bits)':ce-entropy(truth)};t=f'True probabilities are (.8,.2), while the model assigns ({p:g},{1-p:g}). Cross-entropy is {bits(ce)}, the average cost of coding real outcomes with the model. '+(f'The excess over the true entropy, {ce-entropy(truth):.4g} bits, is the price of the wrong model (KL divergence). ' if abs(p-.8)>1e-9 else 'Here the model matches the truth, so the excess (the KL divergence) is zero. ')+f'Perplexity {2**ce:.4g} means the model is as unsure as a fair pick among that many options.'\n", " elif d==3:\n", " x=np.linspace(0,.5,201);capacity=[1-entropy([a,1-a]) for a in x];fig,ax=canvas('Bit-flip probability ε','Capacity (bits per channel use)','Noise limits a binary symmetric channel');ax.plot(x,capacity);m={'Flip probability':p,'Channel capacity':1-entropy([p,1-p])};t=f'The ideal memoryless binary symmetric channel has capacity {bits(m[\"Channel capacity\"])} per use at flip probability {p:g}. '+('A perfect channel: every bit gets through.' if p==0 else ('Each sent bit is pure noise; no code can recover anything.' if p==.5 else f'So you need about {1/m[\"Channel capacity\"]:.3g} sent bits per data bit, even with ideal coding. Real codes need somewhat more.'))\n", " elif d==4:\n", " snr=np.logspace(-1,4,300);cap=.5*np.log2(1+snr);fig,ax=canvas('Signal-to-noise power ratio (log scale)','Capacity (bits per real sample)','Capacity grows with the log of signal power');ax.semilogx(snr,cap,label='C = ½ log₂(1 + SNR)');s=10**(p/10);c=.5*math.log2(1+s);c2=.5*math.log2(1+2*s);ax.scatter([s],[c],s=80,color='#a26913',zorder=3,label=f'Selected: {p} dB');ax.scatter([2*s],[c2],s=60,marker='x',color='#aa4e37',zorder=3,label='Same, with double the power');m={'SNR (dB)':p,'SNR as a power ratio':s,'Capacity (bits per real sample)':c,'Capacity with double power':c2,'Gain from doubling power (bits)':c2-c};t=f'At {p} dB (power ratio {s:g}), the ideal Gaussian channel carries {bits(round(c,4))} per real sample. Doubling signal power adds {c2-c:.3g} bits. '+('When signal equals noise, doubling power still buys a 58% capacity gain. At high SNR the same doubling adds only about half a bit on top of many.' if p==0 else 'At high SNR each doubling adds only about half a bit per real sample, so more bandwidth (more samples per second) usually beats more power.')\n", " elif d==5:\n", " k=np.arange(1,25);fpr=(1-np.exp(-k/p))**k;kopt=p*math.log(2);kb=int(k[np.argmin(fpr)]);fig,ax=canvas('Hash functions k','False-positive rate (log scale)','Too few or too many hashes both hurt');ax.semilogy(k,fpr,'o-',ms=4,label=f'(1 − e^(−k/{p:g}))^k, {p:g} bits per item');ax.axvline(kopt,color='#a26913',linestyle=':',label=f'Optimum (m/n)·ln 2 = {kopt:.3g}');integer_ticks(ax);m={'Bits per item m/n':p,'Ideal k = (m/n) ln 2':kopt,'Best whole k':kb,'False-positive rate at best k':float(fpr.min()),'False-positive rate at k=1':float(fpr[0]),'Rate at k=24':float(fpr[-1])};t=f'With {p:g} bits per stored item, the false-positive rate is smallest near k=(m/n)ln 2={kopt:.3g}; the best whole number is {kb}, giving {100*fpr.min():.3g}%. One hash gives {100*fpr[0]:.3g}%, and 24 hashes give {100*fpr[-1]:.3g}% because the bit array fills up. '+('With so little memory, even the best k leaves about 1 false alarm in 7 lookups of absent items.' if p==4 else ('Each doubling of memory squares the best rate, roughly.' if p==8 else 'At 16 bits per item the best rate falls below 0.1%, but only near the optimum k.'))\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_16(d,p):\n", " if d==1:\n", " corr=np.linspace(-1,1,201);var=.5+.5*corr;fig,ax=canvas('Correlation ρ','Area standard uncertainty (cm²)','Covariance can reinforce or cancel first-order error');ax.plot(corr,np.sqrt(np.maximum(var,0)));u=math.sqrt(max(.5+.5*p,0));m={'Nominal area (cm²)':50,'First-order standard uncertainty (cm²)':u,'Expanded uncertainty k=2 (cm²)':2*u};t=f'A=LW with L=10±.1 cm, W=5±.05 cm, and correlation {p:g} gives first-order u(A)={u:.6g} cm². '+('The linear terms cancel exactly here; this does not imply zero nonlinear uncertainty.' if p==-1 else ('With no correlation, the two contributions add in quadrature.' if p==0 else 'Positive correlation makes the contributions reinforce, giving the largest uncertainty.' if p>0 else 'Negative correlation partly cancels the contributions.'))\n", " elif d==2:\n", " n=np.arange(1,501);fig,ax=canvas('Repeated readings n','RMS error','A fixed bias survives averaging');ax.plot(n,np.sqrt(1/n+p*p),label='RMS total');ax.plot(n,1/np.sqrt(n),'--',label='Random component');ax.axhline(abs(p),linestyle=':',label='Bias floor');m={'Single-reading random SD':1,'Fixed bias':p,'RMS error after 100 readings':math.sqrt(.01+p*p)};t=f'With independent unit-SD noise and fixed bias {p:g}, MSE of the mean is 1/n+b². After 100 readings the RMS error is {math.sqrt(.01+p*p):.3g}. '+('With no bias, more readings keep helping.' if p==0 else f'Averaging cannot push the error below the bias {p:g}; only calibration removes it.')\n", " elif d==3:\n", " rng=np.random.default_rng(1603);z=rng.normal(2,p,100000);y=z*z;fig,ax=canvas('Transformed value x²','Probability density','A nonlinear transform shifts the center');ax.hist(y,bins=80,density=True,label='100,000 constructed samples');ax.axvline(4,color='#a26913',label='Square of input mean');m={'Seed':1603,'Monte Carlo mean of x²':float(y.mean()),'Exact mean of x²':4+p*p,'Monte Carlo standard deviation':float(y.std(ddof=1)),'Straight-line estimate of SD (4σ)':4*p};t=f'For Gaussian x with mean 2 and SD {p:g}, E[x²]=4+σ²={4+p*p:g}. The constructed Monte Carlo result differs from squaring the mean. '+f'Straight-line estimate 4σ={4*p:.3g} versus simulated SD {float(y.std(ddof=1)):.3g}: '+('close enough here.' if abs(y.std(ddof=1)-4*p)<.05*4*p else 'the gap grows with σ, so simulate instead.')+''\n", " elif d==4:\n", " u=np.array([4.,2.,1.]);v=u.copy();v[p-1]/=2;base=math.sqrt((u*u).sum());new=math.sqrt((v*v).sum());fig,ax=canvas('Contributor','Standard uncertainty (mm)','Halve the biggest term first');x=np.arange(1,4);ax.bar(x-.2,u,.4,label='Before');ax.bar(x+.2,v,.4,label=f'After halving contributor {p}');ax.axhline(base,color='gray',linestyle='dashed',label=f'Combined before {base:.3g} mm');ax.axhline(new,color='#a26913',linestyle=':',label=f'Combined after {new:.3g} mm');ax.set_xticks(x,['1 (4 mm)','2 (2 mm)','3 (1 mm)']);m={'Combined before (mm)':base,'Combined after (mm)':new,'Reduction (%)':100*(1-new/base)};t=f'Contributions 4, 2 and 1 mm combine as √(16+4+1)={base:.4g} mm. Halving contributor {p} gives {new:.4g} mm, a {100*(1-new/base):.3g}% cut. '+('Squaring makes the largest term dominate, so this is the effort that pays.' if p==1 else 'Squaring makes the 4 mm term dominate, so effort spent here barely moves the total.')\n", " elif d==5:\n", " from math import lgamma\n", " def tcdf(x,v):\n", " z=np.linspace(0,x,4001);pdf=np.exp(lgamma((v+1)/2)-lgamma(v/2)-.5*math.log(v*math.pi)-(v+1)/2*np.log1p(z*z/v));return .5+float(np.sum((pdf[1:]+pdf[:-1])/2*np.diff(z)))\n", " nus=np.array([2,3,4,5,6,8,10,15,20,30,50,100]);cov=[100*(2*tcdf(2,v)-1) for v in nus];fig,ax=canvas('Effective degrees of freedom ν','Coverage of ±2u (%)','k=2 means about 95% only with enough data');ax.semilogx(nus,cov,'o-',label='Student t coverage of ±2u');ax.axhline(95.45,color='gray',linestyle='dashed',label='Normal limit 95.45%');c=100*(2*tcdf(2,p)-1);ax.scatter([p],[c],s=80,color='#a26913',zorder=3,label=f'Selected ν={p}')\n", " kneed=2.;lo,hi=1.9,20.\n", " for _ in range(50):\n", " mid=(lo+hi)/2;lo,hi=(mid,hi) if 2*tcdf(mid,p)-1<.9545 else (lo,mid)\n", " kneed=(lo+hi)/2;m={'Degrees of freedom':p,'Coverage of ±2u (%)':c,'Factor needed for 95.45% coverage':kneed};t=f'With ν={p} effective degrees of freedom, the interval ±2u covers about {c:.3g}% of a Student t distribution. Reaching the normal 95.45% would need k≈{kneed:.3g}. '+('With only a few readings, k=2 badly overstates the confidence.' if p<5 else ('The shortfall is now small, but report ν so a reader can check it.' if p<30 else 'With this much data, k=2 is close to its nominal 95% meaning.'))\n", "\n", "#### chapter_17\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_17(d,p):\n", " if d==1:\n", " r=np.linspace(0,.2,201);npv=400/(1+r)+400/(1+r)**2+400/(1+r)**3-1000;fig,ax=canvas('Annual discount rate','NPV (hypothetical currency units)','The discount rate can reverse a decision');ax.plot(r,npv);ax.axhline(0,color='gray');a=sum(400/(1+p)**k for k in (1,2,3))-1000;ax.scatter([p],[a]);m={'Initial cost':1000,'Three year-end payments':400,'Assumed annual rate':p,'NPV':a};t=f'Three year-end payments of 400 against cost 1000 have NPV {a:.6g} at assumed rate {100*p:g}%, so the project '+('passes' if a>0 else 'fails')+' the positive-NPV screen (the break-even rate is about 9.7%). These hypothetical cash flows illustrate timing, not a current investment recommendation.'\n", " elif d==2:\n", " x=np.linspace(0,.8,201);fig,ax=canvas('Fractional loss','Required fractional recovery','Loss and recovery use different bases');ax.plot(x,x/(1-x));m={'Loss fraction':p,'Required gain fraction':p/(1-p)};t=f'A {100*p:g}% loss leaves {100*(1-p):g}% of the original value. Recovering requires {100*p/(1-p):.6g}% of the reduced base.'\n", " elif d==3:\n", " periods=np.arange(1,13);effective=(1+.12/periods)**periods-1;fig,ax=canvas('Compounding periods per year','Effective annual rate','Quoted annual rates need a convention');ax.plot(periods,effective,'o-');m={'Nominal annual rate':.12,'Periods per year':p,'Effective annual rate':(1+.12/p)**p-1};t=f'A nominal annual rate of 12% compounded '+('once' if p==1 else f'{p:g} times')+f' per year gives effective annual rate {100*((1+.12/p)**p-1):.6g}%. Compare rates only after matching the convention.'\n", " elif d==4:\n", " r=np.linspace(1,25,200);fig,ax=canvas('Annual return r (%)','Rule of 72 minus exact (years)','Where the rule of 72 is right');ax.plot(r,72/r-np.log(2)/np.log(1+r/100),label='72/r minus exact ln2/ln(1+r/100)');ax.axhline(0,color='gray',lw=.8);ex=math.log(2)/math.log(1+p/100);ax.scatter([p],[72/p-ex],color='#a26913',zorder=3);ax.axvline(p,color='#a26913',linestyle=':',label='Selected rate');m={'Annual return (%)':p,'Exact doubling time (years)':ex,'Rule of 72 (years)':72/p,'Rule error (years)':72/p-ex};t=f'At {p:g}% a year, money doubles in {ex:.3g} years; the rule says {72/p:.3g}. '+('The shortcut is within a few days here, good enough for mental math.' if abs(72/p-ex)<.1 else ('At low rates the rule runs about a year long; 70/r is closer.' if p<5 else 'At high rates the rule runs short; use the exact formula when the answer matters.'))\n", " elif d==5:\n", " g=np.linspace(0,.0475,300);fig,ax=canvas('Growth rate g (%)','Value of growing perpetuity','Value explodes as growth approaches the discount rate');ax.plot(100*g,100/(.05-g),label='V = 100/(r−g), r=5%');ax.axvline(5,color='gray',linestyle='dashed',label='g = r: formula breaks');v=100/(.05-p);v2=100/(.05-p-.0025);ax.scatter([100*p],[v],s=80,color='#a26913',zorder=3,label=f'Selected g={100*p:g}%');ax.set_xlim(0,5.2);m={'Discount rate r (%)':5,'Growth rate g (%)':100*p,'Value (next payment 100)':v,'Value if g is 0.25 point higher':v2,'Change from that 0.25 point (%)':100*(v2/v-1)};t=f'With next payment 100, r=5% and g={100*p:g}%, the value is 100/(r−g)={v:,.0f}. Raising g by a quarter of a percentage point changes the value by {100*(v2/v-1):.3g}%. '+('With a 4 point spread between r and g, the estimate is fairly robust.' if p<.02 else ('Compared with g=1%, halving the spread to 2 points doubles the value and makes it about twice as sensitive to g.' if p<.04 else 'With only half a point of spread, a tiny change in assumed growth doubles the value, so the number is mostly a guess about g. At g≥r the formula gives no finite value at all.'))\n", "\n", "#### chapter_19\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_18(d,p):\n", " if d==1:\n", " # Lumped model diagnostic; properties explicitly assumed.\n", " r=np.logspace(-4,-1,100);k=200;h=p;bi=h*r/(3*k);fig,ax=canvas('Sphere radius (m)','Biot number','Screen a lumped thermal approximation');ax.loglog(r,bi,label='Biot number');ax.axhline(.1,linestyle='--',label='Common small-Bi screen');ax.axvline(.01,color='#a26913',linestyle=':',label='Selected radius .01 m');b=h*.01/(3*k);tau=2700*900*.01/(3*h);m={'Radius (m)':.01,'Conductivity (W/m/K)':k,'Density (kg/m³)':2700,'Specific heat (J/kg/K)':900,'Heat transfer h (W/m²/K)':h,'Biot number':b,'Screen Bi < .1 passed':b<.1,'Lumped time constant (s)':tau};t=f'Lc=r/3 gives Bi={b:.6g}. '+(f'The screen passes, so the lumped time constant τ=ρcLc/h={tau:.6g} s is a reasonable estimate under assumed aluminium-like properties.' if b<.1 else f'This fails the .1 screen: internal gradients matter, so the lumped τ={tau:.6g} s should not be trusted; use a conduction model.')+' The .1 screen is a rule of thumb; it does not validate real material properties or external heat transfer.'\n", " elif d==2:\n", " length=np.logspace(-3,0,100);diff=length**2/.01;adv=length/p;fig,ax=canvas('Length L (m)','Transport time (s)','Compare diffusion and advection scales');ax.loglog(length,diff,label='Diffusion L²/D');ax.loglog(length,adv,label='Advection L/U');ax.axvline(.1,color='#a26913',linestyle=':',label='L=.1 m (reported)');m={'Speed U (m/s)':p,'Diffusivity D (m²/s)':.01,'Peclet at L=.1m':p*.1/.01,'Equal-time length (m)':.01/p};t=f'At L=.1 m, Pe=UL/D={10*p:g}. '+('Diffusion is faster here, so spreading dominates.' if p*10<1 else ('Flow and diffusion take equal time here.' if p*10==1 else 'Flow carries material across before it diffuses, so advection dominates.'))+' Boundaries and geometry still shape the details.'\n", " elif d==3:\n", " speed=np.logspace(-3,1,100);re=1000*speed*.01/.001;fig,ax=canvas('Speed U (m/s)','Reynolds number','A dimensionless ratio compares inertia and viscosity');ax.loglog(speed,re);m={'Density (kg/m³)':1000,'Length (m)':.01,'Dynamic viscosity (Pa s)':.001,'Selected Reynolds number':10000*p};t=f'With the disclosed density, viscosity and length, U={p:g} m/s gives Re={10000*p:g}. '+('Viscosity dominates, so the flow is smooth and orderly.' if p<.01 else ('Inertia outweighs viscosity, yet many flows are still smooth at this size; pipe flow, for example, usually stays laminar below about 2000.' if p<.5 else 'Inertia dominates; turbulence is likely in most geometries.'))+' The exact switch point depends on geometry, so no single cutoff fits every flow.'\n", " elif d==4:\n", " a=1e-5;L=np.linspace(.002,.05,200);fig,ax=canvas('Slab thickness L (cm)','Diffusion time L²/α (s)','Double the thickness, quadruple the wait');ax.plot(100*L,L*L/a,label='t = L²/α, α=1e-5 m²/s');tt=p*p/a;ax.scatter([100*p],[tt],color='#a26913',zorder=3,label=f'Selected L={100*p:g} cm');m={'Thickness (cm)':100*p,'Thermal diffusivity (m²/s)':a,'Penetration time (s)':tt,'Time vs 2 cm slab':tt/40};t=f'Heat diffuses through {100*p:g} cm in about L²/α={tt:.3g} s (Fourier number 1). '+('Half the thickness takes a quarter of the time.' if p<.02 else ('This is the reference slab.' if p==.02 else 'Twice the thickness takes four times as long, not twice.'))+' Time grows with the square of distance because diffusion is a random walk.'\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_19(d,p):\n", " if d==1:\n", " state=np.array([2.,2.]);values=[];norms=[]\n", " for _ in range(31):\n", " values.append(.5*(state[0]**2+10*state[1]**2));norms.append(np.linalg.norm([state[0],10*state[1]]));state-=p*np.array([state[0],10*state[1]])\n", " fig,ax=canvas('Iteration','Objective','A step can shrink or amplify the stiff direction');ax.semilogy(range(31),np.maximum(values,1e-18));m={'Step size':p,'Initial objective':values[0],'Objective after 30 steps':values[-1],'Final gradient norm':norms[-1]};t=f'For f=(x²+10y²)/2 the largest Hessian eigenvalue is 10. Step {p:g} '+((('is exactly 1/L, the safe default: it wipes out the stiff y-direction in one step, and x then shrinks by 0.9 per step.' if p==.1 else 'contracts both directions, but the slow x-direction shrinks by only 0.95 per step.') if 0opt*10 else ('rounding dominates, so a smaller step makes it worse' if pec*3 else 'At low degree both are rough; the gap opens as degree rises.')\n", " elif d==5:\n", " tiny=1e-16;checks=sorted(set(np.unique(np.logspace(1,math.log10(p),40).astype(int))));naive=1.;s=1.;comp=0.;en=[];ek=[];k=0\n", " for target in checks:\n", " while k1, so this step is unstable: the numerical solution grows while the true solution decays.' if abs(g)>1 else ('The factor is negative, so the stable trajectory oscillates in sign; stability does not guarantee accuracy.' if g<0 else 'The positive factor below one gives a stable, monotone decay.'))\n", " elif d==2:\n", " hs=1/2**np.arange(1,8);errors=[]\n", " for h in hs:\n", " y=1.;z=-h;factor=1+z+z*z/2+z**3/6+z**4/24\n", " for _ in range(round(1/h)):y*=factor\n", " errors.append(abs(y-math.exp(-1)))\n", " i=list(hs).index(p);fig,ax=canvas('Step size h','Endpoint error at t=1','Halving the step cuts RK4 error about sixteenfold');ax.loglog(hs,errors,'o-',label='Computed RK4 error');ax.loglog(hs,errors[-1]*(hs/hs[-1])**4,'--',label='Fourth-order comparison');m={'Selected step':p,'Endpoint absolute error':errors[i],'Coarser / selected error':errors[i-1]/errors[i] if i else 'No coarser step'};t='These trajectories solve y′=−y, y(0)=1 to t=1. Halving h approaches a factor-of-sixteen global error reduction. Roundoff eventually limits such a trend.'\n", " elif d==3:\n", " h=p;n=round(40/h);t=np.arange(n+1)*h;qe=1.;pe=0.;qs=1.;ps=0.;ee=[];es=[]\n", " for _ in t:\n", " ee.append((qe*qe+pe*pe)/2);es.append((qs*qs+ps*ps)/2);qe,pe=qe+h*pe,pe-h*qe;ps-=h*qs;qs+=h*ps\n", " fig,ax=canvas('Time','Oscillator energy','An invariant reveals integration drift');ax.plot(t,ee,label='Explicit Euler');ax.plot(t,es,label='Symplectic Euler');ax.axhline(.5,linestyle='--',label='Exact energy');m={'Step':h,'Explicit final energy':ee[-1],'Symplectic final energy':es[-1]};t=f'The normalized oscillator q′=p, p′=−q has exact energy .5. Explicit Euler gains energy every step and ends at {ee[-1]:.4g}, about {ee[-1]/.5:,.0f} times too much. Symplectic Euler stays within {max(abs(np.array(es)-.5)):.2g} of .5. That bounded error is why long orbit and molecule runs use symplectic methods. It still does not prove the timing (phase) is right.'\n", " elif d==4:\n", " h=.025;n=round(2/h);ts=np.arange(n+1)*h;ye=[0.];yi=[0.]\n", " for k in range(n):ye.append(ye[-1]+h*(-p*(ye[-1]-math.cos(ts[k]))));yi.append((yi[-1]+h*p*math.cos(ts[k+1]))/(1+h*p))\n", " ye=np.array(ye);yi=np.array(yi);dense=np.linspace(0,2,400);ref=lambda s:(p*p*np.cos(s)+p*np.sin(s)-p*p*np.exp(-p*s))/(p*p+1)\n", " fig,ax=canvas('Time (s)','State y',f'Stiffness: decay rate λ={p:g} per second, step h={h} s');ax.plot(dense,ref(dense),'k',lw=1,label='Exact solution');ax.plot(ts,np.clip(ye,-3,3),'o-',ms=3,label='Explicit Euler (clipped at ±3)');ax.plot(ts,yi,'s-',ms=3,label='Implicit (backward) Euler');ax.set_ylim(-3,3)\n", " g=1-h*p;m={'Decay rate λ (1/s)':p,'Step h (s)':h,'Explicit factor 1−hλ':g,'Explicit stable step limit 2/λ (s)':2/p,'Explicit steps needed on [0,2]':math.ceil(2/(2/p)),'Explicit max error':float(abs(ye-ref(ts)).max()),'Implicit max error':float(abs(yi-ref(ts)).max())}\n", " t=f'The solution just follows cos t, which a step of {h} s resolves easily. Explicit Euler, though, needs h below 2/λ={2/p:.3g} s to stay stable. '+(f'At λ={p:g} that limit is loose, so both methods track the curve.' if abs(g)<=1 and g>=0 else (f'At λ={p:g} the step is stable but the factor {g:g} is negative, so explicit Euler overshoots and zigzags around the true curve for the first few steps, until repeated factors of −0.5 die out; implicit Euler does not.' if abs(g)<=1 else f'At λ={p:g} the factor is {g:g}, so explicit Euler explodes even though the true curve is smooth. That is stiffness: stability, not accuracy, forces about {math.ceil(p):d} tiny steps. An implicit method takes the large step safely.'))\n", " elif d==5:\n", " h=2*math.pi/p;n=10*p;q=1.;v=0.;qs=[q]\n", " f=lambda q,v:(v,-q)\n", " for _ in range(n):\n", " k1=f(q,v);k2=f(q+h/2*k1[0],v+h/2*k1[1]);k3=f(q+h/2*k2[0],v+h/2*k2[1]);k4=f(q+h*k3[0],v+h*k3[1]);q,v=q+h/6*(k1[0]+2*k2[0]+2*k3[0]+k4[0]),v+h/6*(k1[1]+2*k2[1]+2*k3[1]+k4[1]);qs.append(q)\n", " ts=np.arange(n+1)*h;amp=math.hypot(q,v);ph=math.degrees(math.atan2(-v,q));ph=(ph+180)%360-180\n", " fig,ax=canvas('Time (periods)','Position q',f'RK4 with {p} steps per period, after 10 periods');dense=np.linspace(0,ts[-1],2000);ax.plot(dense/(2*math.pi),np.cos(dense),'k',lw=1,label='Exact cos t');ax.plot(ts/(2*math.pi),qs,'o-',ms=3,label='RK4 steps');ax.set_xlim(8,10)\n", " m={'Steps per period':p,'Step h':h,'Amplitude after 10 periods':amp,'Amplitude loss (%)':100*(1-amp),'Phase error after 10 periods (degrees)':ph}\n", " t=f'With {p} steps per period, after 10 periods RK4 keeps {100*amp:.4g}% of the amplitude and is {abs(ph):.3g}° off in phase. '+('That is far too coarse: the steps barely sketch the wave, and the amplitude has visibly decayed.' if p<6 else ('That is usable for a few periods, but the errors grow every cycle, so long runs need more steps.' if 100*(1-amp)>.1 or abs(ph)>1 else 'The steps sit on the exact curve; at this resolution RK4 error is far below what the plot can show.'))+' Count steps per shortest period before trusting any oscillation.'\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def diffusion_solution(n,ratio,end=.02):\n", " x=np.linspace(0,1,n+1);dx=1/n;steps=math.ceil(end/(ratio*dx*dx));dt=end/steps;u=np.sin(np.pi*x);u[0]=u[-1]=0\n", " for _ in range(steps):\n", " v=u.copy();v[1:-1]=u[1:-1]+dt/dx**2*(u[:-2]-2*u[1:-1]+u[2:]);u=v\n", " exact=np.exp(-np.pi**2*end)*np.sin(np.pi*x)\n", " return x,u,exact,dt/dx**2,float(np.sqrt(np.mean((u-exact)**2)))\n", "\n", "\n", "def chapter_23(d,p):\n", " if d==1:\n", " n=80;dx=1/n;x=np.arange(n)*dx;initial=np.exp(-((x-.3)/.07)**2);u=initial.copy();steps=20\n", " for _ in range(steps):u=u-p*(u-np.roll(u,1))\n", " shift=steps*p*dx;wrapped=(x-shift-.3+.5)%1-.5;exact=np.exp(-(wrapped/.07)**2);fig,ax=canvas('Periodic x','Transported value','Upwind transport evolves an actual profile');ax.plot(x,exact,label='Shifted analytic profile');ax.plot(x,u,'o-',markersize=2,label='Upwind');m={'Courant number':p,'Steps':steps,'Initial discrete mass':float(initial.sum()*dx),'Final discrete mass':float(u.sum()*dx),'Minimum value':float(u.min())};t=f'The upwind scheme conserves total mass exactly: whatever leaves one cell enters its neighbor. At CFL={p:g}, '+('numerical diffusion spreads and lowers the peak; at CFL=1 the scheme would be an exact grid shift.' if p<1 else 'upwind is an exact grid shift: each step moves the profile one cell, matching the analytic curve.' if p==1 else 'the monotone stability condition fails; conserved mass alone does not establish a usable solution.')\n", " elif d==2:\n", " x,u,exact,ratio,error=diffusion_solution(40,p);fig,ax=canvas('Rod position x','Normalized temperature','Compare computed diffusion with an exact solution');ax.plot(x,exact,label='Exact sine decay');ax.plot(x,u,'o-',markersize=3,label='Explicit finite difference');m={'Grid intervals':40,'Actual dt/dx²':ratio,'RMS error at t=.02':error,'Maximum magnitude':float(abs(u).max())};t=f'Zero endpoints and a sine initial state provide a known heat solution. The actual ratio is {ratio:.6g}; the scheme is stable only when it is ≤.5.'+(' Above .5 it is unstable, yet this plot still looks fine: the sine start holds almost no jagged high-frequency content for the instability to amplify. Run the same ratio to t=.2 and the RMS error explodes to about 10⁶⁰.' if ratio>.5 else ' At or below .5 every mode decays, so the computed curve stays on the exact one.')\n", " elif d==3:\n", " ns=[10,20,40,80];errors=[diffusion_solution(n,.4)[4] for n in ns];fig,ax=canvas('Grid intervals','RMS solution error','Mesh refinement checks the solver');ax.loglog(ns,errors,'o-',label='Executed heat solves');ax.loglog(ns,errors[0]*(np.array(ns[0])/np.array(ns,dtype=float))**2,'--',label='Second-order comparison');i=ns.index(p);m={'Selected intervals':p,'RMS error':errors[i],'Observed order from previous mesh':math.log(errors[i-1]/errors[i],2) if i else 'No previous mesh'};t='The known sine heat solution checks this finite-difference implementation. Holding dt/dx² near .4 makes temporal error decrease with dx² alongside spatial error. This coupled study does not separately measure time and space orders.'\n", " elif d==4:\n", " N=np.linspace(3,40,300);fig,ax=canvas('Grid cells per wavelength','Numerical / true wave speed','Too few cells make waves travel at the wrong speed',two=True);ax[0].plot(N,np.sin(2*np.pi/N)/(2*np.pi/N),label='Centered second-order derivative');ax[0].axhline(1,color='k',lw=.8,linestyle='dashed',label='Exact speed');ax[0].axvline(p,color='#a26913',linestyle=':',label='Selected input')\n", " r=math.sin(2*math.pi/p)/(2*math.pi/p);x=np.linspace(0,3,600);ax[1].plot(x,np.sin(2*np.pi*(x-5)),'k',label='Exact wave after 5 wavelengths');ax[1].plot(x,np.sin(2*np.pi*(x-5*r)),label='Computed wave');ax[1].set(xlabel='Position (wavelengths)',ylabel='Wave height',title=f'{p} cells per wavelength')\n", " lag=5*(1-r)*360;m={'Cells per wavelength':p,'Speed ratio':r,'Speed error (%)':100*(1-r),'Phase lag after 5 wavelengths (degrees)':lag}\n", " t=f'With {p} cells per wavelength the computed wave moves at {100*r:.3g}% of the true speed. After traveling 5 wavelengths it lags by {lag:.3g}°. '+('The crest is more than a full wavelength behind (because the wave repeats, the plot makes it look slightly ahead): the computed wave is useless.' if lag>360 else ('The speed looks close, yet the crest is now a third of a wavelength late. Ten cells is a floor for short trips, not long ones.' if lag>90 else 'The crest arrives only slightly late, good enough for short runs.'))+' Phase error grows with distance traveled, so long runs need more cells or a higher-order scheme.'\n", " elif d==5:\n", " n=20;dx=1/n;a=1.;D=a*dx/p;x=np.linspace(0,1,n+1);A=np.zeros((n-1,n-1));b=np.zeros(n-1)\n", " lo=-D/dx**2-a/(2*dx);di=2*D/dx**2;up=-D/dx**2+a/(2*dx)\n", " for i in range(n-1):\n", " A[i,i]=di\n", " if i>0:A[i,i-1]=lo\n", " if i500 else f'{p:g} Hz is below the 500 Hz Nyquist limit (half the sample rate), so it appears where it belongs.')\n", " elif d==2:\n", " fs=1000;n=int(fs*p);t=np.arange(n)/fs;y=np.sin(2*np.pi*100*t)+np.sin(2*np.pi*100.2*t);window=np.hanning(n);nfft=8*n;f=np.fft.rfftfreq(nfft,1/fs);amp=2*abs(np.fft.rfft(y*window,nfft))/window.sum();fig,ax=canvas('Frequency (Hz)','Hann-windowed amplitude','Longer records change the two-tone spectrum');ax.plot(f,amp,label='8× padded FFT');ax.axvline(100,color='#a26913',linestyle=':',label='True tones');ax.axvline(100.2,color='#a26913',linestyle=':');ax.set_xlim(99,101.2)\n", " band=(f>99.5)&(f<100.7);fb=f[band];ab=amp[band];peaks=[float(fb[i]) for i in range(1,len(ab)-1) if ab[i]>ab[i-1] and ab[i]>=ab[i+1] and ab[i]>.3*ab.max()];resolved=.2>=4/p\n", " m={'Duration (s)':p,'Hann main-lobe half-width 2/T (Hz)':2/p,'Padded bin spacing (Hz)':fs/nfft,'Tone separation (Hz)':.2,'Spectral peaks found (Hz)':', '.join(f'{a:.4g}' for a in peaks)};t=f'The {p:g}-second record contains tones at 100 and 100.2 Hz (dotted lines). '+(f'The Hann main lobe (half-width {2/p:g} Hz) is wider than the 0.2 Hz separation, so the tones are not resolved. '+('The two peaks shown sit at the wrong frequencies: they come from phase interference, not resolution.' if len(peaks)>1 else 'They merge into one lobe.') if not resolved else 'The main lobes are now narrow enough that the peaks land on the true tone frequencies.')+' Zero padding only refines the plotted grid; duration and window govern resolution.'\n", " elif d==3:\n", " fs=1000;n=256;t=np.arange(n)/fs;y=np.sin(2*np.pi*103.3*t);window=np.ones(n) if p=='rectangular' else np.hanning(n);f=np.fft.rfftfreq(8192,1/fs);amp=2*abs(np.fft.rfft(y*window,8192))/window.sum();fig,ax=canvas('Frequency (Hz)','Amplitude (dB relative to 1)','Windows trade sidelobes against main-lobe width');ax.plot(f,20*np.log10(np.maximum(amp,1e-12)));ax.set(xlim=(50,160),ylim=(-100,5));m={'Window':p,'Samples':n,'Tone (Hz)':103.3,'Window average (amplitude correction)':float(window.mean())};t=('With no window, leakage is still at about −24 dB twenty hertz from the tone. ' if p=='rectangular' else 'The Hann window drops leakage twenty hertz away to about −49 dB, but its central peak is twice as wide. ')+'The tone is not coherent with the 256-sample record. A Hann window reduces distant leakage while widening its main lobe. Dividing by the window sum corrects coherent gain; it does not remove every off-bin amplitude bias.'\n", " elif d==4:\n", " fs=1000;n=3000;t_=np.arange(n)/fs;y=np.sin(2*np.pi*50*t_)+np.sin(2*np.pi*380*t_);fs2=fs/p;nyq=fs2/2\n", " k=np.arange(-100,101);cut=.8*nyq/fs;h=2*cut*np.sinc(2*cut*k)*np.hanning(len(k));h/=h.sum();yf=np.convolve(y,h,mode='same')\n", " fig,ax=canvas('Frequency (Hz)','One-sided amplitude',f'Downsample 1000 Hz by {p}: new Nyquist {nyq:.4g} Hz')\n", " for sig,lab,lw in [(y[::p],'Keep every sample (no filter)',3),(yf[::p],'Low-pass first, then keep',1.2)]:\n", " a=2*abs(np.fft.rfft(sig*np.hanning(len(sig))))/np.hanning(len(sig)).sum();ax.plot(np.fft.rfftfreq(len(sig),1/fs2),a,lw=lw,label=lab)\n", " ax.axvline(50,color='k',linestyle=':',label='Real 50 Hz tone');ax.set_xlim(0,nyq)\n", " al=abs((380+fs2/2)%fs2-fs2/2);m={'Downsampling factor':p,'New sample rate (Hz)':fs2,'New Nyquist (Hz)':nyq,'380 Hz tone appears at (Hz)':al if 380>nyq else 380.}\n", " t=('At factor 1 nothing is thrown away, so both tones appear where they belong: 50 and 380 Hz.' if p==1 else f'The new Nyquist limit is {nyq:.4g} Hz, below the 380 Hz tone. Without a filter that tone folds down to a fake {al:.3g} Hz peak'+(', right beside the real 50 Hz tone, where nobody could tell them apart.' if al<80 else ' that looks just like a real signal.')+' Filtering first removes it, leaving only the true 50 Hz.')+' Once aliasing happens, no later processing can undo it.'\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_25(d,p):\n", " if d==1:\n", " t=np.linspace(0,2,501);y=1-np.exp(-2*np.pi*p*t);fig,ax=canvas('Time (s)','Unit-step response','A first-order loop connects bandwidth and rise time');ax.plot(t,y);rise=math.log(9)/(2*math.pi*p);m={'Bandwidth (Hz)':p,'Exact 10–90% rise time (s)':rise,'Rule .35 / bandwidth (s)':.35/p};t=f'For this normalized first-order closed-loop model, 10–90% rise time is ln(9)/(2πf)={rise:.6g} s. The .35/f rule agrees closely here, but different pole patterns need separate verification.'\n", " elif d==2:\n", " f=np.logspace(-1,2,200);lag=360*f*p;fig,ax=canvas('Frequency (Hz)','Delay phase lag (degrees)','Latency consumes phase margin');ax.semilogx(f,lag);ax.axvline(5,color='#a26913',label='Assumed crossover 5 Hz');m={'Delay (s)':p,'Lag at 5 Hz (degrees)':1800*p,'Nominal margin (degrees)':60,'Fixed-crossover remaining margin':60-1800*p};t=f'Delay {p:g} s contributes {1800*p:g}° lag at 5 Hz. Subtracting it from a nominal 60° margin leaves {60-1800*p:g}°. '+('A negative margin means the loop would likely oscillate or go unstable: cut the delay or lower the crossover.' if 60-1800*p<0 else ('That is below the usual 45° floor, so expect overshoot and ringing.' if 60-1800*p<45 else 'That is still comfortable.'))+' This fixed-crossover screen is not a full stability proof.'\n", " elif d==3:\n", " dt=.005;t=np.arange(0,12+dt,dt);y=0.;integral=0.;ys=[];us=[];zs=[]\n", " for time in t:\n", " target=2. if time<4 else .5;error=target-y;raw=2*error+integral;u=np.clip(raw,-1,1)\n", " if p=='off' or abs(raw-u)<1e-12 or error*(raw-u)<0:integral+=dt*error\n", " y+=dt*(-y+u);ys.append(y);us.append(u);zs.append(integral)\n", " fig,ax=canvas('Time (s)','Plant output','Saturation exposes integral windup',two=True);ax[0].plot(t,ys,label='Plant output');ax[0].plot(t,np.where(t<4,2.,.5),'--',label='Requested setpoint');ax[1].plot(t,zs,label='Integral state');ax[1].plot(t,us,label='Clipped actuator');ax[1].set(ylabel='Controller states',title=f'Conditional integration: {p}');m={'Anti-windup':p,'Actuator limits':'[−1,1]','Final output':ys[-1],'Integral state just before t=4':zs[round(4/dt)-1]};t='A normalized first-order plant uses PI gains Kp=2, Ki=1 and actuator limits ±1. The setpoint is unreachable for four seconds, then drops to .5. '+(f'With anti-windup off, the integral stores {zs[round(4/dt)-1]:.3g} units of unusable push, so at t=12 s the output is still {ys[-1]:.3g} instead of .5.' if p=='off' else f'With conditional integration on, the integral stops growing while the actuator is pinned, so the output reaches {ys[-1]:.3g}, close to the .5 target.')+' Any controller with integral action and a limited actuator needs this guard.'\n", " elif d==4:\n", " dt=.005;ts=np.arange(0,10+dt,dt);y=0.;I=0.;ys=[]\n", " for s in ts:\n", " e=1-y;u=2*e+p*I;dist=-.5 if s>=5 else 0.;I+=dt*e;y+=dt*(-y+u+dist);ys.append(y)\n", " fig,ax=canvas('Time (s)','Plant output',f'Constant disturbance at t=5 s, integral gain Ki={p:g}');ax.plot(ts,ys,label='Plant output');ax.axhline(1,color='k',linestyle='dashed',label='Setpoint');ax.axvline(5,color='#a26913',linestyle=':',label='Disturbance −0.5 starts')\n", " m={'Integral gain Ki':p,'Output before disturbance (t=5 s)':ys[round(5/dt)-1],'Final output (t=10 s)':ys[-1],'Final error':1-ys[-1]}\n", " t=(f'With no integral action the output settles at {ys[-1]:.3g}, short of the setpoint by {1-ys[-1]:.3g}. A proportional controller needs a leftover error to keep pushing, and the disturbance makes that gap bigger.' if p==0 else f'Integral action keeps adding up the error until it is gone. Final error is {1-ys[-1]:.2g}'+(', but the slow integral takes seconds to clean up the disturbance.' if p<2 else ', and a larger Ki removes it faster. The price is already visible: the output overshoots the setpoint by about 8% at the start, and a still larger Ki would ring more.'))\n", " elif d==5:\n", " pole=math.tan(math.radians(p));k=math.hypot(1,pole);dt=.002;ts=np.arange(0,20+dt,dt);y=0.;v=0.;ys=[]\n", " for _ in ts:\n", " ys.append(y);acc=k*(1-y)-pole*v;v+=dt*acc;y+=dt*v\n", " ys=np.array(ys);os_=100*(ys.max()-1);fig,ax=canvas('Time (s)','Output',f'Step response with {p:g}° phase margin, crossover 1 rad/s');ax.plot(ts,ys,label='Closed-loop output');ax.axhline(1,color='k',linestyle='dashed',label='Setpoint')\n", " m={'Phase margin (degrees)':p,'Open-loop pole (rad/s)':pole,'Loop gain':k,'Overshoot (%)':float(os_),'Peak output':float(ys.max())}\n", " t=f'The loop L(s)=k/(s(s+a)) crosses unity gain at 1 rad/s with {p:g}° of phase margin. Its step response overshoots by {os_:.3g}%. '+('With only 30°, the output rings for several cycles before settling: a small extra delay could make it unstable.' if p<40 else ('45° gives a modest overshoot and quick settling, a common working compromise.' if p<55 else '60° gives little overshoot at the cost of a slightly slower rise.'))+' Margin is a starting screen; check the actual response.'\n", " return result(fig,ax,m,t)\n", "\n", "plt.rcParams.update({'font.family': 'DejaVu Sans', 'font.size': 11, 'axes.spines.top': False, 'axes.spines.right': False, 'axes.labelcolor': '#172a3b', 'text.color': '#172a3b', 'svg.fonttype': 'none'})\n", "plt.rcParams['axes.prop_cycle']=cycler(color=['#136f75', '#b77518', '#334c72', '#aa4e37'])\n", "print('Calculation definitions loaded; all inputs are constructed.')\n" ] }, { "cell_type": "markdown", "id": "ch21-cell02", "metadata": {}, "source": [ "## C21-D01: Preserve a small logarithmic change\n", "\n", "Why can log(1+x) vanish at x=10⁻¹⁶?\n", "\n", "Compare mathematically equivalent evaluations after floating-point rounding.\n", "\n", "$$\n", "\\operatorname{log1p}(x)=\\log(1+x)\n", "$$\n", "\n", "**Symbols and inputs:** Small x. Binary64 arithmetic, positive x; stable function does not validate the mathematical model.\n", "\n", "**Predict:** Why can log(1+x) vanish at x=10⁻¹⁶?" ] }, { "cell_type": "code", "execution_count": 2, "id": "ch21-cell03", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:58:20.828398Z", "iopub.status.busy": "2026-10-03T00:58:20.828344Z", "iopub.status.idle": "2026-10-03T00:58:20.992302Z", "shell.execute_reply": "2026-10-03T00:58:20.992239Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "Preserve a small logarithmic change" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Direct log(1+x):** 1.000088900581841e-12\n", "- **Stable log1p(x):** 9.999999999995e-13" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "At x=1e-12, 1+x keeps only part of x, so log(1+x) has relative error 8.9e-05. log1p never forms 1+x, so it keeps every digit of x. Use it whenever x can be tiny, such as a daily interest rate or a small probability." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(21,1,1e-12)\n", "buffer=io.BytesIO()\n", "figure.savefig(buffer,format='png',dpi=140,bbox_inches='tight',pad_inches=.16)\n", "display(Image(data=buffer.getvalue(),alt='Preserve a small logarithmic change'))\n", "plt.close(figure)\n", "display(Markdown('\\n'.join('- **'+str(k)+':** '+str(v) for k,v in metrics.items())))\n", "display(Markdown(interpretation))\n" ] }, { "cell_type": "markdown", "id": "ch21-cell04", "metadata": {}, "source": [ "**Use the idea:** Use rule 21.1.2 when its stated conditions fit. Compare the calculation with your own decision threshold; retain the relevant error or uncertainty.\n", "\n", "**Assumptions and limits:** Binary64 arithmetic, positive x; stable function does not validate the mathematical model.\n", "\n", "
Why can log(1+x) vanish at x=10⁻¹⁶?\n", "\n", "The addition can round to exactly one. log1p works without first losing that small increment.\n", "\n", "
\n", "\n", "**Book source:** [Rule 21.1.2: Use log1p and expm1 for small arguments](source.html)." ] }, { "cell_type": "markdown", "id": "ch21-cell05", "metadata": {}, "source": [ "## C21-D02: Bound speedup before buying more processors\n", "\n", "What is the ceiling when s=.1?\n", "\n", "The ideal strong-scaling curve bends toward a serial-fraction ceiling.\n", "\n", "$$\n", "S(P)=\\frac1{s+(1-s)/P}\n", "$$\n", "\n", "**Symbols and inputs:** Serial fraction s. Fixed-work Amdahl model; communication and contention omitted. This is not measured speedup.\n", "\n", "**Predict:** What is the ceiling when s=.1?" ] }, { "cell_type": "code", "execution_count": 3, "id": "ch21-cell06", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:58:20.993312Z", "iopub.status.busy": "2026-10-03T00:58:20.993243Z", "iopub.status.idle": "2026-10-03T00:58:21.058035Z", "shell.execute_reply": "2026-10-03T00:58:21.057977Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "Bound speedup before buying more processors" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Serial fraction:** 0.1\n", "- **Ideal eight-processor speedup:** 4.705882352941176\n", "- **Ideal ceiling:** 10.0" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "Serial fraction 0.1 limits ideal speedup to 10. Communication, bandwidth and scheduling can reduce actual speedup further. This is a bound calculation, not a benchmark. Eight processors give at most 4.71 times the one-processor speed, so shrink the serial part before buying hardware." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(21,2,0.1)\n", "buffer=io.BytesIO()\n", "figure.savefig(buffer,format='png',dpi=140,bbox_inches='tight',pad_inches=.16)\n", "display(Image(data=buffer.getvalue(),alt='Bound speedup before buying more processors'))\n", "plt.close(figure)\n", "display(Markdown('\\n'.join('- **'+str(k)+':** '+str(v) for k,v in metrics.items())))\n", "display(Markdown(interpretation))\n" ] }, { "cell_type": "markdown", "id": "ch21-cell07", "metadata": {}, "source": [ "**Use the idea:** Use rule 21.3.2 when its stated conditions fit. Compare the calculation with your own decision threshold; retain the relevant error or uncertainty.\n", "\n", "**Assumptions and limits:** Fixed-work Amdahl model; communication and contention omitted. This is not measured speedup.\n", "\n", "
What is the ceiling when s=.1?\n", "\n", "Ten, even with infinitely many processors under the ideal model.\n", "\n", "
\n", "\n", "**Book source:** [Rule 21.3.2: Use Amdahl's law to bound strong scaling](source.html)." ] }, { "cell_type": "markdown", "id": "ch21-cell08", "metadata": {}, "source": [ "## C21-D03: Balance checkpoint overhead against lost work\n", "\n", "If failure interval quadruples, how does the optimal interval change?\n", "\n", "Frequent checkpoints waste save time; infrequent checkpoints expose more work to loss.\n", "\n", "$$\n", "L(T)\\approx C/T+T/(2M),\\quad T_*\\approx\\sqrt{2CM}\n", "$$\n", "\n", "**Symbols and inputs:** Mean failure interval M (s). C=10s; small-overhead, approximate memoryless-failure model, recovery cost omitted.\n", "\n", "**Predict:** If failure interval quadruples, how does the optimal interval change?" ] }, { "cell_type": "code", "execution_count": 4, "id": "ch21-cell09", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:58:21.058978Z", "iopub.status.busy": "2026-10-03T00:58:21.058926Z", "iopub.status.idle": "2026-10-03T00:58:21.135231Z", "shell.execute_reply": "2026-10-03T00:58:21.135175Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "Balance checkpoint overhead against lost work" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Checkpoint cost (s):** 10.0\n", "- **Mean failure interval (s):** 10000\n", "- **Approximate optimum (s):** 447.21359549995793\n", "- **Approximate minimum loss fraction:** 0.044721359549995794" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "The leading model C/T+T/(2M) balances checkpoint cost C=10 s with assumed mean failure interval M=10000 s. Its optimum is 447.214 s; recovery cost and nonmemoryless failures require a richer model." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(21,3,10000)\n", "buffer=io.BytesIO()\n", "figure.savefig(buffer,format='png',dpi=140,bbox_inches='tight',pad_inches=.16)\n", "display(Image(data=buffer.getvalue(),alt='Balance checkpoint overhead against lost work'))\n", "plt.close(figure)\n", "display(Markdown('\\n'.join('- **'+str(k)+':** '+str(v) for k,v in metrics.items())))\n", "display(Markdown(interpretation))\n" ] }, { "cell_type": "markdown", "id": "ch21-cell10", "metadata": {}, "source": [ "**Use the idea:** Use rule 21.3.3 when its stated conditions fit. Compare the calculation with your own decision threshold; retain the relevant error or uncertainty.\n", "\n", "**Assumptions and limits:** C=10s; small-overhead, approximate memoryless-failure model, recovery cost omitted.\n", "\n", "
If failure interval quadruples, how does the optimal interval change?\n", "\n", "It doubles because the leading optimum scales as √M.\n", "\n", "
\n", "\n", "**Book source:** [Rule 21.3.3: Set checkpoint interval from checkpoint cost and failure rate](source.html)." ] }, { "cell_type": "markdown", "id": "ch21-cell11", "metadata": {}, "source": [ "## C21-D04: See why parallel sums disagree in the last digits\n", "\n", "Is a parallel result wrong if it differs from the serial result in the last digits?\n", "\n", "Add the same 100,000 numbers in different groupings and compare each total with the exactly rounded sum.\n", "\n", "$$\n", "(a+b)+c\\neq a+(b+c)\\ \\text{in floating point}\n", "$$\n", "\n", "**Symbols and inputs:** Partial sums (threads). Binary64; values span eight orders of magnitude; each chunk is summed left to right, then the chunk totals are added. Fixed seed 21.\n", "\n", "**Predict:** Is a parallel result wrong if it differs from the serial result in the last digits?" ] }, { "cell_type": "code", "execution_count": 5, "id": "ch21-cell12", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:58:21.136255Z", "iopub.status.busy": "2026-10-03T00:58:21.136170Z", "iopub.status.idle": "2026-10-03T00:58:21.249467Z", "shell.execute_reply": "2026-10-03T00:58:21.249397Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "See why parallel sums disagree in the last digits" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Values summed:** 100000\n", "- **Partial sums:** 16\n", "- **Error (last-place units):** 14.0\n", "- **Serial one-sum error (last-place units):** 50.0\n", "- **Relative error:** 1.759452092926235e-15" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "Splitting 100,000 numbers into 16 partial sums gives -463159.67116400891; the exact sum is -463159.67116400972. They differ by 14 units in the last place, a relative error of 2e-15. A plain serial loop is off by 50 units in the last place. Each thread count adds in a different order, and floating addition is not associative. So a parallel run can disagree with a serial run in the last digits without either one being wrong. Compare results with a tolerance, not with ==." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(21,4,16)\n", "buffer=io.BytesIO()\n", "figure.savefig(buffer,format='png',dpi=140,bbox_inches='tight',pad_inches=.16)\n", "display(Image(data=buffer.getvalue(),alt='See why parallel sums disagree in the last digits'))\n", "plt.close(figure)\n", "display(Markdown('\\n'.join('- **'+str(k)+':** '+str(v) for k,v in metrics.items())))\n", "display(Markdown(interpretation))\n" ] }, { "cell_type": "markdown", "id": "ch21-cell13", "metadata": {}, "source": [ "**Use the idea:** Use rule 21.2.1 when its stated conditions fit. Compare the calculation with your own decision threshold; retain the relevant error or uncertainty.\n", "\n", "**Assumptions and limits:** Binary64; values span eight orders of magnitude; each chunk is summed left to right, then the chunk totals are added. Fixed seed 21.\n", "\n", "
Is a parallel result wrong if it differs from the serial result in the last digits?\n", "\n", "No. Both are rounded answers that took different paths. Compare them with a tolerance, not with exact equality.\n", "\n", "
\n", "\n", "**Book source:** [Rule 21.2.1: Expect parallel floating reductions to change low bits](source.html)." ] }, { "cell_type": "markdown", "id": "ch21-cell14", "metadata": {}, "source": [ "## C21-D05: Find out whether memory or arithmetic sets the speed limit\n", "\n", "A kernel does 1 FLOP per byte. Will a chip with twice the arithmetic peak make it faster?\n", "\n", "Plot the roofline for a machine with a 1000 GFLOP/s arithmetic peak and 100 GB/s memory bandwidth. The kernel dot shows its ceiling.\n", "\n", "$$\n", "P\\le\\min\\left(P_{peak},\\,B_{mem}I\\right)\n", "$$\n", "\n", "**Symbols and inputs:** Arithmetic intensity I (FLOPs/byte). Idealized roofline; caches, latency and instruction mix omitted. A ceiling, not a measured speed.\n", "\n", "**Predict:** A kernel does 1 FLOP per byte. Will a chip with twice the arithmetic peak make it faster?" ] }, { "cell_type": "code", "execution_count": 6, "id": "ch21-cell15", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:58:21.251455Z", "iopub.status.busy": "2026-10-03T00:58:21.251370Z", "iopub.status.idle": "2026-10-03T00:58:21.406318Z", "shell.execute_reply": "2026-10-03T00:58:21.406260Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABZkAAAKJCAYAAADZQidKAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjExLjIsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvgI3uAAAAAAlwSFlzAAAViAAAFYgBxNdAoAAA/UhJREFUeJzs3QV0FFcXwPGLBAgJ7u7u7lDcpbgVD+5uxd3dKbTlg1JogRZ3K+7u7hCCRAgJ5DvvhV0SIkRXkv/vnDmzeTuz+2Z2Jrt79859Uby8vLwEAAAAAAAAAIAQiBqSlQAAAAAAAAAAIMgMAAAAAAAAAAgVMpkBAAAAAAAAACFGkBkAAAAAAAAAEGIEmQEAAAAAAAAAIUaQGQAAAAAAAAAQYgSZAQAAAAAAAAAhRpAZAAAAAAAAABBiBJkBAAAAAAAAACFGkBkAAAAAAAAAEGIEmQEAAAAAAAAAIUaQGQAAAAAAAAAQYgSZAQAAAAAAAAAhRpAZAAAAAAAAABBiBJkBAAAAAAAAACFGkBkAAAAAAAAAEGIEmQEAAAAAAAAAIUaQGQAAAAAAAAAQYgSZAQAAAAAAAAAhRpAZAAAAAAAAABBiBJkBAAAAAAAAACEWPeSrAgAAS/f46XP5Y8NWuXL9lrx3cREvLy8/y2RIm1qmjBzgq236ghVy7PQ5KVW0oPTu1NqEPQYQVGFxno6YNEeu3rwt1SqUlfYtGkTqnc//PcvD8Rn8YzWk9wEAEFoEmQEA+Mb2vYdk+f/W+33TjBZN7Oxi66Bs6WKFpEzxQhI1quVeFHT89Hlp3rm/uLi6Bbrca6e3ftqu3Lgth46dloQJ4odjDwGERlicp+cuXZUTZy9K5gzpIv2Lwf89y8PxGfxjNaT3AQAQWgSZAQD4xuOnL/SXsMDMXbZKcmXLLIunj5HMGdJa5D4cOGaaDjBnTJdaundoKamSJ5MoUb7ev/qvzbJx2x5zdhFAOBk/c5EO0JUtXlh6OPwUqfcz+8Ly9om5nx8AAIQ9gswAAARizoRhkjxpYn37o4enPHj0RDZt2yPHz1yQy9dvSROHPnJw0+86w9mS3H/0RK7fuqtvTx7RX8oUL+xnmYNHTwW4fv+ubaV1k7qSJHGicO0ngJAL7Dy9dPWG/rEsKedwkPdFZPq/Z+7jw9zPb+1CeqxGpmMcAGB6BJkBAAhEkfx5JEO61L7a2jVvIP1HTpZV6//VNY/VvFPrJha1H1Uw3CBrpvTBXj9H1kySQzKFca8AhCXO07DF/kREP1Y5xgEA4clyC0kCAGDBBvfqaLx96HjgpTXM4YP7R+PtWDFjmrUvAAAAAICIjUxmAABCIHHCBJIgXlxxevtOXrxyDHA5V7cP8u+OfXL8zHl58eq1xLSxkTSpU0ilsiWldLGC332e4K6v6ixv2LrL12B+bXoO0YMWKvHjxZWlM8Z+93kDG4F+xKQ5cvXmbalWoay0b9FA9/HPTdvk5NmL8u69s6RNnVLqVa8oRQrk+e7zHD52Wvb9d1yX93D74C5JEiWQEoULSJ1qFcQ2VvgFx7/dBtXvPzZslbMXr8jHjx6SK3sWade8vt5fBp6enrqG9X8nzshLRydJnSKZNK5bXQrmzRku22nKPob0OP22jy4urrLu3x1y+vxlefnqtdSoXFbKFi8iA0ZP0csP79tF8uXKHuDjPX/5SnoMGSdeXl7St0tbKVE4/3f3ram2o1XjekHuh3qt9h4+LhevXJenz1/Km3fvJa69neTMlllqVCoXaB334PTFv/PUMHDp5Wu39N+qJEGj9r18PcdPjetKnaoVAtyHwTmfLflcCu6+COz/nk/HTp+X/YePy50Hj3Td+2RJEukBYetULS/p0qSS4Hr24pUuw3Tx6g15/eat2MW2leRJEku2zBmkZuUfJEH8uGbbJ2HRv9A+v0+W/H4T0uMiJP0K6rFqjvf2h0+eyfp/tuuSYp8+fdKDijavX0tfFaYea8q8ZXq5tUtnWvTgyQCA4CPIDABACKggibOLq74dL469v8vsO3xceg4dLy8dX/u5b9HKP6REkfyyZNoYSZI4YZitf+f+Qz+DFh49ec54O0ki/58rOCPQq8GaTpy9qL843nvwWJp16id3HzzytYwKIvR0+EmG9u7k7+Or9boMHCVnL171c58KUE2as0SWTB/j75fZ984u0q7XUH27yg+lxOGnxkHapoC24erNO9K8Uz8dDDTYsvuALF+9Xv75fYFkSp9WB8Kadewrl67d9PU4v67dKGMH95QOLRuF+Xaaqo+hOU599fHGbWnRZYA8efbCeL8KQqmAqOrbtZt35JfVf8vs8d6vnX/+t36zrhUeP24cyZ87R4DLmWM7gmrFmr91sMbD09PPfSqwOnH2Eh3AGTOop78BluD0xb/z9NuBS9WPYN/+EFa+dDF/+x6S89mSz6Xg7ovA/u8pd+8/ku5DxuqAv38mzFosQ3t1DNZAdv9b/68MnzhLBxf9M2TcDFkyY4xUr1jWLPskNP3zj6mPz9D+Hw6KkB4XoenX945Vc723r/57swwbP/Ob4+WQLFy5RqaNGiTx4tobX//Pnz8TZAaACIYgMwAAIaC+JBmCSDmy+K2LeOTkWfmp20Dx9PwkCePHk/YtGkqeHFnE9YO77D5wRP7avFMHf+u37Snb1y7VmWFhsX6LBrWlbInCcubCFZk0Z6luWzl3osS2jaVvx4gRI8xeb7cPH6RFl/4SM2YMGTe0t6RPk0oH+H753186423O0t+laMG8UqlsCV/rPXj8VGo07ySvnd5IbFtbafpjDSlWKK/YxY4tt+8+0EG6ew8fS2OHPrL9j6V+AnwfPTyMX1JVllhoqGyzVt0GSbIkiaVv5zaSInlS3Yc5y34Xx9dvpEOfn2Xnn8t14MzpzVv5uV9XXeP61WsnWfzrWh04HTllnpQqVkhyZMkYpttpij6G9jj12ceWXQeKvV1sHSjMmD6N2ESPLqlSJNP3t21WXwaNmSb/bN8jYwb1kHhx4/h5DBVw+N9f/+rbTevXDFZmoam2Iyiev3ils3arVywjWTKmk+RJk0j06NHk8bMX8s+2PTqIs2zVekkQL57069o2wMcJaV+8nzetjJ+5WM5fviZliheSHh1a+lomY7o0YXY+W/K5FNJ9EVAgsUazjvrqFfV61qteSf+vVcE6FSRV96ssepVBH1SXrt6UAaOn6mM/d/Ys0rB2VUmbOoUOvKlg7PXbd2Xzzv2+rkwx5T4JTf8s5fgMq//DYX1chHe/QiOk+3rnvsPSb8RkfSVKmlQppH3zBpIpQ1qdBb155z7pO2KSdGvX3GTbAQAwAy8AAODLslXrvZLlLKWnO/ce+tk7R0+d8ypYsb6+P02+H7zu3n/k6/5Pnz55FavaWN9fsMKPXo+fPvfzGOv/3WF8jrHTF4Tp+sqOfYeN9795+87fV1itp+6v8GNrP/e16zVM39ex3wg/99Vu0dm47c079/dyd//o634XVzevkjWa6mWadOjjZ/16rbvp+7IVr+Z16+59P/e/d3bxqtakg16mYbuefu5/9drJuG0DRk3xCgnDNqTOW05vq6enp6/7z1y44pU8V2m9TMsuA7zK1G7h9drpra9lnN689cpRqqZeZtCYaWG+neHdx7A4znz2sUHbnl4f3N29/OPs4uqVpVhVveyS39b6u8yOvYf0/Wqbvj2nAmPK7QiKFy8d/bxWPs1dtko/V8bClfQxEJq+BHaeNnXoo+/rOnB0oP0N7flsDedSUPdFYPuzRrOO+j51HJ8+fznQ1z+oJsxapB+zeLUmXm4fPvi7zMePHl6OTm/Msk9C07/vMdXxGdr99D0hPS5C26/AjtWQ3heafe3h4aH//6r7ytdr5fX23Xs/jz9nyW/6/4Thf7FaBwAQsVAECQCAQKjL71W9SDXVa9VNClWsr+ePnz7XGYbLZo2T9Gl911o8cOSkzkBSRg/qKSmTJ/XzuA1qVdEZXcrv6zbpuoVhtb6pRIkSRWaNHSIxYtj4aldZ04aasSprU2XBGajLgg3lOyYM66Mvn/+W2q8ThvXVt1XGssr48imuvb38uWymnkJSKsOnaNGiypSR/SXal5rVBgXy5JC8ObPp27sOHJEJQ/v4qTuqslVVrU1DLU6fwmI7w7uPYXmceX76JNNHD5SYAWTKq8zhxnWr6du//fmPv8v8+ucm46Xy355TgTHldgSFKsfx7WvlU+fWTcTWNpbO/FX1SQMSFn0J7/PZ2s6lkDp++ryxFMLI/t0CrR0dUPkj/7i5eZcUULVqAxqg1cYmus7ON8c+CWn/ItL7TXgcF5ZwTIf1vt733wl9tYYyYXhfietPGbHuHVrqKzIAABEXQWYAAAJx8txF/QVPTSr4YfgSlThRAtm6ZomuCfyto6e8vzyqQFK1CqUDfOwGtarq+dt3znL1xp0wW99U1KW9AQVUcufIoueubm7i6ONS6gNHTui5uuy/WiA1PFVgSg2sqJz6JhCnghplSxTRkypHELptyCeJAqhpmf3LJfvqy3KpAAaNM1zC/OjJM1/tYbGd4d3HsDzO1GB+3xvwTJXMUMGLm3fuGZ/b50BRqqayYbngMPV2BIUKvqjBvCbNXiId+43QtU0NP1ap258/eQdnHj4JOHAUVn0Jz/PZ2s6lkDpw9JSex4oZQxrW8T6OwoIaCFI//pGTsux/6/Ugj0Hqj4n2SUj7F5Heb8LjuLCEYzqs9/WJMxeMn42KF8rn77rq/78a+BQAEHFRkxkAgEDMmTBMkidNrG+/efde16j8/c9N8srRSZo49JENK+f5ybo0DNKVMW1qiR494LdaVY/UQGVGG768hXZ9U0mbKkWA9/nMYnJ1dRVJlEDfvvvAO+NU1a5s/2XwPi8v7+W8xMtnOS/54O6dRRecGqfBlSZl8gDvi2MfW89VDVz15dg/KttMUVmpPoXldoZXH8PyOAtKsF9l66lapSpg9dvajVKicH7jfavWbdKBWVXvtWKZ4t99LHNux/fcvvdAHPr8rAfY+p5vX5Ow7kt4n8/Wdi6F1MMvWaSqVnBYZpY3rF1Ffvtzo66hP3zCLBk7bYHkz51d8ufJIUUL5JVyJYsY94s59klI+xdZ3m9CelxYwjEd1vvaMNhnZn+ysn3KRCYzAERoBJkBAAhEkfx59KXCBnWqVpAWDWtLzead9Jeqjv1+1hnNPoNbhi+FatCcwPi8/8NH9zBb31RsbHxfSutTFPkaSPr8+euXZpX9pKiR59XltUFh2B/m2gaVOR3gMl8CZioY4FNYbmd49TEsj7OABtL7VrtmDXSQecuuA3rAt8QJE4iHh6es+Xurvr91kx/1oGLBYY7tCIir2wdp2rGfDj6pgQtrV62gL6FPliSR2MaKJVGjer8WnfuPktdv3vp5TcKyL6Y4n63tXAqpoB5jwaXeN9b/MkeWr1onf/6zXW7euS/Hz1zQkxoMUR1DrZv+KIN7OvgqV2GqfRLS/kWW95uQHheWcEyH9b429C+wc1z5tgQHACBiIcgMAEAwpUudUiYO6ysOfX+WC1duyG9/bpJ2zRsY748fN46eqyBaYF45fs1MMlwSGxbrWzLDtqnR6lX91qBIn/ZrkN9aWMN2huVxFlB26rcq/1BS0qRKoYOwazduk27tmsu2vQflxStHfcl5s/o1xRq2IyDb9xzU26bqEm/6fYGxFrFPKojqFoSAUWj7ElFYwrlkqDkcHtmkqs5tD4ef9PTipaOu16vKNO3Y958uLbNo5R/6ypl5k342yz4JSf8sRXjvp5AeF5ZwTIc1wza9DqCcjsH37gcAWDeCzAAAhEDtquV1hqK6jHjGopXS9Mea+su4zzqWDx491dnOKZIl8fcxjp76OsBVjqze64TF+pbMEHR7/vKVFMyby2SXWpuaNWynOY4zlaXcqnFdGT9zkaxa9490bdtMfv1jo76vbvVKIRpAzJLOl2u37nr3KWsmfwPMyqVrN8XN7YOEuwgSpA6TcymU+0LVxzaUWVHlUPwbqC0sJE2SSKpWKK2nYX06y6Ax0/SPmH9v2aUHiDOUKjDXPglq/8Lr+S3t/3BIjwtreH8ILkPd9Ru378m7984BHgunzl0ycc8AAKbEwH8AAIRQv65t9Vxlca38429je+UfSulMRmX+L//zd101gNKK1X/p24Xz55YkPmqchnZ9S1a9UlmJbWurLxOeveQ3iaisYTvNdZw1b1BLZy3fffBIVqz5W46cPBuiAf8s8XyJ9qXUh8rMDqgUxoyFK8QU1PH3vbrPkeVcCu2+qFK+lB5YUpkwc7GYgspk/6FUUX1b1St/+97ZovZJYP0zxfNbwv/hkB4X1vD+EFyVypbUx4SHp6f88uV/7bfUoJ5bdh8wed8AAKZDkBkAgBCqWKaEHv1dWbBija7HahgAq0m96vr28v/9pb9EqrqzBirrqUXXgfL42Qv9pax/13a+Hje061syVYPXEJyfu2yVDJswS1+C/S21L3fsPSwjJ8/1c997Zxdp1L6Xnpb+/qdE1O0Mb+Y6zhIliC91qlXUt0dMnqODseo8UgOKWdN2+KdQ/tx6/vylo4yaOk/cP3403uf05p30GjZBzl++bpLyNhm+DEh6+vxl/dzWKizOpdDuC9WHXg4/6dsqSNap/0jjgJMGHz96yL879snfm3cG+XEXrlyjy8a8dPRb6kU9vnpf0c+fKIGk+DIArSn3SUj7ZynHZ3j/Hw7pcWEN7w/BpQZArlOtgr49bcEv+koV9eODgarn3bLrwEAHFQQAWD/KZQAAEAr9uraTll0G6GxmlZWpaswqYwf3klt37suJsxdl4uwlsnDFGsmaKb3OXLpy47Z8+vRJLze0V0djNphPoV3fkql9pOrnqm1a/r/1er9lTJdaEidKqAdEevnqtbx0fC2enp/0JbejB/Xwtf5HDw85dOy0vp3BgutUhnY7TcFcx5mqYf7npm1620OTxWxp50vFMsWleKF8cuz0eT0w2toNWyVThrQ6u+/ajTs6yL1q4RTpOXS8yNvwL+kz/5fV+hgrXLmB3h+Gy/J/alxXD2JqLUJ7LoXFvujVsZU8fPxM/vfXv7Jp2x75Z/teyZIxnSRMEF9evnKUR0+e6x8VHFo2kvq1qgRpuw4eOakHflPHRcIE8SR5ksQSx95OHJ3eyq279/UPMCpLf9yQ3r4GlzXVPglN/yzl+Azv/8MhPS6s4f0huFTJlMvXbsqtuw+k/6gpMnnuMsmUPo28efdert+6q19jFZTvOmiMXj64g7wCACwfQWYAAEKhUlnvbGY1GNKCFaulTdMfxS62rZ7W/TJbFvyyWlas2aAvn1cBMEV9Yc+fO4f079ZOr++f0K5v6Ub27yYVSheT+ctX63IJ6kupmnxuf+VyhaVq+TJizSx9O811nKmsZcN5o4Ixhgy4kLKU80U912/zJ+sM7b/+3amDKypTU1HbO2ZQTylSII+YgqoXO330IB10V8Eqta8NypcuJpHpXAqLfaFe2+ljBukfKVRw9Pzla7r+rIEqAaOO46AGmJWu7ZpLsqSJZd/h4zr73fH1G+N9Knhbskh+GdCtvRQtmNcs+yS0/bOU4zM8/w+H5riw9PeHkFylogY8HTNtgWzculu/rmpSx4raB5OG95O9h48Zt40gMwBEPFG8AioYBwBAJKUud1VZWkqRAnnFNlbMQJd/8Pip3HvwSN/OkyObJIjv+1J49Var6s+qEehj2ESXNKlSBqsmbEjWd3R6ozOKlJJFCvibZXb3/iN5+OSpzh5Tgw/5dPXGbf3lMEniRJLjy4A+BucuXZN3799LyuTJJHOGtAHWwD194XKQ9qHKNr17/6Gu6an6kjRxQn05saHO7rdUKYSjp7zr+KZIllRnjQVXULZBDeSkSi3Y29npQR79oy5xvnbrjr5dtkSRQJ8zuNtp6j6G5DgLSh8DUrF+G7l8/ZZ0b99ChvftImHF1NsREHUOXL99Vz59+iypUiSTlMmTGu87fvq8zm7MmC6NpE6ZPMR9Cew8NVCXrBv2h4eHh27z+byhPZ+t4VwK6r4Iyv40eP3mrR5s0t3dXZInTaz/F8WIYSMhpf5nP3v+Um+TyhZW/VKBuKAKr30SVv0L6fOb+/0muEJ6XAS3X4EdqyG9Lyz3tbOLqy6R4eX1WdKnTW0c1FUN+qpKhKjBUfdu+PW7+wUAYF0IMgMAAMCkDh07JY3a99aZbMe2r6VOJwBEcGo8hTK1W8izF690ySRVXgMAELFQCAkAAAAm8/bde/l50hx9u2blcgSYASCCmDJvudy5/9BPu7pKoVmnfjrAHD16NGndpJ5Z+gcACF9kMgMAACBcubi6SZseg+XjRw+5evOOvHvvrGuV7vl7pWRKHzblKQAA5pWuQAVdCkjV2k+dIqnEtrWVx89eyMPHT401rEcP7CEdWzXmpQKACIiB/wAAABCuPD095dCx08a/UyRLIpN/7keAGQAikIE9OsgfG7boesyvnb4OFKlKIxXKm0v6dG4tFcoUN2sfAQDhh0xmAAAAhHuQ+cjJszqLLXGihJIpXZpQDZIGALBcb96+k2cvX8lrp7d6gMgMaVNL3Dj25u4WACCcEWQGAAAAAAAAAIQYA/8BAAAAAAAAAEKMIDMAAAAAAAAAIMQIMgMAAAAAAAAAQowgMwAAAAAAAAAgxAgyWygHBwc9AQAAAAAAAIAli27uDsB/ly5dilS7xtnZWc/t7e3N3RUAQcA5C1gfzlvA+hQtWlTPT5w4Ye6uAAgi3m8B68I5G3bIZAYAAAAAAAAAhBiZzAAAAABggdavX2/uLgAAAAQJQWYAAAAAsEAJEyY0dxcAAACChHIZAAAAAGCBNm7cqCcAAABLRyYzAAAAAFigOXPm6HnLli3N3RUAAIBAkckMAAAAAAAAAAgxgswAAAAAAAAAgBCjXIaV+/jxozx9+lTc3d3l8+fPYq0+ffqk59GiRTN3VwAEAecsTC1q1KgSM2ZMSZEihcSIEYMXAAAAAAAsCJnMVh5gfvDggbi6uhoDPtYcPFATAOvAOQtTU+9z6v1Ove+p9z8AAAAAgOUgk9mKqQxmDw8PsbOzk1SpUll1FjBZkYB14ZyFOY65x48fi4uLi37/S5cuHS8CgAhvxIgR5u4CAABAkBBktmKqRIZi7QFmAAC+R73Pqfe7GzduGN//ACCi++GHH8zdBQAAgCChPkEoqTrInp6eevLy8jL5c0eJEoUAMwAg0gSa1fueNY9BAADBcfv2bT0BAABYOoLMoTRkyBCJFSuWntSARBkyZJChQ4fqupEAAAAAEFIODg56AgAAsHQEmUNp8uTJxkxmZ2dn+eWXX2TZsmXSuXPnsHmFAAAAAAAAAMCCEWQOQzFixJDy5ctL165d5c8//9SD8iHicf/4Uc5duiY79h6WbXsOGqcjJ88al3FxcdVtd+8/kogqLLfx6Klzcv7yNbEkb96+09v34PFTq3jcsHLmwmXZdeCIWY6R4Dy3pe7HiHruh+d2PX3+UrbvPSQeHp5h/tgAAAAAANMgyBweOzVqVF9zhM7zl698BXNVMOLwsdPy4qWjyXftjdv3pHStFlKtSQdp3WOwtO051DiNmjrPuNyT5y9127a9ByWiCqttvH7rrjRq30uev3glluT2vQd6+/YdPm4VjxtW5ixdJd0GjTHLMfLtc79776zP+XsPHlvNfgzteRHYNlvadoVVX21jxZSeQ8fLijV/h0FPAQAAAADmEF0igbt374qLi4skTJhQUqZMGaR11Mj1jx8/1rWWU6RIoQcaCsynT5/0OseOHZP58+frWs1qgCKE3pkLV3Rw41vqNalavrTMGjdE4seLa5JdPXX+cnn4+KnkypZZ0qRKYWw/fPy0r+Xs7WJLtQplJGO6NBJRhdU2jp42X3JmyyxVypcOs74hYhwjDx491ef+mEE9pWOrxmINIuo2+7ddYdVX9f+7Q8tGMmPhCmlSr7rEixsnjHoNAAAAADCVCBlk/vjxo2zYsEF27typp0ePvC/vbd++va6XHBgnJycZOHCgrF692jh4X6pUqXRbjx49Agw229nZ6ef18vKS+vXrS//+/cNhyyK3rJnS6wCH2scvHV/L+cvXdVZzv5HRZPmscSbpw9UbtyVb5gyy5++VvtrL1f3J198pkiWRlXMnSkQWFtuospj3HjomU0cOCLN+wXJYy3mgrpZIliRxiO+3xm0OrvDerhYNasmsxb/Kmr+3SOc2TcPteQDA2tStW9fcXQAAAIi8QeYnT55I06Zfv6TGiRNH3r9//931VFC5UqVKcubMGf13+vTp9WB+KqO5V69e8vDhQ5k6daq/63748EHXYL5w4YJ07NhRypQpI8ePHxcbG5sw3LLIrVHtqtLD4Wsw99LVm1K7ZWcdaFb1Qu3sYvtZ59qtO/L46XOJa28veXNlk5gxYgT4+IEtq+qQqvtVcDtV8mT6EnEld46skiZlcj+Ppfpz8NgpyZ45o2RIl9pYQ1bVHs6VPYukTZVCHj15pstvJE2cSHJlzxzgDxiqT7fuPpCoUaNInhxZQ521/W0/7j98LHfuP5KM6VJLujSpjMs5u7jqOsmq7EuhvLkkRgybMN/G39dtEpvo0aVOtQqB9lFdjn/n/kNJkTyp5MiSMcBtC+q++uDuLrfuPJAXrxwlZYqkehuCSv3IsffwMV0/tmyJIhLbNpaERlC2LSj9Dcnxpbbh7MUr+vHz5MgmCeLH9XP/7oNHJH3a1L76pvbx9Vt3JHOGdPpHF4OrN+/IvQePpFLZkmJjE93fYySoz636/98J7//FV2/eNp5zCeLHk+KF8vnZlqCeT99S+75q4w7S0+En6dGhpZ/7L1+7KY069JFu7Zrr6XtCc14EZ5u/d6yH5HhQ9a0fPHyiz/UsGdP7ek2+3a7A+po5Q1o5efaiv6+7ovqhyp2ULlZI4tjb6bZUKZLpbVT/EwgyA8BX6jsIAACANYgeUQfga9y4sVSpUkVPa9eulQEDvp8pOW3aNB1gVpnLmzdvlvz58+uA0i+//CIODg4yffp0HbwuVKiQv+urgLK6b/bs2TrIfOjQIalQwXfwDGEnd44ski9Xdjl2+ry8cnrjK8isAtDdBo/RmbIG8ePGkZEDu0uzH2v6epygLKvqkI6ZtkDffvvO2Vi+Y/roQdKiYe0A65eO6N9VurZt7quG7KSf+8nNO/d1/dHPnz/r+4oXzi+/z59sDLgYsid7D5/oq+asCsiqQNegng6+gkTHT5+X12/eSvnSxSRWzJiB7jdDPyYM6yMXrlyXPzZs1e3q8bq2bSY/9+sqm3ful34jJ+ltVVQAev0vcyRl8qRhuo27DxzVpTK+vTze8Djjh/bRge4/N20z3leiSH5ZPmu8JIwfL9j7SgU2x81YKKv/3izvnV2My6og3dIZYyV92q9Bdv98/OghvYaNl3927JOJw/uEKsDs6flJ16ENbNuC09/g7vsTZy5I5wGj5MmzF8a6uOOH9fHVRxUoHjx2uuTIkkn+WDrD2D557lL5d8c+qV21vO6Hwagpc/V5VH1f2QCPkaA+9+HjZ2TklLn6tspuVZNStEAe+WfVQuNy6n/0sAmzvru9AcmQNrXejvEzF4mnp6f06dzGeN/FqzekcfveEieOnZ8fQgISmvMiKNsc1GM9OMfD23fvpWO/EXLgyEnjY6pyTw1rV9Xrq9fn2+0KrK9rFk+XHkPGSbFC+eR/C/3+MNt3xCRdduj07r98tZcsWkCmzf9F/6jnX3AaAAAAAGC5ImSQWdVdVoHl4FCBiiVLlujbqqayCjAr6gu7KrPx33//yYoVK/QyixcvDvSxVFazQk3m8OX+8aPOvFP7OUmihMb2l45O0tihj7x2eiOJEyXQGZhPn7/UWX99hk+UhPHiSdUKpYO1rCrToeqRqsCOvX1sKZI/j14/TSq/Wczfo4I9KuiTO7t3cPXsxaty7NQ5mbFopYzs300v4+LqJg3a9tT9SJQwvg7yeX76pAOus5b8JnHi2PvKqpw0d6kcPXlOzuz521cg+Hv9uPvgkRTIk0NixYopp85ekvm/rJbkSRPrgHqK5Ekkf+4ccvXGHZ3pPGXeMpk1bmiYbaMauPHew8fSqkm9QB7nL/3ceXNm1T8iXLxyQ29np34jZN3y2cHeV65ubrL4t7U6uFYwb049V0FRFUxs03OI7P17ZYADdqogrwqynT5/SZdnUcdDaARl20LS36Du+5+6DdQ/IqgyCFkyppO7Dx7LgFFTddarT6WKFpRtew/pALvKcFX/K4+cPKt/iFGZrOpv9X9SBcRPnL0oNSp6B5gDEtTnTp0imZQsUkA/V/YsGSX9lyx7VTYnuNsbGNV39WNRtKhRZfLcZeLh+UkGdm8v5y5dk6YOfXSG8F8r5uhM29D6Xl+/t83B/b8Q1P0zYdZiHWCOF9de8ubMJp8+fZbrt+/K2o1bZVCPDmLrz/+UwPqqjucGtarI7+v+0T8k+PyfpI7fU+cuSd8ubSV6dN8fQQrmyannR0+fI8gMAF/UqVNHX1nZpEkTuXPnDvsFsALqCmeFq5oB6zpnc+TIIX36+E5+QvBEyCBzSFy9elWXxYgXL57UqlXLz/0//fSTDjLv3r3bV3vDhg2ldevWUqRIEYkZM6acPn1aunfvLvny5ZNSpUp993lLlCjhb/ulS5f0Aa4+VAY22KAKMKm5tTNk2AV237Vbd2XLrv06qPXq9RtZ/+8OHcD4sUYliRnDxrgffvnfeh00rlXlBx0UVVl4yso/NuiMxynzl0mlciWCtWzlciX1lL/8j7o8gM8a0Pp5vdQvFV9u6z57z70+exnbVOBGefj4mWz8dZ4UypdL/622oVKDtrJl534Z3qezbvvtz406kNSlTVMZ1MNBZ5QqrxydpIlDH5m7bJU4tGxo/CFDBb1VmQ+13PeOB0M/VDB9y/8W6ZIfysGjJ6VZp/7y86Q50rtTK+nftZ0OwLm4ukq1Jh1l47Y9Ohj39XUJ3TaqALOSNHFCP302PM79h0/kjyXTdaBTef7SUZp36ieHjp3W2bDq8YOzr1QgcfzQ3tKsfk1jORT13ONmLpIlv/2pg6YqcOazD+r4U/1v2XWgnq9ZMkOK5M8d4vMuONsWkv4GZd//suYvHeRtXr+mTBzeVwf71Hk1ac5Smbf8fxI3jr1x+9Tj/71lly5/ULxwPrl8/ZY4vn6jg48qKKsC3mogzJNnL4ib2wcpWSR/oOdBUJ9bZXWPjNNNl7JoWq+GOPzUyMc+/BSs7Q0K1Rd1vKvB5x49eSrb9x6WhAniybpls/QPL0F9vUNzXnxvm4NzrAdn/1y5cVsHgvdt+FUP8Oe9HZ/lr8079Q8L6rm/3a7v9fWnRnXk17UbZfVf//rKDleBZ9W/Zj/W8LNPkyT2/rHwwaMnge5vdbyo/gX2/gj/GcaaAGDZ1P+5TZs2ybp16+TgwYP6f+LJk1+vNgEAAGGvZMmSuopBZGBvbx8uj0uQ+YsrV67oed68ef3NQC5QwDuQc/fuXZ2pHCuW92XyI0aMkEmTJknXrl31F940adLokhqqftq3WVqmlDx5cov7Mhk7dmx59uxZiNdXAQ81GaiAUOsm9XR5B59UHVIVfFdBI0PQWGnT9Ee9/pkLV/Tl4SqrLzjLhpXmDWoZAz6KCu6UKVFYtu05ZGxTg+GpS+BVJvGeQ0d9rZ8vd3a5tnGbDjYZ6uGqgF9wqcClIcCsqPrCqp6qutq+X5e2xsvu7WLH1gF2lVGrgosqgzIstvHNO+866SojNiD1a1U2BmGVZEkSycAeHaRdr2H6tVPPEZx9ZWsbS7+27947y4XL18Xp7TsdrFIlE5QLV24Yg7YGat35v3gfY5t+m6frEIeFoGxbSPoblH1/7NR5nb0+emAP4/8p9XqrDN71/+7UGdQGpYt591EFtFWQWc1j29pKu+b1dVBT/a2CzP+dOKuX87lN/gnOcwdFULY3KFQf1P8BVXbmz03bdbB7/fLZOts6rIS2r8H9vxDU51QZxKq8hqqnbfifoP4vNqpTLcTbmiNrJimcP7es2bBVenVspR9PXX2i/q9WKlvC3ysuDP9nnd68C/HzAoC1u3//vvTu3dtPYgsAAIClI8j8xevXr/U8WTL/L4mOHz++zlR2d3eXN2/e6CCuISi9evXqEL8AR4/6DhR8m+Ec2K8LhmC4f0FxFWC2tCBzUEqI+He/oRyAugxbla3w8PSUW3fv60xQFVDRGao+1nN0eiMpkib2VULDQAVQVOBYBesSJogfrGUNVOzVTz9VPNZHe9So3vMoUaP4eJ28tyNT+jR+1lc1eFWWispcUYG3Zy8c9XZ26j8ywH319r1ziEqyGPqh9uW368eLY6/LA3x7aVf8eHGMl+snTZIoTLbRkDH5wf2jn2UNj6PKAXx7nwpoKq+d3ur7grOvVJBr2PiZsnbjNr3Ot9772KeGPvy2dqNedv7kEZItGAMEBiQ42xaS/gZl36vjPk3KFLq8gu++RZOsmdLpUhGGx1CD/qVJlUKXRRgYrYMcOXFWihXKK/Z2dlK0QF4dXO7SppkcOXVW0qZOoZc38O8YCc5zR/uyvvofENAxEpTtDSpV312VxFHnu7rCQWWLjxncM8jrB7TNwelrYNscnGM9OM+pajkrTTv20z8AqJIZKhDduE41HWwPcLsC6auifiDpPniszs6vUKa47Nh7WJzevNXt/i3v7v7R+MNWYP/b1A8C6v7w+vU9MmDfAZZH/V+eN2+eDBs2TFxcvo7DoNja2uqBxdWVk1x+D1g+Q/lMQ2IaAOs4Z1OnTs3n5FAiyPzFx4/eX24D++Cm7lNBZsMBaMlU1nBE61Oj2lWlh8NPxr8nzV6i65COn7lQxg3pbWxXGcmPnj431or1SWXiei8TK9jLhpWAav76ZGsbU/etXMmiAS6jgsHh0Y+oUX3vh7B8bJ9U5q6igk4BUVml33J08m4zZJ4HZ1/NW/Y/WbX+X13buECWHBI3bhyJHi2afPTw0Fmiqr7tt/p3a6fLtPQfOVkSJYgvP5QK+HmCIyjbFpL+BmXfq8Ehnzx/4X+/vvTBJ5XN/Ne/O3VdahWI7d2ptW4vVbSAzF76uzi7uMqZ81ekQe0qYf7c3xOU7Q0KlZH9U9dBepDLtctmytLf/tT/X9Q+ViVLvv3/EBKh7WtI/i8E5TnVAJajB/XQg/rduHNfZ82reswzF62Uf1ct1D9IhYQaUHHE5Lnyv7826yCzmqdLkzLAc8jwv0CV0AGAyOTy5ct6DJjjx78O6qqCUyNHjpQ///xT/yA4a9Yss/YRQNAZSnrxoy5gHThnww5B5m8CoAFl/6ogpNuXy7it4c3i5cuXEtGp0gIqi1LVT27TtL5kzpBWt+fImlmXEVj3z3ZpXLe6cfmHT57J3sPHdBaf4RL44CxrSupyeDUQXL+ubSWPj5IWBo+fPg+TgcjMSZV8UKUyVD3YgKhawCqgqYJgBv9b/6+e58iWKdj7SgUSVWbmqV3rjRmays59h3XQNqCgnRqIr4lDX2ndfbAsnz1eX+4fWkHZtpD0NyhyZsusaymrzFLDIJjKmQuXdc1lFdT2qXSxQrLm7y2y9Pd1OtBsKKFRqlhBGT9rsSz+da3Oui79nVIZwX3u6Dbe2awf3N0lPKl65Oq1zZIpvaxdMlMSxI8rg3t1lKjRoukazZ6enjJ5RP8wCTR/T2DbHF7/FwzrqexgNfipmlRQOE/Z2rqusiptEty+KqqOuKrXvPT3P3VNb3U8D+vTOcD9qF5/RQ1yCQCRgUpemTBhgkycONE46JDyww8/6MHGs2TJIufOnTNrHwEAAIKKIPMXqVKlMtZB88+jR4/0ZWwqqyBhQrKsLIHK0FPZdzWbd5JxMxbKyrkTdbsaUExl4fUbMVkuXLkuBfLk1INdqQCZGpisQ4uGxiBHcJY1JfW8azdslfptekjD2lUlT86sEjtWLHn4+KkuW3D7/kM5sWOdcfnjp8/rzNjypYvpTFFref1KFi0gR0+e03WG/cu4fOX4Wqo3dZBWjeuJXWxb2X3wiGzeuV8SJ0oglcuVCva+UtnTqt7x+JmLpHihfDpLVWVt/rVlV6B9VbVi1y2fJc069ZN2PYfK0hljfQVIQ7L/g7JtIe3v9zT9sYY+7jv1HyHtWzTUgd879x/q8hBqEM1vGYLKi379Q/8woAKc6oc3NVd/q3rd3ssVCtPnTp4ksZ6r5ZMlSSxx49jpuuFqX4QVVYu4VbdBuobwH0tm+Kq/rupEq8zxKfOWSfKkSaRvl68D2IWXwLY5uP8XgqpOyy6SJWN6nZmuSqOosjjqRxAlsP9/QXl9WjWuKwtXrhGHvj9LDBsb/foH5PT5y/pcUMF0AIjojhw5Ih06dNCDjxuoAcinTZums5oN/3+XLVtmxl4CAAAEHUHmL/Ll8/5SfOnSJV1zWdVg9kmN7KzkyZMnzC7PRuipjLc61SrIpm17dJBFDYJWrFA+PRDe5LnLZNmq9b6WV4OS9e3S1vh3cJY1JVV/euHUkdJ98DhZseZvP/d/G2SbNHepDtae2fO3vwNqWaomdWvI1t0HdYZjmeKF/dzfqXUTWf3XFhk2Yaav7Mi5E4YbM4CDs686tmoiW3Yd0NmZalKiR48m44f2kUFjpgXaV5Vhu3bJDGnRZYB06DNcFk0bLTUrlwvx/g/KtoWmv4EpUTi/dGnbTBauWCPzf/laU75cySK6D6okhk8qgJglYzq5eee+1KhUVv8PVD+6qXmJIvn1IHIqSGmo1x1Wz62yyMuWKCwHj56SXsPG67aiBfLIP6sWSljJlD6tjBzQXQdtv83gVlRgWZVvqFaxjJhCYNsc3P8LQZUyeTLZf+SEnnxSV3GoHwJC0leD9GlTSbkSRfRj169ZWRInTODvY6lM+J37/9PLxPDnhw4AiCjev38vQ4cOlfnz5+sfbA1+/PFHXZM5ZcqUZu0fAABASBFk/kIN5Fe0aFE5ceKErnk2atQo405Sl0rPnOkdCKpbt66EFzXIh6Fch7pkLiSDukVEKpuzWoUykjG9dzmMbw3t3UkPGHXs1HkdZFb6dG6j65Zu2r5HZybHtbeXsiULS+0q5f38SBCcZdUl5P5djl6meCFfA4ypQe10n33UMlUBGdWWNlUKP+vnyp5F3+fz+WpUKifHt+eRvzbvlEvXb8rnT58lTarkOvhdtkQRX+sXK5BX4sWJowft+p7A+lG2ZBGJ82VAPp8yZUir11FZhmG5jZXKldCZk2s3bfM3yKyCXzvXLZdf/9ggdx480gHcFg1q64CnT0HdVwXy5JD9m37TZSlULe5kiRNJwzpV9TaoAd+yZc4Q6LbY2cWW/y2aJiMmzZENW3dJ7hxZJF3qlPq4UbV8g1JL1vC4xQvl12VeAtu20PY3sH0/sn83vX+27j4gHz64S+H8uaVlwzo6W9kwKKNPrZv+KIePndbBWJ8a1akm6juyf6+ff8dIcJ97+azxOsB++dpNXZZBBbNDsr2BadusfqD3t2xUR4IqLM6LgLY5OMd6cJ7zn1UL5PDx0zpYrLKiVTa3Gvzvx5qVjT94BPRaBtZXA5Xhr4LMrZvUC3C/qR8qVCkWNSggAERUW7dulc6dO8vDhw99fQdRAef69f1/L/r555/13PBdBAAAwFJF8fL5E3oEcuvWLeMAfStXrpTp06frD2+jR4/WbeoStFy5cvla559//tFBZBXcHTBggNSrV09nG6h1t2/fLgkSJNCPG17lMlRg29A/w8iWPj+EfuvatWt6nj17drF2KitSIbAe+ahgWe9hE+TwltU6YKucPn9JajbvrOvgBhaYsgSq1EPJGs3kl9njdQAwsuCcRVCojxhVm3QQV1c3Obx5dYDLVG7YTv/AsnDq1x94I8N7n6kxqAlgvrFSevfuLatX+/4/qMplTJkyRX/HCIhKglFUIgwA68D7LWBdOGfDToTNZFYBYjVSs09///23ngzBTJWh7FOdOnVk8ODBMmnSJOPkc2DAtWvXhms9ZhXY7tatm75dvXp1Aq6IFNTl8cdOndOZ6IYgszV58vSFzoSNTAFm4HvuPXgsl67dlF0Hjug64sN6dwpw2eu37+ps7KF9OrNjAUQo6ke0//3vfzrA7OjoaGzPlCmTHtivQoUKZu0fAABAWIqwQWY1GnNgfJY28EmN7lyxYkVZsWKF3LhxQ2LGjClFihSRHj16SMaMGSU82dnZ6UmxsaEmJSIHdVXB1FEDxVqVLl5ITwC+UvWVR0yeo28nTZxIl1sJSPbMGWXFHO+BWwEgolCDiXfp0kW2bdtmbFNJLv369ZORI0fqBBYAAICIJMIGmTds2BDidStVqqQnAOYRWD1ZAJYvfZqUUr1iGUmRLKl0atVY4saxN3eXAMBk5aQWLFggQ4YM0eOtGOTPn1+WL18uBQsW5JUAAAARUoQNMgOwXpnSp5WVc8lsBKxVlfKl9QQAkcmVK1d0neWjR48a29RVkWrcFZXBzJWKAAAgIiPIDAAAAAAh9PHjR11yb/z48eLh4WFsL1u2rCxdulSyZs0a4n27ceNGXhcAAGAVCDIDAAAAQAgcO3ZMZy/7HHA8bty4MnXqVN0eNWrUUO1X9VgAAADWgCCzBVF121xdXfVtlQWhBgcBAAAAYFmcnZ1l2LBhMnfuXPHy8jK2161bV+bPny+pUqUKk+dZt26dnrdt2zZMHg8AACC8hO6ndYQplfGQNGlSPZ0+fVqePHnCHgYAAAAsyPbt2yVXrlwyZ84cY4A5WbJkOiCsBh8PqwCzsnDhQj0BAABYOoLMFmTAgAHy4sULPRUqVEhSpkxp7i4BAAAAEJFXr17JTz/9JNWrV5cHDx4Y90m7du30oH8NGzaUKFGisK8AAECkRLkMC2JnZ6cnhdGnAQAAAPNT2cpr1qyRXr166UCzQcaMGWXJkiVSsWJFs/YPAADAEpDJDAAAAAD+UBnLtWrVkhYtWhgDzGowv/79+8vFixcJMAMAAHxBkBkR0v2Hj2X9vzvk1WunIC2/eed+OXzstET2/QDreD1fvnpt7q4AABChff78WebNm6drL2/dutXYnjdvXjl+/LgeSyV27Nhm7SMAAIAloVwGLN6TZy/kyMmzxr9VrTv72LElW+YMkj6t/wOrHD11XnoPnyCbfpsviRMm+O5zDBk3Q3JnzyylixeSiCS4++Fbd+4/lDMXrkj50sUkUYL4wV7/8rWbcu3WXYkXN45UKlsi0GUvXLku9x8+kQTx4kqRgnkkZowYITo+vvVDqaJ62w3L5c6RRbJnzhikx1bB3ItXb4izq6skjB9fCuTJIXaxbf1ddtP2PeLh4Wn8W/U/dcrkkjdnVokWLZqE1NUbt/VUv1YV4+v514o5kiRxQgkrD588k+Onz0uZ4oUkWZLEYfa4AABYo6tXr0qHDh3kyJEjxraYMWPKyJEjdQazKcvajRkzxmTPBQAAEBoEmWHxzl++Jt0Hj/X3PhUUWzBllCRJ5DuAqoLPDWpVkcTftEc2od0Ph46dlkFjpsmW1YuCHGT+4O4uk+YslW17DuqgsZIrW+YAg8yPnz6X9r2Hy7lLV41tqr8LJo+QsiWKhOr4UAwBdsNyw3p3+m6Q+f6jJzJ8wizZffCocdR4JYaNjbRoWFuG9+3iJ9g8YNRUeffe2c9jqUDznAnDpGSRAhIS42ctFsfXTjrIHF5On7uk983qRdMIMgMAIq2PHz/K5MmTZdy4cfq2QZkyZWTp0qWSLVs2k/epdOnSJn9OAACAkCDIDKuRO3sWnb2sgn4vHV/L8dMXdBC0788T5fcFU3wtW7xQPj1FdubYD+/eOcuilX/o2zmyZpJbd+4Heilq6+6D5dK1m5IiWRIplC+XPHj0RC5cuSFtegyVfRt/lXSpUwbr+PhWcAPst+89kDo/dRXH12/ENlZMKZQvtySIH1cHw89duiYr1vyts7s3/jZf3+9THHs7qfJDKX3b2cVVL/foyTO9jUe3/RHsbHJXtw9y+Ngp6d2pdbDWAwAAwaNKYKjs5UuXLhnb4sSJI1OmTJGOHTvqOszmcP36dT0vVChiXW0HAAAiHoLMFsTFxUVcXV31bQ8Pj1BdYh8R1a1WQXo4/GT8+9bdB1K1cXvZc+iYDujZ28X2Vbv25LlLxlIJPr10dJJT5y7qSx1LFMondj7W+5bPZVWwVj2Hqt8cP24cP6U1Pn36JOcvX5dHT5/pch5FCuTRQceguHnnvs60Vdm+cePYy4mzF3WpBhU0zZopfYAByDPnL4vjmzeSPEliKZg3l9jY+D6l/dsPPp9LlbE4ff6yPHn+QjKnTys5s2U2rqsCpGcvXtG39/13Qu4+eKxvq/7kzRlwJk+sWDFlRP+uUqNiOZ1JnbV4tQCX3bbnkA4wF86fW/5cNkti28bS7RNnL5bZS36X+b+slikj+ofo+AipLgNH6wBz1fKlZcbYwb4yuK/fuisd+gzX+2/CzEUydkgvX+smS5JI5k8e4Suru0XnAfLfiTOyfc8hadmojjG4rgLpT549l7hx4kiOrBn9zRQ/cOSEfHD/qPvyLfVji3rtnj5/KZnSp/H12hnKnKjs6ZTJk/pZ9+ipc7p8yI81KsmV67fl+JkLuv3w8TPy+s1bfTtD2lQ6wO7z+VTpEJWdbmsbS5cOUecBAADW/vl7+PDhMnv2bF9XL9WuXVsWLFggqVOnNmv/unTpoucnTpwwaz8AAAC+hyCzBVEDiIwePdr4t7k/1Fq6zBnSSp6c2eTYqXPi6PTGV5A5oFrEy/63XsZOWyDuXy6BVEGyZbPG+/v4y1atkzHTFshHDw/9d7y49rJ85nh/6zerWr99f54k9x56B2IVVU5h1IDu8lPjut/dln2Hj8uIyXPkf4umyoSZi+Xy9VvG++rXrCyzxg2VGDG+1v/7c9M2+XnSbHn77mt5BpUJPHv8UF8lJvzbD4bnWrd8lkyZu1xOnrtoXL5h7aoyd+JwXff6jw1b5I8N3gPdTJv/i3GZzm2aBhpkVkHyrm2bS1DsOvCfng/q0cEYYFb6dmkrK9ZskF37/xMJYpA5LKgg64XL1yVLxvSyZMYYP3WhVdB/1cKpUrZ2S1m1/h8Z2KNDoD8kxIoZUxrUrqKDzI+fvdBtN27fkzY9Bsud+498leFQx8n4ob19rb9j32FJkyqFzgj36c3b91KrRWcdZDZQgeiFU0fp/Rg1SlTpMWSctGvewM9jfvzoocuT5MyaSZdS2bhtt87OVhasWG1crnmDWsYg89mLV6Xn0PFy8869r9sWK6YM7N4+yK81AACWZufOndKpUye5d+/r+1vSpEll7ty50qhRI/15CAAAAEFjnuu+4K8BAwbIixcv9KQuiUuZMmhlAiIrlcl778EjiR49miRNnOi7y6vgqqqzqwLM+XJll2oVyuhAcKf+I8Ttwwdfy+49dEyGT5ytA8z5c+fQy9rb2UnH/iP9LKsGZWveqZ8OMGfPklFqVionpYsV0sG8AaOnyv7/gp55MnT8THnw+KkeaE89RqyYMeTvLbtkwuzFxmUOHzstvYZN0AFmFXysXrGMpE+TSme0qrIMKsM7KFSt5Wu37kj5UkX186mA6vp/d8jGrbv1/QXy5tTZqopaRgUk1ZQvkABzcF27eVdfflq0YF5f7aovBfPk1Nv09t37ID3Wpeu3dP99TsdOnw9Wfw4dO6nnbZr+GODAg6p8R7WKZcTtg7ucPPs1QB8QFbRW4sWx1/MBo6boAHOGtKmlRqWy8kPJojqjfM3fW3ytp7KdVU3oquW9y2/4NGb6fLl6446ULVFYypUsIrFtbXVAevjEWfp+lUFerkQR+evfHTqb2qetew7Ka6c30qqJ948fuXNklWJf9r865gyvc+EvAWaVDd+4Q28dYM6SMZ3us3pOr89e+keYf3bsDcKeBQDAcjg6Okrr1q2latWqvgLMbdq0kStXrkjjxo0JMAMAAAQTmcwWxM7OTk+KKUetthaGIKK6lPHVayf5e/MuefbilTSrX9NPbVz/zFv+P+/5pJ91xq6iAs5dB46RLbv2+1pWlWlQFk0dJfVqVNK3VdC4+5Cx8s9230E1leXr+emTrJw7UQejDVRZijotu8j8X/6ny1UERRSJIgf/WaWzkg1Zr+oxfv1jg/Tv2k5na89a8pveB2MH9xSHnxobS3WooLjKSF24Yo1MHzPou8+lsmyPbP3DOGjiiTMXpG6rbrJ932H5sWZlafZjTb3NKou1f7d2vkonhBWnt291vWP/ArrJkib2XubNOx2E/Z5N2/boyaealX8IVk3qR0+e63meHFkCXS53tsz6uVRpFJ/eO7voY1RxcXXTWfYbt+3RX1R/KF3UeFyoMhbrf5ltrO/o6ekpf23e5euxVJbyK0cnf0tlfPjgLvs2rJR0aVIZA8GqjvTajdtkcA8HSZokkbRuWk/29zwhW3Yd0EFjg/+t/0f/KFO9Qln9d73qFVUtDF0yo2vbZlKhTHFfz6WON1WORpUB8fk46geeeq276/OqTtUKQdq/AACYk/r8tHbtWunZs6e8fPnS2J4+fXpZsmSJVK5c2az9AwAAsGYEmSOwEiVK+GnLnz+/LFy40Fjj7dy5c36WOXr0qJ6rD9srVqzwc7+qT1egQAE5efKk/pD+LQcHB2nXrp2uK122bFlfjxka3wYRVeCuS9tmMqRnx++uq7JCT527pGv/GgLMigpuqmCtzyCzYdki+fMYA8yKKlcxZlBPX0Fm9WVl/5ETOrtVBeIMAUaDjOnTyOnz3nWNg6Jnx5+MAWZD/eO2zerLzMW/yrmLV6Vk0QI6e1aVbTAEmBVVv3vkgG6y7p/tcuy039fUP306tzEGmBWVTZwqRTJ58tS7rIMpfP7sJdGi+l97PFq0LwHYT59CPPCfIRM7qDw8PfU8evTA/zVG/1L72sPDd9+ev3SU7oPH+mpTx6kqB5I9c0b9d7FCeXWg+frte5IjS0bj8zWpV93XeiozWZUeKV4ov5/n79KmmTHArKjbqozJ6KnzdQ3umpXL6QEI1bGkynoYgsMqGK1KgvTu2MpP/e7ArgBInjSxPtZ9Ht/qPMmUPq2u76x+jPBZzgUAAEvz6NEj/dl38+bNxjb1Y2/v3r1lzJgxxkQPAAAAhAxBZlgNQxBRBQJVkE6VqTh++rwOZn8vwKUCwCprWdVx/pYaGM1nPWfjshn9LquCbd8uqzJWb9976Ce46FNQg3BZMqTz25bRu+2V0xtj3/wbDFBlJquyGY+e+M6uDYgqqfAtVdLB3cO7XrUpxLGLLS9eOuoA5rd1D9+8fafncYM4eGJYDPyXJFFCPX/w6IkUzJszwOXU4Hd6+cS+B5VU9ZlVcFdRr3fqFMl1OROfg/LNHDtEJs5eIvVbd9dXLOTNlU3KlyomTX+socu3+AwyVyhdzN9gcOYvx4RPqo604ujkZPzhoUXD2jrTXg0EmDFdGln992a9n1V7UL149VoHlAM7vt++d/b1gwUAAJZCvYctWrRIBg8eLO/ffy3BlSdPHlm2bJkULRq0q83MpWHDhubuAgAAQJAQZI7Avpc9bMhoDkjHjh31FJAiRYoE+hwqgBYWGcwBBRHnLP1dJsxaLKOmzpOpowYGuq4KwKrg2qvXb/yt7awCxX6WdfQO1vmk6vD6t6wKVAdWliGoA8eoMiDfevmlHyoAaRsrln4sQ5vfZV9LbB+Byu+V5jA3VZf4yo3bcu3WXWNWr8GFKzd0QF+VfjCVIvlzy/L/rZe/Nu/0lcXuk6pxvG3PQX3bULfYIFmSRLqsRGDix4srk0f0l4nD++razGcvXpHl//tLFv36h2xfu1QSJYgvd+8/0j+k9OnU2t/H8O/YVK+9Yhf7648gLRvWkVmLf5X/rf9XhvTqqMtpVCpbQlKnTC5BpUrRqMcs42OgS0X9MKCo4zEmWcwAAAt07do1fYXd4cOHjW0xYsSQESNG6LFQ1G1L17VrV3N3AQAAIEgIMsNq9XT4SQ+qt/rvLdKuRUM/QUqfVFapyv49dPSU3L73QF/mb6CCioaAmWFZlT186NgpXV7AZ1mC39Zu9LWsyjLNmzObPHn2QkYN6C5JEntnwhqoZe89eBzk0gS//rFR13U2BKVVBrQh+1RlcqvHUdncqmTGhSvX9XMbbNq+R5drMGTShgWbL2UjVCA+PJQsWlC27D4gy35f56uO9Pa9h3RGtn/1iMNT1QplJFHC+LLrwBFZ9r/10qGF7+whVTu534jJej+r2sXqx4XgUOs/fvpcH1PqEl2VWa8mFfT9sXV3XbalVeN6sn3fIT2gZcWyfkveKL+v2ySN6lTV2cqGmtyr1v2jb6vjxGfmfdUfSsvaTdv0AJaqhrl/9bqjB/I6F8qXS9flVkFqn8Fp9ZzK/UdPdFkPAAAshbrKbcqUKboMxsePX6/QKl26tCxdulSyZ89u1v4BAABERASZYdVUjeQqjdvLmGnzZc3i6YEu26JBbRkxeY7Uat5Z2jSrrwNwJ89dlE1b90iMbwZabF6/ls6QrtG8k7Ru8qMkT5pIzly4In/9u9N7WR+ZyT06tJQOfYZLhfpt9CBqmb6U5Lj74JHs2v+f5MmZTRZPGx2k7Tl+9oLUa9VNalX5QZcFWffPDrl+664ONhpqNf/UqK4MmzBT6rfpIa2b1NMlMi5fv6Vr7ypqwLewYgiiTl+wQh48eioxY8bQwXqfwW3/7Nx3WN45u+jbajvevHtvrOebPEliKf0lK7ZBrcoydd4y+d9f/4qrm5uUKV5Y7j96LEt+X6fvb9+igYTXAJLfUlnTKsA/deQAad97uAyfMEsHfVXQXmUfq1rVG7buklt3H+ig6oShfYL93O7uH6VEjWZ6IMhCeXNJiuRJxPH1G/ljwxZfA37u2PefFCuYL8ABD1X2d83mneXHGpX0DxlqcMFzl67qOuLf1qVu1aSeDuQPGT9D0qZOoUtzBPQ6q0H8nN68FVvbWJIhbSo92GP39i2kiUNfqdKovdStXlH/AKMC4Crbeu+h45IyeRJZs2RGsPcFAADhQY0Z0r59e7l48aKxzd7eXiZPniydO3c2DrprLWrUqKHnBw96X0UFAABgqQgyw6rlzpFFD2qmBrw7cOSklCtZJMBl2zWvr7OTVZbqzEUrje1De3eSpV+CmgYdWjaUg8dOyd5Dx2TGwq+DH6psThWIUyUEDFRAeET/rrp0x9JVvh9HfZGpW93/sgv+Gdans4yfsVCOn7lgbEuTKoVMGdHf+HfbZj/K6fOX5O8tu2T+L6t9ra8GdKtYxv/s15AoViifDkAeO31eT4oaYO57QeYx0xfoYKzBY7cPxpq+5UsVNQaZVfB23uQR4tD3Z9mwdbeefG5L2RIBv55hNYCkgQrWqyBzjUrlZNG0UTJ4zHQ5evKcnnxSmcfqRwP/alp/jxowMG2qFPq4UpNPeqDJ6pXE6c07nak+sn+3AB9nUPcOMn3hChk5Za6vUh2zJwz1s2zZEoUlY7rUujTHsN6d/P1ynS9XNr1dKlCtJqV5g1o6yKxeA3X8DZswS1as+dvPumVK+C6jAQCAObi4uOgyGLNmzdJ1mA1q1qypS8SlSZPGKl+YDx/C52oyAACAsEaQ2cI+HLu6uhov8zNcCh/ZqSCnCiRnC6AcxuCeDvrLhCofYQgyqwCgWiexj8HIVEmA3+ZPlk3b98qRE2f03ypLVWWVPn3+0lcpAHXfqgVTdDDy6KlzOsNULasGcFODtiX+MkCcQde2zaVWlfKyeec+uXPvoa7xp4KWVcuX8lVu43uKF8wnO9f9ooPmqj5ztkwZdLBPDShnoIKEC6aM1NnWew4f05mnKsCogqP5cvm+/NO//aAyUVVb/Hh+s2QrlSshUaN+Pe5UMH3rmiWyduNWnZnt4eEp+b4TYFaq/FBa8uV65e99PgfB089ZtoQc/GeVrP9nuzx4/FQHnmtULCtFCuSRsDg+vl0uID5LndStVlFn/G7bc0guXr2uB1xMGD++FC+UV5fJMJSX+LZmeBz7wMtGxIwRQ45u+0P/IHLi7EV59uKlJE6YQIqpxy1dXJdFUceQKkWhjp1vGV5P1Qc1oOAfG7fpx1DlX9RxkjB+PD/rqMcsWaSAPHryXJrWr+Vvv9T/mo2/zZc/NmzV5WRUmRaf9aZ/alxXKpUrKf9s3yu37t7Xy6sfPyqVLS7ZMge+3wEACG+7d+/W44jcvXvX2JYkSRKZM2eONGnSJMhjYwAAACDkonj5LDALsxo1apSMHv21rELq1Knl4cOHgQ5mokSEunKG+q6WFFh//vKVJEuS2Ffb6GnzZeGKNTJj7GAd5A0rS377U5fy2L1+hc7ORuSlSq+oQf8ObPo9TB7v3XtnKV6tiZQoUkCWzxonEfmcReQQkd77TM3Z2dlYOgCICF6/fi39+vWTlSu/XqGmtGrVSmbMmCGJEplu8ODwUrRoUT0/ceKEubsCIIh4vwWsC+ds2CGT2YKoUa67dfO+RL569eoEb8ysXqvuUjh/bsmXO7t88vyky2fsOXhU4sW115m2QHhIlCC+VG4b+sEbVQ3x67fvytqN2+T1m7fS9Efvmo4AAFg7lSOzbt066dGjh7x48cLYni5dOlm8eLFUrVrVrP0DAACIjAgyWxA7Ozs9+RwADOajykmoshVq8lnuYPb4YbqkAxAeJvuovx0aajDB3/7cpG+rH0tUWRIAACzJR7d34vbmmXi4O4tNTHuxjZ9cYtgG/hnr8ePH0rVrV/nnH+8BjxVVDqNXr14yduzYCJepnyULV7gBAADrQJAZCMCm3xbIll375cLVG/L23XtdY7lejUp64LawFlidZCAkCuTNKa4fPkimdGmkQ8tG1KMEAFhMFvKLm0fk+sFf5MG5LeL12dN4X5So0SVt/pqSrWw7SZqlpK/3LjX+xpIlS2TQoEHy7t07Y3vu3Lll2bJlUqxYMYmIVGY2AACANaAms4UqUcI76/Do0aORoi4l9V0B68I5C3OJSO99pka9OZib44PzcuS37vLmydXvLhs/ZQ4p1Xq+JEyTV65fv64H9jt48KDxfjXI8vDhw3XQWd2OqDhvAevDeQtYF87ZsEMmMwAAAIBw9fTaAdm/6Cfx/OgapOVVIHr79FryNG51GTblV3F3dzfeV7JkSVm6dKnkzJlTIrrBgwfr+bx588zdFQAAgEARZAYAAAAQrhnMwQkwG3z66Cpxn66X5HE85b676HrLkyZNki5dukjUqFElMjhx4oS5uwAAABAkBJkBAAAAhFsN5v9+7RbsALNBLJso0rGCvfznXFIWLlwkadOmDfM+AgAAIPQiRwoAAAAAAJNTg/y9fepdSz2k0iSKLstnDiPADAAAYMEIMgMAAAAIF9cP/hImj3Pj0IoweRwAAACED8plwF8f3d6J25tn4uHuLDYx7cU2fnKJYRuXvQUAAIAgf558cG5LmOytB2c368fj8ygAAIBlIshsQVxcXMTV1btenYeHh0SLFs3kNfPUJY0q40R9IfD67Gm8L0rU6JI2f03JVradJM1SUqJEiWLSvgEAAMC6qIQFn58nQ0M9jtvb55EuyLxlS9gE6QEAAMIb5TIsyNSpUyVp0qR6On36tDx58sSko35vHl9Wds6qK/fPbPLzhUD9rdrV/Wq51w8viLW7dfeB/Lp2o7x46SjW7s9N22T3waPfXe7qjdt6m1+/eSvW6sHjp3obHj15Zu6uAACAQKgr4sKSx4f3kW5/29ra6gkAAMDSEWS2IAMGDJAXL17oqVChQpIyZUqTPO/Tawdk54za8ubJ1SAtr5bbMb2WXs+U3r57L/+dOCPr/tkuO/cdljv3H4bq8U6duySDxkyTuw8eSXi6fuuuDoq+dHQKt+cYO32hLF+17rvLHTp2Wm/zk6cvxFpdvnZTb8OVG7fN3RUAABAIVXItLNnEihPp9veaNWv0BAAAYOkol2FB7Ozs9KTY2NiYLIN5/6KfxPOjd5mOoFLLq/Wq9P1XEqXNJ+FdxmPGwpWycOUacXbx3c/c2bPIkN4dpWKZEmKpjp0+r4OiubNnliSJEpi7OwAAACahxvRQJdfComSGehzbeMkkslm6dKmeOzg4mLsrAAAAgSKTORJTwdv/fu0W7ACzgVrvyG/d9eOEp0W//iFT5y/XAeb8uXNIwzpVpUalspIlYzq5dO2m7D98IlyfHwAAAMGn6ifHSVcqTHZd2gK1Il09ZgAAAGtCJnMkpgb5e/v0WqgeQ5XOeHHrqCTLUlLCy9+bd+n5yrkTpVqFMr7uu3L9lr9lKD5+9JATZy7Iw6fPxD52bCleOH+wsoiDs76Hh6ecOn9JHjx6KgkTxJOCeXNKogTxjVnMx0+f17e37j4ol67d0rdVVnOhfLlD9HwPnzzTj2ljE13KFC8sCePHk9BS+3DbngMSN04cqVe9orH9xu17cunqDfH89ElyZM0keXJk9bOf1mzYIjmzZpIiBfLoOtfnLl3V258mVQpd3qRq+dKSLEkiOXLyrDx8/EzSpk4hJQrn93fwSMO+vP/widjaxpRiBfNJ8qSJQ719AADAtNRg1qNGjZItazbL4NqhL3OhBp8GAACA5SLIHIldP/hLmD1OeAaZ3T9+lDj2dn4CzErObJn9tO09dEz6jpgkz168MrbFjBFDhvbuJJ1aN/nu8wVn/T2HjsqAUVPlybOvNY5tbWPJz327SLvmDeTvzTvl7y3eQfL5v6w2LtO5TVNjkDk4zzdn6e8yee4y+fTpk/7bLratLJkxRkLj3oPH0qxTP/ng7i6rF0/Xba9eO0mPIeNk3+HjvpYtX6qoLJo2WuLF9f6y6Pbhgy4F4tCykWzavkeWrVqv21VguXrFsvo+FSxfsGKNroFtULZEYVm1YKrEiPG1LIwKyKvnfPj4qbHNJnp06d2ptfTr2jZU2wgAAExn3759urzD7dve4yc8dPSUNIlC/rUjfsockjSz5ZZGAwAAAEHmSOuj2zt5cG5LmDzWg7Ob9eOF1yWMKqv3t7Ub5fc/N0nzBrUkWrRoAS574cp1adNjiHz08JBC+XJJxnRp5N17Zzl49KSMnDJXMqRLLVV+KBUm65+5cEXadB8iHp6ekil9GsmdI6u4uX2Q0xcuy97Dx3WQuXihfDobWAVQVYmPxAm9s5MLfwkwB+f5duw9LBNmLdYZwCWLFJAUyZLI2YtXpNvAMboPIXHu0jVp2XWAzoZe/8tsSZUimQ5g/9R1oJy9eFVSJk+q+xXDxkZnGO/774T0HTFZls8a5+txtu4+IE+ev9T9ypA2teTOkcV438gp8+Td+/dSvWIZXWt8/38n5ODRU/LbnxulQ8tGehmVAd28U39xdXOTvLmySdZM6cXV1U0OHDmpS6WkS5NSGtauGqJtBAAApvHmzRs9kPWyZct8tT+IUUbS25yTTx5uwX7M6DFiS6nW8/29AgoAAACWg0zmSMrtzbMwGYRFUY/j9vZ5uAWZh/bqqMtiDBg9VUZNnSf5cmWXXNky6+BzxbLFJVbMmMZlp833zs5et3yWLiVh8ODxU6ne1EEPHhhYkDk466vgpwruDu7pID0dfpKoUb1LnLu6fZBjp87p2/VrVZH3Lq46yNytXXNfJTKC+3zqtqICvDUqldO3PT09pdewCfLX5p3B3q8qg7pDn58lT44s8uu8SRI/nvfrt33vYR1g/qlRHZn0cz9jUF8Fn7sNGiMbt+2R+4+eSLrUKY2P9fjZC/l9wRSpXO5rRvsfG7bqeayYMWT72j+MJURUQLl8vVay68ARY5B51pJfdVb0tyVRnr98JTWadZKFK9YQZAYAwIL9/fff0q1bN3n27JmxLU2aNLJw4UKpWbOmPL12INiDTasA8w+df5eEafJKZDVhwgRzdwEAACBICDJHUh7uzmH7eB/eS3hRwc/N/1skh4+f0YFRFXBWQdWlq9bper1Lpo+RogXz6gEIDx0/rbNx79x/pCef0qRMIecuXg3weYKz/ufPn+XoybM641aVc/Aptm0sqVCm+He3KzjPpwK8KnO6WMG8xgCzEj16dBnZv1uwg8zr/tkuy1ev1wHsBVNG+grUHzh6Us9VFvOq9f/6Wi/xlzrRqu6yzyBzqaIFfQWYferarrkxwKxkzpBWsmfJKE+evTS2HTxySr+Wz186yq9rN/reD6lS6BrUqmyKKiMCAAAsx9OnT6V79+46yGygso5VwFkFSOPE8S6xlSJ7OanS9189aLQa0yMoJTJUBnNkDjArxYt//zMlAACAJSDIHEnZxLQP28eLFfoBXb6ndLGCejIEaFXZhS4DRolD35/lyJY18tnLS5eruPvgka4FHBA1WJ3PWsAGzi6uQV5f1S/+4P5RsmXOEOLtCc7zqSxfVVIjY/o0fu5PmiSR2NvFDtZz/77uHz3v27mtrwCz8srxtZ6r2s8BeffO948UKnAcEBUs/5a9fWx57+xi/Pul42v9mga2H969d5EkiQgyAwBgCdT79vLly6V///7y9u1bY3uOHDl0uYySJf3++JwobT6pNeygHjT6+oHlunSbzyvrokSNLmkL1NKD/KkazJTIELl8+bLeN8WKFTPRKwsAABAyBJkjKdv4yfUH+bAomaEexzZesjDpV5CfM0oUKV+6mPxYs7KsWPO3nLt8TWf5qpIVqVMmkx9KFg1w3ahR/a/pZxsrZpDXV9nKqozE46fPQ7wNwXs+W72sz8EBDVxcXHXAOjjmT/5ZRkyeK4079Ja1y2ZKnhxZjffZxfYOWDerX1MPvOefLJnS+/pb1WwOSFBKKKoguRrEMLBSJqrsBgAAML9bt25Jx44d9QB/BmrchSFDhsjQoUMl5jc/YH/7GU4NGK0mNaaHKrmmrohTCQvq82R4lV+zVj169NDzEydOmLsrAAAAgSLIHEmpD/Bp89eU+2c2hfqxVMZJeH4hOHPhsuTNmU2Xhvg2w1eVbTDUQVb3F8iTQ+4+eCy9OrbSZSh8UvWLb9594OdxDIK7fr5c2XQJC1Vb+NtSEbfvPZBM6b2ze21svJd3dnEL1fNlz5xBDh87LVdv3JYcWTMZl1v46x8SXCq7eOOv86RB257SqF0v+WPpTMmfO7u+r0iB3Lqchqp93abpj37WVc+vyoSEpcL5c8uJMxekc5umevBDn1Rpkms370gce7swfU4AABA86rPJjBkzZOTIkfLhwwdju8qyVdnLuXP7Hnvie9TnR4LKAAAAEQNB5khMXYoYFkFm9TjhqefQ8fLm3Xv5oVRRSZsqpSSMH1fX7t2+95DcvHNfZ8EWye/9pUYFa1t1GyQV67eRGpXLGQO99x48kj2HjkmRAnlk8bTRAT5XcNbv1q6FtO89TFp3Hyw1K5fTgXC3D+5y+NgpiRs3jqxaMEUvl/pL8HjSnCVy/dZdiRkzhuTOnlkPAhic52vVpJ4MHjtdarfsIi0a1JZkSRPJqXOXZPeBoyHK8lVB7Q2/zpOG7XrqjOY1i6fpPjWsXU3mLF0lQ8bNkO17Duk+xI1jJ0+ev9QDAqpBDe+d2WMcEDAsqIETVcC7auMOUr1iWcmSMZ1Ejx5N7j14LPv+Oy6Z0qWRNUtmhNnzAQCA4Dl79qy0b99ezw1ix46t6y6rmsxh+bkAAAAA1ocgcySWNEtJPahKUAZfCYhaX9XMC08q8PnX5h2y/p8dfp8/bhyZM3G4HhxQUeUWJo/oLyMnz5HVf232tawq/ZAjS8ZAnys466vA8rDenWTS3GXy7459ejJQGbkGxQrlk3RpUuoArZoM96vtCs7ztWpcV46cPCv/bN8ri39ba2wfO7inDgqHRIpkSWTDynnSoF0vaeLQV1YvmqYHUVyzeLq07TlE9h85oSefcmbNJNHD+ItkicL5Zc6EYTJw9DT5c9M2X/epL621q5QP0+cDAABB4+bmJqNHj5Zp06bpgYgNqlSpIosXL5b06cP26iYAAABYJ4LMFsTFxUVcXb1r63p4eIR7RoiqiadG7d4xvZZ4fgxeTV8leozYev3wHpRl9vihMnJAN9l/+LguLeHo9Ebi2MeWHFkyScWyJfyUUWjdpJ5Ur1BGtu09JHfuPdSD/KVPk0oqlSshyZIk9jVYnQrc+mwLzvpKD4efpE61CrJ1z0FdnzlJooR6cEIVQDaIGSOGbPtjqfy9eafuv3ptC/u4P6jPp2oyL5k+RhrVqSb/nTijg9CqTIcKCqtazSmSJ/3uvlQBYrXNCRPE8zVw4N8r58rMRSt1H3LnyKozifdv/E32HDwmZy5eFlfXDzrzuWDenPr5DGLEiKEfr0jBPH6ey7B/kyf1vc+Uqj+UlrfvfQ8e2LB2VV1ne9vug3Lz7n0dyFbB+Qqli0vqlMmNy6VNlUI/bhofbQAAIOwdOHBAHBwc5ObNm8a2hAkTyqxZs6Rly5YMzAcAAACjKF5qaGhYhFGjRulMEYPUqVPLw4cPA1z+2rVrep49u3ct3ZB6eu2A7F/0U7ACzSrA/EPn3yVF9nISFgyZMVxqCVgHzlmYS1i990VGzs7eP+7Z29ubuyuwcG/evJFBgwbJkiVLfLU3bdpUZs+eLUmTfv+HbYQNVQNb6du3L7sUsBK83wLWhXM27BBkttBM5urVq+uA6/Hjx03yRdvxwXk58lv3IJXOUCUyVAZzwjRfM1pDi4AVYF04Z2EuBJlDjg/QCIqNGzdK165d5enTp74SHxYuXCi1atViJ5oY5y1gfThvAevCORt2KJdhQezs7PSk2NjYmPS5E6XNJ7WGHZQXt47K9QPL5cG5LeL12dN4f5So0SVtgVp6kD9Vgzm8S2QAAADAdJ49eyY9evSQ9evX+2pXAeeJEydK3Lje418AAAAA/iHIDCMVOE6WpaSePrq9E7e3z8Xjw3uxiRVHbOMlkxi2fLkAAACISFTlvBUrVki/fv10mQyDbNmyybJly6R06dJm7V9kpwZYVI4cOWLurgAAAASKIDP8pQLKBJUBAAAirtu3b0vHjh1l7969xrbo0aPL4MGDZdiwYRIrViyz9g8inp5frywEAACwZASZAQAAgEgWuJw1a5aMGDFC3NzcjO1FihTR2ct584bduBsAAACIHAgyAwAAAJHEuXPnpEOHDnL69GljW+zYsWXcuHHSs2dPPfA0AAAAEFxRg70GLEbUqFF1Hb3Pnz+buysAAIQ79X6n3vfU+x+A4Pnw4YMMHTpUChcu7CvAXLlyZbl06ZL06dOHADMAAABCjExmK6Zq5n369Enc3d3F1tbW3N0BACBcqfc7w/sfgKA7ePCgODg4yI0bN4xtCRIkkJkzZ0qrVq304M+wTDlz5jR3FwAAAIKEb2lWLE6cOPoL9/PnzyV16tR86QYAROgasur9zvD+B+D73r59K4MGDZLFixf7am/cuLHMmTNHkiVLxm60cPPmzTN3FwAAAIKEILMVS5Qokbx580YP2HLz5k2rzkJRlz8r1rwNQGTCOQtzHXMqi1m9/wEI3D///CNdu3aVx48fG9tSpkwpCxculDp16rD7AAAAEKYoamjFVE3KtGnTSty4ca2+PqWqs0ltacB6cM7C1NT7nHq/U+971v6eB4QnlfHfpEkTqVu3rq8Ac+fOneXKlSsEmK1M//799QQAAGDpyGS2cjFjxpRUqVKJtXN2dtZze3t7c3cFQBBwzgKA5WX7//rrr9K3b19xcnIytmfNmlWWLl0qZcuWNWv/EDJnzpxh1wEAAKtAKhAAAABgxe7cuSNVqlSRtm3bGgPMqrTM0KFD5fz58wSYAQAAEO7IZAYAAACs0KdPn2T27Nny888/i6urq7G9UKFCsnz5csmXL59Z+wcAAIDIgyAzAAAAYGUuXLggHTp0kJMnTxrbbG1tZezYsdKrVy+dyQwAAACYCp8+AQAAACvx4cMHGTdunEyePFk8PT2N7RUrVpTFixdLpkyZzNo/AAAARE4EmQEAAAArcOjQIXFwcJDr168b2+LHjy8zZsyQNm3aSJQoUczaP4S9HTt2sFsBAIBVIMhsQVxcXIz19Dw8PCRatGjm7hIAAADM7N27dzJ48GBZuHChr/ZGjRrJnDlzJHny5GbrG8KXjY0NuxgAAFiFqObuAL6aOnWqJE2aVE+nT5+WJ0+esHsAAAAisX///Vdy5szpK8CcMmVK2bhxo/z5558EmCO43377TU8AAACWLoqXl5eXuTsBv5nM1atX15nMx48fjxS7x9nZWc/t7e3N3RUAQcA5C1gfzlvr8uLFC+nZs6esXbvWV3vHjh11PWZVJgMRX9GiRfX8xIkT5u4KgCDi/RawLpyzYYdyGRbEzs5OTwqXxgEAAEQ+Kv/j999/lz59+sjr16+N7VmyZJGlS5dKuXLlzNo/AAAAwD+UywAAAAAswL1796RatWrSunVrY4BZXdmm6jGfP3+eADMAAAAsFpnMAAAAgBl9+vRJ5s6dK8OGDTOWTlMKFiwoy5YtkwIFCvD6AAAAwKIRZAYAAADM5OLFi9KhQwdfNXdjxYolY8aM0SUzokfn4zoAAAAsH59aAQAAABNzd3eX8ePHy8SJE8XT09PYXr58eVmyZIlkzpyZ1wQydepU9gIAALAKJg8yu3/8KGcuXJH7D5/Iq9dO4uHhIYkSxpfkSRJLofy5JVECRsoGAABAxPXff//p7OVr164Z2+LFiyfTp0+Xdu3aSZQoUczaP1iOQoUKmbsLAAAAlhNk/uDuLlt2HZA1f2+Rk2cv6kCzf9QH6qyZ0ku96hWleYNakixJYlN0DwAAAAh379+/lyFDhsiCBQvEy8vL2N6gQQNdkzlFihS8CvBFDfiolCpVij0DAAAsWhQvn59wwyG4vPT3dbLgl9Xi9PadbkuYIL7kz51dUiZLIvHjxRWb6NH1fY5Ob+TilRty7+FjvVz06NGkXvVKMring6ROmVwimxIlSuj50aNHJTJwdnbWc3t7e3N3BUAQcM4C1ofz1ry2bNkinTt3lkePHhnbVFB5/vz58uOPP5q1b7BcRYsW1XOfNbsBWDbebwHrwjlrBZnMl67elNbdB8njZy90dnLnNk2lTtUKkiFd6kDXc3rzTnYd+E/+2rxTNmzdLZt37pORA7pL22b1w6urAAAAQLh4+fKl9OrVS9asWeOrXZXLUPV248enVBwAAACsX7gFmW/dvS+pUiSTGWOHSLmSRYK8XoL4caVx3ep6uv/oicxa/KucPn+ZIDMAAACshrpYcNWqVdKnTx9xdHQ0tmfKlEmWLl2qB/gDAAAAIopwCzJXrVBG6tWoFKrHSJc6pcwcO0TcPriHWb8AAACA8HT//n1dGmP79u3GtmjRokm/fv1k1KhRYmtrywsAAACACCXcgsy2sWJa5GMBAAAA4eHTp0+6xvLQoUPFxcXF2J4/f35Zvny5FCxYkB0PAACACCncgswh/WCusjwAAAAAa3L58mVdZ/nYsWPGtlixYunM5b59+4qNjY1Z+wfr1LJlS3N3AQAAwDKDzJev3ZRjpy9I7uyZpVihfLrt+ctX0nXgGDl2+rykSpFU5k4YbrwPAAAAsFTu7u4yceJEmTBhgnh4eBjbf/jhB1myZIlkyZLFrP2DdWvXrp25uwAAABAkUcXEhk+aLcMmzBQvH22DxkyX/06ckRgxbOTBo6fSrvcw+eBOHWYAAABYrqNHj+oSGKNHjzYGmOPFi6eDy3v27CHADAAAgEjDpEHmJ89eyNGT5yR1yuRS/Eum8us3b2XXgSMybdRAuX5km+TNmVUcX7+RbbsPmrJrAAAAQJC8f/9eevbsKaVKlZIrV64Y23/88Uf9t4ODg0SNavJcDkRAFSpU0BMAAIClM+mn37sPHul5pvRpjG0nz1yUqFGiSP1aVXQmc93qlXT75eu3TNk1AAAA4Lu2bdsmuXPnlrlz54qXl/e1ecmTJ5f169fL33//LSlTpmQvAgAAINIxaZD5vbP3KNu2sWIZ2y5duylZM6WX2LbebUkSJdDzl45OpuwaAAAAEKCXL1/qQdhq1KghDx48MLa3b99eZy83aNCAvQcAAIBIy6QD/yVNnMhXRrNy/Mx5yZMzq/FvR6c3eh4/XhxTdg0AAADwQ2Urr169Wnr37i2vXr0ytmfMmFGWLl1KKQMAAADA1JnM2TJnkLhx7OX6rbuy9Pc/ZePW3fLfibPyQ6lixmXuPXjsp6QGAAAAYGoqY7lmzZo6g9kQYFa1lvv37y8XL14kwAwAAACYI5PZLratOPzUSKYvWCE/T5qj27JkTC81K5XTtz9//qwHAVQf3qv8UNqUXQMAAACMn0kXLFggQ4YMEWdnZ+NeyZcvnyxfvlwKFSrEnoJJ5M2blz0NAACsgkmDzEr/ru0kXeqUOoM5ZfKkOuhsY+PdjTv3H+kM5moVykjypIlN3TUAAABEcqq+cocOHeTo0aPGtpgxY8rIkSN1BrONjY1Z+4fIZdasWebuAgAAQJBE8TIMix0OnF1cxTZWTIkWLVp4PUWEVaJECT33+QUnIjNkCdnb25u7KwCCgHMWsD6ct4H7+PGjTJo0ScaPH69vG5QtW1bXXs6a9esYIoCpcN4C1ofzFrAunLNWUpN594EjkqdsHek1bIJs33tI3D64h+fTAQAAAMF27NgxKViwoM5WNgSY48aNK4sWLZJ9+/YRYIbZqAEn1QQAABCpy2WkT5taUiRLIms3btWTrW0s+aFkEalWoaxU+aGUJIgfNzyf3uq4uLiIq6urvu3h4UEGOAAAQDhnrgwfPlzmzJkjPi/uq1u3rsyfP19SpUrF/odZXbhwgVcAAABYhXANMufPnV32/L1SHjx+Ktt2H5Rtew/Jzv1HZNueQxI9ejQpVjCfVK9YRtdgTp0yuUR2U6dOldGjRxv/Tp06tVn7AwAAEFHt2LFDOnXqJPfv3ze2JU2aVObNmycNGzaUKFGimLV/AAAAgDUJ15rM/nF0eiM79/8n2/cckoNHTxpLaOTNmVVnOKugc46smSSyZzJXr15dZzIfP35cIgNq4ADWhXMWsD6ct95evXolffv2ld9//93X/mnbtq1MmzZNEiZMaJbXB/BP0aJF9fzEiRPsIMBK8H4LWBfOWSsOMvvk6vZB9h0+Ltv2HpQ9B46K09t3uj19mlRSrWIZqV6hjBQpkEeiRg3X0tEWiYH/AFgy3ogB6xPZz1v1kfePP/6QXr16ycuXL43tGTJkkCVLlkilSpXM2j/APwSZAesT2d9vAWvDOWsl5TK+J7ZtLKlZuZyePD095eipc7qUxo69h2TRyj/01KhONZk7cbg5uwkAAAAr9vDhQ+nSpYts2bLF2KaSGNSAamPGjBE7Ozuz9g8AAACwdmYNMvsUPXp0KVO8sJ4mDOsj5y9f03Wco0aLZu6uAQAAwAp9/vxZFi5cKIMHDzZmqSh58+aVZcuWSZEiRczaP+B79u7dy04CAABWwaRB5o8fPcTDw0Ps7GJ/d9l8ubLrCQAAAAiua9euSYcOHeS///4ztsWIEUNGjBghAwcOFBsbG3YqAAAAYE1B5n937JOZi1bKlRu39d9JEyeSJvWqy4Bu7SVGDD7gAwAAIGx8/PhRpkyZImPHjtW3DUqXLi1Lly6V7NlJYoD1+OWXX/S8Z8+e5u4KAACAeYPM6//dId0Hj/XV9uKVo8xdtkruPngky2aOC+8uAAAAIBI4ceKEzl6+ePGisS1OnDgyefJk6dSpU6QcTBrWbdWqVXpOkBkAAFi6cP2k/enTJxk/c5G+XbJIAdn023zZt+FX6dq2uW7bvHO/nLlwOTy7AAAAgAjOxcVF+vbtKyVKlPAVYK5du7ZcuXJFD/pHgBkAAACw0kzmazfvyNPnLyVuHHtZOXeinisj+neVW3fvy879/8m+wyekYN5c4dkNAAAARFA7d+7UWcr37t0ztiVJkkTmzp0rjRs3lihRopi1fwAAAEBkEK6ZzI+ePNfzfLmyGQPMBmVLeo/m/ejps/DsAgAAACIgR0dHadOmjVStWtVXgLl169Zy9epVadKkCQFmAAAAICJkMru5u+t5wgTx/dyX+Eubm9uH8OwCAAAAIhAvLy/5888/dY3aFy9eGNvTp08vixcvlipVqpi1fwAAAEBkFL4D/3l5fX+RcO0AAAAAIopHjx5J165d5d9//zW2qXIYvXv3lrFjx4qdnZ1Z+weEtZkzZ7JTAQCAVQjfIPMXrxyd5L8TZ3y1Xb99L8D7lMQJE0i2zBlM0T0AAABYsM+fP+ss5UGDBsn79++N7blz55Zly5ZJsWLFzNo/ILzky5ePnQsAAKyCSYLMKojsXyA5sPvqVq8oi6eNNkHvAAAAYKmuX78uDg4OcujQIWNbjBgxZPjw4TrorG4DEdXp06f1vFy5cubuCgAAgPmCzPHixpFc2TKHaN00KZOHeX8AAABgHTw8PGTq1KkyZswYcf8yzodSqlQpWbp0qeTIkcOs/QNMYcCAAXp+4sQJdjgAAIi8QebypYvpCQAAAAiqU6dOSfv27eXChQvGNnt7e5k0aZJ06dJFokaNys4EAAAALAif0AEAAGARXFxcpH///rrGss8Ac82aNeXKlSvSrVs3AswAAABAZK3JDAAAAARm9+7d0rFjR7l7966xLXHixDJnzhxp2rSpRIkShR0IAAAAWCiTB5lfvnotJ89dlGcvXomn5ydJmCCe5MmRVbJlzmDqrgAAAMDMXr9+rbOXV6xY4av9p59+khkzZuhAMwAAAADLZrIg85Xrt2T8rMWy5+BRf+/PnCGt9O/aTurVqGSqLgEAAMBMvLy8ZP369dKjRw95/vy5sT1dunSyaNEiqVatGq8NIr02bdpE+n0AAACsg0mCzJt37pfug8fIB/eP+u8UyZJI+rSpJIaNjTx9/lJu3X2gp84DRsmx0+dl0s/9TNEtAAAAmMHjx491feVNmzYZ21Q5jJ49e8q4ceP0IH8ARFq1asVuAAAAViHcg8yXr900BphLFMkvI/t3l/y5s/ta5sVLR5mz7HdZ/r+/ZOUfGyRt6hTStW3z8O4aAAAATOjz58+ydOlSGThwoLx7987YnitXLlm2bJkUL16c1wPwwcPDg/0BAACsQtTwfgJVIkMFmCuXKynrl8/2E2BWkiZJJOOG9JYJw/rov2csXClOb75+8QAAAIB1u3HjhpQvX146d+5sDDDb2NjIqFGj5MyZMwSYAX9UrVpVTwAAAJE6yPzm7Ts5cOSkRI8eTaaMHCDRokULdPm2zepLwbw5xdnFVXYfPBKeXQMAAICJMjEnTpwoefPmlYMHDxrbS5QoIefOnZORI0dKjBgxeC0AAAAAKxauQebL12/Jp0+fJH/uHLoOc1BUr1BGzy9euRGeXQMAAEA4O336tBQtWlSGDh0q7u7uus3Ozk7mzJkjhw4dkpw5c/IaAAAAABFAOGcyv9fzZIkTBXmdZEkT67nTW8plAAAAWCNXV1ddd1kFmFW2skH16tXlypUr0qNHj+9e4QYAAADAeoTrwH92sW31/O175yCv8/add2Da3i52uPULAAAA4WPv3r3SsWNHuX37trEtUaJEMnv2bGnevLlEiRKFXQ8AAABEMOEaZM6cIa2en7lwRVxcXMUuCIHjQ8dO63mmL+sCAADA8jk5OcmAAQNk+fLlvtpbtGghM2fOlCRJglY6DcBXBQsWZHcAAACrEK7lMlKnTC65smUWVzc3mbrgl+8u/9+JM7LrwBGJGjWqVC5bIjy7BgAAgDDy119/6frKPgPMadKkka1bt8qqVasIMAMhNG3aND0BAABE6iCz0r9bOz1ftPIPGT1tvri4uvlZxsvLSzZu3S1tew7VtxvVqSbp0qQK764BAAAgFJ48eSL169eXhg0byrNnz3SbKoehai5fvnxZ12AGAAAAEPFF8VJR3XA2ZtoCWbBitb4dL669lCleWDKkTS3Ro0eXFy8ddQbzvYeP9f15c2aVDSvnBam0RkRWooR3JvfRo0clMnB29q7bbW9vb+6uAAgCzlkgcp+3nz9/1lnLqjzG27dvje05cuTQ7YbPMQBCp02bNnq+cuVKdiVgJficDFgXzlkrqclsMKJ/V8mUPo1MmL1YHF+/kc079/vtSPRo0rReDRk9qKdxwEAAAABYlps3b+qB/fbv//p5zsbGRoYOHSpDhgyRmDFjmrV/QERy5coVc3cBAADAcoLMSouGtaV+rSqy+8AROXn2ojx/5SieHp6SIH5cyZ0jq1QuV1JSpUhmqu4AAAAgGDw8PGTGjBkyatQo+fDhg7G9WLFismzZMsmdOzf7EwAAAIikTBZkVmxjxZTaVcvrKSDXb92VrbsPSLbMGaRGpXKm7B4AAAD8cebMGenQoYOcPXvW2GZnZycTJkyQbt26SbRo0dhvAAAAQCQW7gP/BdfVG7dl8txlsmn7XrE2Hz9+NHcXAAAAwoybm5sMGjRIihYt6ivAXLVqVbl06ZL07NmTADMAAAAAywsyW5sTJ05I06ZNJVGiRBI3blzJkCGDTJ8+XQ+IAwAAYK1UzeW8efPKlClT5NOnT7pNfd75/fffZdu2bZI+fXpzdxGI8NRA6WoCAACwdHxiCaVWrVrpGoTqMtI0adLI1q1bpVGjRuLk5CTjxo0Lm1cJAADARN68eSMDBgzQdZZ9atasmcyaNUuSJk3KawGYyM6dO9nXAADAKpDJHErdu3eX9evXS7p06SRq1KhSq1YtadGihaxcuTJsXiEAAAAT2bBhg+TMmdNXgFn9iL5582ZZvXo1AWYAAAAA/iLIHAZBZj87NWpUiRIlSmgfGgAAwCSePn0qDRo0kPr16+vbivosowb1u3z5stSsWZNXAjCDJUuW6AkAAMDSRfhyGao2svpy5OLiorNvMmbMGKT13r17J/fu3ZNYsWLpdYJaC+3Zs2fy559/Sp06dULZcwAAgPDl5eUlv/zyi/Tv31+XyTDInj27zmYuVaoULwFgRn/88Yee9+3bl9cBAABE3kxm9cXF09MzWFNYDJjn7u4uy5cvlyZNmkiSJEn0oDUlSpSQCRMmfHfdFy9e6JqDiRMnlnz58km2bNkkWbJket3v9e3jx4/6OVVAOijPBQAAYC63bt2SihUrSocOHYwBZvUZ5ueff5Zz584RYAYAAABgGZnMm7btkc4DRompqcs81RcmQ+kKNRK6o6Pjd9d7//69VKhQQWc+q/XUgH6q7f79+zJs2DB58uSJzJs3z9911ajrqhazGgBw165dkjp16jDfLgAAgNBSP+rPnDlTRowYIR8+fDC2Fy1aVGcv58mTh50MAAAAIFgiZE1mVeKiXbt2+vIylZk8ePDgIK03efJkHWBOnz69XLlyRS5evKhLZqjHUUHn+fPny7Fjx/zN2HZwcJAtW7bIP//8I8WLFw+HrQIAAAidCxcuSLFixWTgwIHGAHPs2LF10PnIkSMEmAEAAABYXiZzrSo/yO1yO0O0bnSbkHctefLkulxGcKhSGIaR1BcsWKDLZBioEhj79u2TxYsXy9KlS/0EkXv16qVHXFcB5vLly4e43wAAAOHBzc1NRo4cKbNnz9ZXXxlUrlxZf77JkCEDOx4AAACAZQaZVV2/oA6YZ24qc/n58+eSMGFCqVq1qp/7mzdvrr+E7d2711e7qluoMpxXrlypLzP1OWhO/Pjxv/u8qla0fy5duiQ5cuQQZ2dniQxcXV3N3QUAwcA5C1iPw4cPS/fu3eX27dvGtgQJEsikSZP0OBRRokSJNJ83AGszZcoUPeccBawHn5MB6xIZz1l7e/tweVzriACbwNWrV/Vc1SFUpTG+lT9/fj1X9ZlVNpCtra3+W2Uwx4kTR3r06KEnn1TQOmbMmCbpPwAAgE9v377VP4avWLHCV3uDBg104Cpp0qTsMMDC5cyZ09xdAAAAMH+Q+fCx0zJ90QopXbSQ9Ova1tj+wd1d3r1zllixYkrcOOETPQ+u169f63lAX7jixo2rA8bu7u46W9kQZPaZFRQSR48eDTTDObx+XbBUkW17AWvHOQtYpk2bNknXrl31oMUGKVOm1LWXGzdubNa+AQg6w3gwlSpVYrcBVobPyYB14Zy18IH/Xr12kqMnz8mNO/d8tW/fc0jy/lBXBoyeKpbCw8NDzwMr72FjY6PnHz9+NFm/AAAAgurZs2fSqFEjqVevnq8Ac5cuXeTkyZNSo0YNdiZgRYYOHaonAAAAS0e5jC/UyOqKi4tLgAMDqjIZip2dnaleHwAAgO/y8vLS40P069dPnJycjO1qIGM1sHHp0qWp6QoAAADAOjOZrUmaNGn0/N4931nXBg8fPtSjsatgtBocEAAAwBLcuXNHKleuLO3atTMGmNWVWcOGDZNz587pADMAAAAAhCeCzF/ky5dPj65++fJlcXR09LOj9u/fr+d58+b1d2BAAAAAU/L09JTp06dL7ty5Zc+ePcb2IkWKyOnTp2XcuHESK1YsXhQAAAAA4Y5o6RdqwL+SJUvqbOWpU33XilY1mGfMmKFvqxqH4UWV6nj58qWeVI1oVaIDAADgW+fPn9eDBPfv399YzksNSqyCzmpQYfWjOAAAAABEqJrMqk6gyrYxMARPv233SWULhyZj+MKFC+Lq6qpvP3jwQM9V8NYwQrPKWi5WrJivdX7++WepVq2aTJkyRQd8VUD5/fv3eiR29XhJkiSRzp07S3hRwe3Ro0cb/06dOnW4PRcAALA+Hz58kLFjx+rPKj4/Q1WqVEkWL14sGTNmNGv/AIQtBwcHdikAALAKUbxUpDecbNy6WzoPGBWidetWryiLp30NuAaXunRUlb4ISLRo0fwNcI8fP14Hm7/dLfHixZPNmzeHa11DFdg2BMarV6+u+3j8+HGJDJydnfXc3t7e3F0BEAScs4DpHTx4UAecbty4YWxLkCCBvtqqdevW+gf0wHDeAtaH8xawPpy3gHXhnLWyTGZz1VgOLGCpBsTxjxokp0KFCnqEdvUlLmbMmLq2ocpgTpUqVTj2WMTOzk5Pio2NTbg+FwAAsA7v3r2TQYMGyaJFi3y1N2rUSObMmSPJkyc3W98AhC9DORwSMQAAQKTOZFaZwu7uH0O0bnSb6BIzRgyJrFSdRUXVVYwM+OUIsC6cs4Bp/Pvvv9KlSxd5/PixsS1lypSyYMECqVu3brAei/MWsD5FixbV8xMnTpi7KwCCiPdbwLpwzlpJJrPKFg4oYxgAAAD+e/78ufTs2VP+/PNPX+2dOnWSyZMn6zJeAAAAAGApiAADAABYCHWB2W+//SZ9+vQRJycnY3vWrFll6dKlUrZsWbP2DwAAAADMEmQ2lMzwWf7i9r0HsufgMX+XT5o4odSrUSm8uwUAAGBR7t69qzOVd+3aZWxTgwAPHDhQRowYIbFixTJr/wAAAADAbEHm6QtXysxFK2Vg9w7St0sb3Xbxyg0ZMXlOgOvEiWMnFct41ySOTFxcXMTV1VXf9vDw0F8sAQBAxPbp0yc9gN/w4cONnwOUQoUKyfLly/VgxgAAAAAQqYPMu/b/p+fVKpT2c1+6NCmlVNGCxr8/enjI+n92yISZiyNlkHnq1KkyevRo49+pU6c2a38AAED4unDhgnTo0EFOnjxpbLO1tZUxY8ZI7969GdsCiOQMA/8BAABE6iCzo9MbuXTtpiROlEByZsvs5/78uXPIjDGDfbXduHVXLly5IWcvXpUCeXJIZDJgwADp1q2bvl29enUymQEAiKA+fPgg48ePl0mTJunSYgYVKlSQJUuWSKZMmczaPwCWQf2PAAAAsAZRw/PBnz57qecpkyUJ8jqGDOb/TpyRyMbOzk6SJEmiJxsbG4kaNVxfHgAAYAaHDx+WAgUKyLhx44wB5vjx4+vSGLt37ybADAAAAMDqhGsU89Vr71HREydKGOR1kiVNrOcPHj8Nt34BAACY2rt37/QVS2XKlJFr164Z2xs0aCBXrlyRdu3aSZQoUXhhABipwUDVBAAAEKnLZbi4uul5rJgxfLXXq1FJT/6x/TJyuqub97oAAADWbvPmzdKlSxd59OiRsS1FihQyf/58+fHHH83aNwCW6+bNm+buAgAAgPkzmePFsdfzl6+8M5qD4qXjaz1PEDduuPULAADAFF68eCHNmjWT2rVr+wowOzg46OxlAswAAAAAIoJwzWTOkimdnl+6dkNc3T5IbFvvLOXAnDx70de6AAAA1sbLy0tWrVolvXv3ltevvX9AVzJnzixLly6VH374waz9AwAAAACryWROliSxZM+SUdw+uMuqdf98d/lbdx/I7oNHdT3CssWLhGfXAAAAwsW9e/ekevXq0qpVK2OAOVq0aDJo0CC5cOECAWYAAAAAEU64BpmVTq2b6PmEWYtk14EjAS738MkzaddrqHz69ElqVCwr6dOmksjGxcVFXr58qScPDw/5/PmzubsEAACCSH2GmT17tuTOnVt27NhhbC9YsKCcPHlSJk2aJLa2tuxPAEEWK1YsPQEAAFi6KF7qes5wpB6+dffBsnP/f/rvH0oWlco/lJJ0aVJK9GjRdA3mo6fOyYYtu3TGc7IkiWTXul8kaZJEEtmMGjVKRo8ebfw7derU8vDhQ4kMnJ2d9dze3ruONwDLxjkL+Hbp0iXp0KGDHD9+3NimAkPqfb1v374SPXq4VigLEs5bwPpw3gLWh/MWsC6cs1YUZFY+uLvL4LHT5Y8NWwNdLnf2LLJ81jhJlybyZTEbMpldXV31bXWZrbq01ueX1YiMkxqwLpyzgDd3d3eZMGGCTJw4UV+FZKBqLqvay6oGs6XgvAWsD+ctYH04bwHrwjkbdkySVhMrZkyZNW6otG/RUP7cuE1OnL0oL145ioenpySMH0/y5Mgq1SqUkZqVy0nUqOFewcNi2dnZ6UmxsbExd3cAAEAgjhw5orOXr169amyLFy+eTJs2Tdq3b6/HmACA0FiwYIGeDxw4kB0JAAAsmkmv3VTBZDUBAABYq/fv38vQoUNl/vz5uiyYwY8//ijz5s2TlClTmrV/ACKO9evX6zlBZgAAYOnMXyAQAADASmzdulU6d+7sa8yE5MmT64Bz/fr1zdo3AAAAADCXcKtN8eTZC3F28a4vHBoqQ+jmnfth0icAAICQePnypbRo0UJq1qzpK8CsymVcuXKFADMAAACASC3cgswnzlyQIpUbypylv8ubt++Cvb6np6ds3rlfKtZvI9MW/BIufQQAAPjej92rVq2SHDlyyOrVq43tmTJlkj179ujB/RIkSMBOBAAAABCphVu5jCIF8kih/LllwqzFMn3BCqlUtoTUrlpet6VJmdzfdd6+ey/nLl2Tnfv/k03b98grRyfJmC61NK9fK7y6CQAA4K/79+9Lly5dZNu2bca2aNGiSb9+/WTkyJESO3Zs9hwAAAAAhGeQOVWKZLJqwRQ5fOy0TF+0QrbsPqAnJXGiBJIyWRKJHy+uRI8eXWc6v3rtJA8fPzMOoJM+TSrp27mN/NSortjYUDoaAACYxqdPn3SNZTW4n4uLi7E9f/78snz5cilYsCAvBQCTWLhwIXsaAABYhXCP3pYuXkhPqq7yHxu2yOHjZ+TStZs6S/lbKrBcokh+qVe9kpQtUViiRIkikYn6Iuvq6l3H2sPDQ2dLAQAA07l8+bKus3zs2DFjW6xYsWTUqFHSt29fsbGx4eUAYDLZsmVjbwMAAKtgshThLBnTyc/9uurbLq5u8ujJM3F0eqNrLyeMH1+SJ0ssiRNG7pqGU6dOldGjRxv/Tp06tVn7AwBAZOHu7i4TJ06UCRMm6B96DcqVK6frLmfJksWs/QMQOR0+fFjPq1WrZu6uAAAABCqKl6E+BSwqk7l69eo6k/n48eMSGTg7O+u5vb29ubsCIAg4ZxGRHD16VGcvX7lyxdgWN25c/eOvao8aNdzGSTYpzlvA+hQtWlTPT5w4Ye6uAAgi3m8B68I5G3YodmxB7Ozs9KRwOS4AAOH/gVLVXZ43b55xTAilbt26uiZzqlSpeAkAAAAAIAgIMgMAgEhn+/bt0qlTJ3nw4IGxLVmyZDrg3KBBg0g3LgQAAAAAhEbEuP4TAAAgCF69eiUtW7bUZal8BpjbtWuny2U0bNiQADMAAAAABBOZzAAAIMJT5TDWrFkjvXr10oFmg4wZM8qSJUukYsWKZu0fAAAAAFgzgswAACBCUxnLXbp0ka1btxrb1GB+ffv2ldGjR0vs2LHN2j8ACIj63wUAAGANCDIDAIAI6fPnz7JgwQIZMmSIcdRoJW/evLJ8+XIpXLiwWfsHAN/TqFEjdhIAALAKBJkBAECEc/XqVenQoYMcOXLE2BYzZkwZOXKk9O/fX2xsbMzaPwAIinfv3um5vb09OwwAAFg0gswAACDC+Pjxo0yaNEnGjx+vbxuUKVNGli5dKtmyZTNr/wAgOOrVq6fnJ06cYMcBAIDIGWR++vylnLt0NcTrp0iWVPLnzh6mfQIAABHX8ePHdfbypUuXjG1x48aVKVOmiIODg67DDAAAAACwoiDz8dPnpfOAUSFev271irJ42miJTFxcXMTV1VXf9vDwkGjRopm7SwAAWDxVb3n48OEyZ84c8fLyMrbXqVNH12ROlSqVWfsHAAAAABFduAWZM6ZPI22b1ff3vsPHT8vNO/clRbIkUjBPTokd21au3bwjF6/ekNi2ttKwdhUpkDenRDZTp07Vo9wbpE6d2qz9AQDA0u3YsUM6deok9+/fN7YlTZpU5s6dqwfMihIliln7BwAAAACRQbgFmfPmzKanb/26dqOsWPO3tGxYW8YN7S2xYsY03rdx627pOmiMLrUxuV4NiWwGDBgg3bp107erV69OJjMAAAFwdHSUPn36yO+//+6rvU2bNjJt2jRJlCgR+w4AAAAAIuLAf84urjJq6jxJmjiRjB/WR2LGiOHr/no1Ksm+/07I2o1bZce+w1KtQhmJTOzs7PSkMOo9AAB+qXIYa9eulZ49e8rLly+N7enTp5clS5ZI5cqV2W0AIoxSpUqZuwsAAABBYtIRcM5cuCxubh8kd44sfgLMBoXyeZfJOHTstCm7BgAALNzDhw91neVmzZoZA8xqML++ffvqwf4IMAOIaMaOHasnAAAAS2fSTGYXVzc9f/feOcBl3r59b8x6BgAA+Pz5syxatEgGDx4s7997f05Q8uTJI8uWLZOiRYuykwAAAAAgsmQyZ0yXRs8vXL4uN27f83O/h4enbNq+V9/OlN57WQAAEHldu3ZNypUrp8csMASYY8SIIePGjZNTp04RYAYQoXXo0EFPAAAAls6kQeZsmTNI8cL55aOHh7ToMkA2bd8jL1+91lnLp85dkhZd+sulazcltq2tNKxd1ZRdAwAAFuTjx486kJwvXz45fPiwsb106dJy/vx5GTZsmA42A0BEdufOHT0BAABYOpOWy1AWThkpjTv0lpt37kunfiP93K8CzIumjZKUyZOaumsAAMACnDx5Utq3by8XL140tsWJE0cmT54snTp10nWYAQAAAACROMicIlkS2fHncvlt7UbZtueg3L7/UD55fpJkSRNL6WIFxeGnxpIudUpTdwsAAJiZi4uL/PzzzzJ79mxdh9mgVq1asmDBAkmThlJaAAAAAGCJTB5kVmLbxpLObZrqCQAAYNeuXTpL+e7du8adkSRJEpkzZ440adJEokSJwk4CAAAAAAvF9aYAAMBsXr9+LW3atJEqVar4CjC3atVKrl69Kk2bNiXADCDSUqWC1AQAAGDpzJLJ/OnTJ9m8a78cPnZaHJ3eSJECeaRLm2by+s1buXrjtiRMEF9yZMlojq4BAAAT8PLyknXr1kmPHj3kxYsXxvZ06dLJ4sWLpWpVBgAGgE2bNrETAACAVTB5kPntu/fSsstAOXnu62A+NjY2ev7p02dp4tBHEsSLJ+f2bZBo0aKZunsAACCcPXr0SLp27Sr//vuvsU2Vw+jVq5eMHTtW7O3teQ0AAAAAwIqYvFzGkHEzdIC5bInC0tPhJ1/3JUmUQH4oVUxeOr6Ww8fPmLprAAAgHKnB/BYtWiQ5c+b0FWDOnTu3HD16VGbOnEmAGQB8UAOhqgkAAMDSmTTI/NLRSTZu2yOxbW1l6YyxkjNbZj/L5MmRVc+PnTonkY2Li4u8fPlSTx4eHvrLOAAAEcH169elfPny0qVLF3n//r1uixEjhowZM0ZOnz4txYoVM3cXAcAiy2VQMgMAAFgDkwaZL165rgOnBfLkkHhx/R/AInWKZHr++NnX+oyRxdSpUyVp0qR6Ul+4nzx5Yu4uAQAQKupH0wkTJki+fPnk4MGDxvaSJUvK2bNn5eeff9bBZgAAAACA9TJpkNntg7uex4vrXWsxShS/y3z08PDuWFR/7ozgBgwYoAc/UlOhQoUkZcqU5u4SAAAhdurUKSlSpIgMGzZM3N29PwOoesvz5s2TQ4cO6bIZAAAAAADrZ9KB/xInjK/nL169DnCZO/ce6nmKZEklsrGzs9OTz8EQAQCwNq6urjJixAhdY9ln6acaNWrIwoULJW3atGbtHwAAAADAioPMeXNl1/WYz1+6Jq9eO+mR5H1ydnGV9f/u0LfLFC9kyq4BAIAwsGfPHunYsaPcuXPH2JY4cWKZM2eONG3a1M97PwAAAADA+pm0XIZtrJjSvkUD8fD0lM79R8n9B491u6eHpxw5eVbqt+kuTm/fSaF8uaRkkQKm7BoAAAgFJycnadeunVSqVMlXgLlly5Zy9epVadasGQFmAAimpUuX6gkAAMDSmTSTWRnYvYNcu3lHdh04IoePn9ZtW3Yf0JOSJlUKWTBlpKm7BQAAQsDLy0v++usv6d69uzx//tzYrkpiLFq0SKpXr85+BYAQypQpE/sOAABYBZMHmW1sosuv8ybJhq27Zd2m7XLt1h1xd/8oKZIlkarlS0un1k0kfry4pu4WAAAIpsePH0u3bt1k06ZNxjZVDqNHjx4ybtw4iRMnDvsUAEJh//79el6rVi32IwAAsGhRvFQKEixOiRIl9Pzo0aMSGTg7O+u5vb29ubsCIAg4ZyM3NZjfsmXLZMCAAfLu3Ttje86cOXW74T0MloXzFrA+RYsW1fMTJ06YuysAgoj3W8C6cM5acSYzAACwXjdu3NAD+x044F3mSrGxsZFhw4bJ4MGDJWbMmGbtHwAAAAAgkgSZP336JJt37ZfDx06Lo9MbKVIgj3Rp00xev3krV2/cloQJ4kuOLBnN0TUAAOAPDw8PmT59uowaNUrc3d2N7cWLF9fZy7ly5WK/AQAAAEAkZfIg89t376Vll4Fy8txFXxlQyqdPn6WJQx9JEC+enNu3QaJFi2bq7gEAgG+cOXNG2rdvL+fOnTO22dnZycSJE6Vr1668XwMAAABAJBfV1E84ZNwMHWAuW6Kw9HT4ydd9SRIlkB9KFZOXjq/l8PEzpu4aAADwwdXVVQYOHKhrgvoMMFerVk0uX76sB/jjB2EAAAAAgEmDzC8dnWTjtj0S29ZWls4YKzmzZfazTJ4cWfX82KmvX2YBAIBp7d27V/LmzStTp07VZa6URIkSyapVq2Tr1q2SLl06XhIACGc9e/bUEwAAgKUzabmMi1eu6xHpC+TJIfHixvF3mdQpkun542cvTNk1AAAgIk5OTjJgwABZvny5r/3RokULmTlzpiRJkoT9BAAmUq9ePfY1AACwCiYNMrt98B4oKF5cez2PEsXvMh89PPQ8alR/7gQAAOHmr7/+ku7du8uzZ8+MbWnSpJFFixZJjRo12PMAYGKvX7/Wc3t77+9PAAAAlsqkQebECePr+YtX3h+W/HPn3kM9T5Esqcn6BQBAZPbkyRMdXN6wYYOxLUqUKNKtWzeZMGGCxInj/9VHAIDw1bBhQz0/ceIEuxoAAFg0kwaZ8+bKrusxn790TV69dtJfYH1ydnGV9f/u0LfLFC9kyq4BABDpeHl5ybJly3R5jLdv3xrbc+TIodtLlixp1v4BAAAAAKyDSQf+s40VU9q3aCAenp7Suf8ouf/gsW739PCUIyfPSv023cXp7TsplC+XlCxSwJRdAwAgUrl165ZUqFBBOnbsaAww29jYyIgRI+Ts2bMEmAEAAAAAlpnJrAzs3kGu3bwjuw4ckcPHT+u2LbsP6ElJkyqFLJgyUiIjFxcXcXV11bc9PDwkWrRo5u4SACCC8fT0lBkzZsjIkSPlw4cPxvZixYrp7OXcuXObtX8AAAAAAOtj8iCzjU10+XXeJNmwdbes27Rdrt26I+7uHyVFsiRStXxp6dS6icSPF1cio6lTp8ro0aONf6dOndqs/QEARCwqQ7l9+/Z6bhA7dmxdd1nVZObHTQAAAABASETxUgUZYXGZzNWrV9df9o8fPy6RgbOzs54zcjZgHThnrYubm5v+EXPatGny6dMnY3uVKlVk8eLFkj59erP2D6bBeQtYH1Uz35CMAsA68H4LWBfOWSvOZP7WB3d38fT8JPZ2sSWys7Oz05OhLiYAAKG1f/9+cXBw0DWYDRImTCizZs2Sli1b+hmEFwBgOVRpIwAAAGtgliDzS0cnmbPkN9m6+4A8fvZCt8Wxt5PSxQpKjw4/ScG8Oc3RLQAAIow3b97IwIEDZenSpb7amzVrpgPMSZMmNVvfAAAAAAARi8mDzDfv3JcGbXvKi1eO+u8YNjYSM2YMee/sItv2HJKd+4/I1JEDpHmDWqbuGgAAEcKGDRukW7du8vTpU191/hcuXCi1avH+CgDWok2bNnq+fv16c3cFAAAgUFHFxLoMGKUDzDmyZpJNv82Xu6d3y83jO+TkrvXyY41KulbkoDHT5M79h6buGgAAVu3Zs2fSsGFDqV+/vq8Ac9euXeXy5csEmAHAyjx48EBPAAAAls6kQeZLV2/KpWs3xdY2lvw2f7IUK5TPOJJ9mpTJZf7kEVK0QB7x8PSUv7fsMmXXAACwWmoM3+XLl0uOHDnkr7/+MrZny5ZNDh06JPPnz5e4ceOatY8AAAAAgIjLpEHmB4+f6Hm+nNl0UNlPZ6JGleqVynov++hrBhYAAPDf7du3pVKlStKhQwddh1mJHj26DB8+XM6dOyelS5dm1wEAAAAAIk5N5nhx4+h5rJgxA1zGcF/8L8sCAAC/PD09ZebMmTJy5Ehxc3MzthcpUkSWLVsmefPmZbcBAAAAACJekLlQvlw6eHzhynVxdnEVe7vYfpY5fPyMnlcqV8KUXQMAwGqoDGWVuXz69GljW+zYsWXcuHHSs2dPYykqAIB1S5Aggbm7AAAAYHnlMlSW8rTRg+S9s4v0GDJWHJ28L+tV1IB/C1eukS279kuLBrWlbIkipuwaAAAW78OHDzJ06FApXLiwrwBz5cqV5dKlS9KnTx8CzAAQgag6+z5r7QMAAFgqk2YyHz99Xtb/u0NSpUgm2/YckgNHTkn2LBkktq2t3Lh9T168ctS3VfC5TY8hvtYtViivdGnTzJTdBQDAYhw8eFAcHBzkxo0bvjLcVMmMVq1aSZQoUczaPwAAAABA5GXSIPPT5y9l+95Dxr9d3dzkzIUrvpZRbT6XMYgZM4ZJ+ggAgCV5+/atDBo0SBYvXuyrvUmTJjJ79mxJliyZ2foGAAhf06dP13NVfx8AAMCSmTTI/EOporJ97bIQrZsgHgMBAgAil02bNknXrl3lyZMnxrZUqVLJggULpE6dOmbtGwAg/G3ZskXPCTIDAABLZ9Igc/x4cSV/vLimfEoAAKzO8+fPpUePHrJu3Tpf7Z07d5ZJkyZJvHjxzNY3AAAAAADMGmQGAAAB8/LykpUrV0q/fv3EycnJ2J41a1ZZunSplC1blt0HAAAAALA4Jg8yO715J4+fPpcE8ePqAQAVDw9PmbFopRw5cUbSpE4hw/t0keRJE5u6awAAmM2dO3ekU6dOsnv3bmNb9OjRZeDAgfLzzz9LrFixeHUAAAAAABbJ5EHmoeNnyIatu2XR1FHGIPOYafNl6SrvS4KPn7kgV6/flt1/rZAoUaKYunsAAJiUp6enHsBPBZLd3NyM7YUKFZLly5dLvnz5eEUAAAAAABYtqqmzmDfv3C8JE8SX2lXL6za3D+7yv782S5umP8qW1YskRbIkcvn6LTl07JQpuwYAgMlduHBBSpQoIf379zcGmG1tbWXatGly7NgxAswAEMmtWLFCTwAAAJbOpEHmO/cfiIenp2TNmE6iRYum206fuySubm7Sr2s7KZQvtzT9saZuP3rqvCm7BgCAyXz48EGGDRums5VPnfr6o2rFihXl4sWLuiazKpUBAIjc0qVLpycAAABLZ9JvsC9evdbzhAniGdsuXrshGdKmliSJEui/06VOqefPX74yZdcAADCJQ4cOiYODg1y/ft3YFj9+fJkxY4a0adOGUlEAACNDnf569eqxVwAAgEUzaZA5YXzv4PLzl47GtjMXrkjObJmNf7u4el8uHDNGDFN2DQCAcPXu3f/buw/4ms43gONPECSxt9iU2iv2nlVaqyhq1EjEqC3UqNmiRovaolWtGlW0Zq1SO2qP2HvHJiGy/p/35d5/bgaZdyS/7+dzPufmvefmvve9OTn3Puc5z/tUvvzyS5kzZ45Je6tWrWTGjBmSLVs23gEAgInx48frNUFmAABg7cxaLqNAvtxinyyZHD15Ro6dOiPXb92R7bv2S/VKLsZtbty+o9e5c2Y3Z9cAAIg3a9eulaJFi5oEmJ2dnWXNmjWyYsUKAswAAAAAAJtm1iBzpgzppcmHdSQoKEgafOoqlT5sLcnt7XWbwa59r2tT1qpSwZxdAwAgzt27d0/atGkjTZo0kZs3bxrb3d3d5fTp09K0aVNGHQAAAABg88w+q9DErwaKQ8oUssfriDhnyyLD+nUzltE4d/GKXLh8VUoWLSRFChUwd9cAAIgTISEhsnjxYhkwYIA8fPh6PgKlYMGCsmDBAqlZsyYjDQAAAABIMMweZE6dykmmjBkS4X2FCuSVK4e3m7tLAADEmcuXL0v37t1l8+bNxrakSZOKh4eHjBw5UhwcHBhtAAAAAECCYvYgMyLn6+srfn5++nZAQIAOSgAAbIMqBaUm8BsxYoTxf7lStmxZ8fT0lDJlyli0fwAA29O/f39LdwEAACBKCDJbkcmTJ8uYMWOMP+fMmdOi/QEARM2JEyfE1dVVvLy8jG0pU6aUsWPH6gBBsmQcbgEA0de4cWOGDQAA2ASzTvyHt1OXUqtJotTi4uIizs7ODBkAWDF/f3/56quvdLZy6ABz7dq1deBZ/V8nwAwAiCkfHx+9AAAAWDtSq6yIk5OTXhR7e3tLdwcA8BZ79uzR2ctnzpwxtqVNm1amTp0qXbp0ETs7O8YPABArrVu31uvQJzIBAACsEZnMAABEw9OnT6VXr15SrVo1kwBzixYtxNvbW7p27UqAGQAAAACQqJDJDABAFK1fv166d+8uN27cMLZlz55dZs2aJc2bN2ccAQAAAACJEpnMAAC8g6qH+dlnn8nHH39sEmB2c3OT06dPE2AGAAAAACRqZDIDABCJkJAQ+fXXX6V///7y4MEDY/t7770n8+fP1xP8AQAAAACQ2FkkyBwUFCTrtuyQ3fsPyYNHj6V8mRLSo1Nbefj4iXifuygZ0qeTIgXzW6JrAABoV69eFXd3d/n777+NI5I0aVIZOHCgjB49WhwcHBgpAEC8qlu3LiMMAABsgtmDzE+ePpP2PQbLwaMnjG329vZ6HRQULK3d+kv6tGnl6D+r9Zd5AADMfSJ05syZMnz4cPH19TW2ly5dWhYuXChly5blDQEAmIU6FgEAANgCs9dkHvr1dzrAXKNyOenj1sHkvswZ00utqhXF58FD2X3gsLm7BgBI5E6dOiVVq1aVfv36GQPMKVOmlIkTJ4qXlxcBZgAAAAAALB1k9nnwSNZs3CaODg6y4LtxUvT998JtU6JIIb3e/99Rc3YNAJCI+fv7y6hRo6RMmTJy4MABY3utWrXk+PHjMmTIEONVNwAAmEu7du30AgAAYO3MWi7jxOmzEhwcLGVKFJG0aVJHuE3O7Fn1+uade+bsGgAgkdq7d6+4urqKt7e3sS1t2rQyefJk6dq1qyRJYvaLfgAA0G7fvs1IAAAAm2DWb84vXvrrddo0qfTazi78Nq8CAl53LEkEdwIAEEeePXsmvXv3lmrVqpkEmJs3by6nT58WNzc3AswAAAAAAFhbJnOmDOn0+t79h5Fuc+nKdb3OnjWL2foFAEhcNm7cKO7u7nL9+utjjpItWzY94V+LFi0s2jcAAAAAAGyNWTOZSxYrrOsxHzt5Ru4/fCR2YVKZn/v6ycq1f+vb1Su5mLNrAIBEwMfHR9q3by+NGjUyCTCrshgqe5kAMwAAAAAAVh5kdkiZQrq2ayEBgYHSfdBouXrtpm4PDAiUvQePyCedvpBHT56KS6liUqV8GXN2DQCQgIWEhMiSJUukaNGiem2QP39+2bZtm3h6ekr69Okt2kcAAMLKlCmTXgAAAKydXYj65m1GAQGB0qXvMNmyc2+E9+fKkV1W/jhd8uR0lsSscuXKer1v3z5JDJ4/f67XqVK9rtcNwLrZ0j579epV6dGjhy6RYaAm8xs4cKCMHj1aHB0dLdo/wFxsab8F8Br7LWB72G8B28I+a6M1mRV7+2Ty88yJsnrDVvn9z01y5sIl8fd/JdmzZpYGtauJ++etJV3aNObuFgAggQkKCpLZs2fL0KFDxdfX19heqlQpWbhwobi4UJYJAAAAAACbDDIbMshafPyBXgAAiGuqvrKrq6vJ1SApUqSQUaNGyaBBg8Te3p5BBwBYvUmTJun12LFjLd0VAAAA66nJDABAfHr16pWMGTNGSpcubRJgrlGjhhw/flxnNRNgBgDYik2bNukFAADA2lkkkxkAgLi2f/9+nb186tQpY1uaNGl0Fpibm5u+igYAAAAAANhQkHn3/kMyde5PMX58tQouMrBn5zjtEwAgYU7UMHz4cPnhhx8k9Fy2TZs2lVmzZkmOHDks2j8AAAAAABK6eAsy33/4SPYdPBrjx2fJlDFO+wMASHjUJcTu7u5y7do1Y1uWLFlk5syZ0rJlS7Gzs7No/wAAAAAASAziLchcv1ZV8dr8e4wf7+iQMk77AwBIOO7fvy/9+/eXX3/91aS9c+fOMmXKFMmQIYPF+gYAAAAAQGITb0FmJ0cHvQAAEFdUOYxly5ZJ3759xcfHx9ieL18+mT9/vtSrV4/BBgAkGGFPpgIAAFgri0/899LfXwIDgySVk6OluwIAsGLXr1+XHj16yPr1641tajI/ldE8ZswYcXJysmj/AACIa87OzgwqAACwCRYJMvs8eCQz5i+WDVt3ys0793Rb6lROUq1iWent2kHKlixqiW4BAKxQcHCwzJkzR7788ks9yZ9ByZIlxdPTU8qXL2/R/gEAEF82btyo161atWKQAQCAVTN7kPn8pavSonMfuXf/gf45ub29pEiRXJ4995WN23bJ5h17ZfIoD/msxcfm7hoAwMp4e3uLq6ur7N2719iWPHlyGTVqlHh4eIi9vb1F+wcAQHyaPHmyXhNkBgAA1i6JuZ+wh8doHWAuUqiA/Ll4llw+tFXOH/hbDm5ZKc0b1ZOgoCAZMnaKXLp63dxdAwBYiVevXsm4ceOkdOnSJgHmatWqybFjx2TYsGEEmAEAAAAASIxB5pPe5+XkmfPi4JBSFs/6Viq6lJKkSZPq+3I5Z5NZ346UCmVKSEBgoKxav8WcXQMAWIkDBw6Ii4uLjBw5UgebldSpU8vs2bNl586dUrhwYUt3EQAAAAAAWCrIfO3mLb0uVfR9HVQOS03g1LBejdfb3rhtzq4BACzM19dXT+JXuXJlOXnypLG9cePGcvr0aT3pnzpOAAAAAACARFyTOW2a1HqdMkWKSLcx3JfuzbYAgIRv8+bN4u7uLleuXDG2Zc6cWX744Qf59NNPxc7OzqL9AwAAAAAAVhJkdilVTAePj58+K899/SSVk2O4bXYfOKzX9WpWNmfXAAAW8ODBAxkwYIAsXrzYpP3zzz+XqVOnSsaMGXlfAACJlprkFgAAwBaY9bpjlaU8ZcwQefbcV3oPHScPHj023qcm/JuzaKms37JD2rVoLDUqlzdn1wAAZhQSEiLLly+XIkWKmASY8+bNK3///bcsWrSIADMAINFr2LChXgAAABJtJvOBQ8dkzqJlEd6XI3tW2bhtl+zc+58ULphPHB0c5NzFK3Lv/gN9WwWfVcC5R6e28dU9AICF3LhxQ3r27Clr1641tqlay3379pVx48aJk5MT7w0AACJy69brOW0KFSrEeAAAgMQZZL5910c2bd/11m38XryQw8dPh2tTj0uRIrnYkmfPnsmePXskffr0UrFiRUt3BwCsTnBwsMybN0+GDBmi/2caFC9eXBYuXCgVKlSwaP8AALA27du312svLy9LdwUAAMAyQeZaVSvIpuWeMX58+rS2MfHfxYsXZezYsfrybn9/f3FxcZGtW7daulsAYFXOnDkjbm5usnv3bmNb8uTJ5auvvpLBgwfr2wAAAAAAwDbFW5A5Xdo0UjptGknobt++LXXq1JHZs2dL06ZNLd0dALAqAQEBMmnSJH0y7tWrV8b2qlWryoIFC3RNZgAAAAAAYNviLcicWFSrVk0vAABTBw8elK5du8qJEyeMbalSpZKJEydKjx49dB1mAAAAAABg+/iGDwCIU76+vjJw4ECpVKmSSYD5o48+ktOnT0uvXr0IMAMAAAAAkIBYJJP56o1bsmjZajl09KQ8fPxEAgODwm1Tv2YVGTe0b6yeJyQkRI4fPy7//vuvDnqUKlVKGjZs+M7HqUu6t2/fLufOnZOUKVNKuXLlpGzZsrHqCwAkBqomfbdu3eTy5cvGtkyZMsmMGTOkTZs2YmdnZ9H+AQBgSz788ENLdwEAAMA6g8wHDh2Tz7oPEl+/F2/d7t6DhzF+jidPnsgXX3whW7Zskbt37xrb1WXb7woy7927V9q2bSvXrl0zaa9fv74sXbpUMmbMGON+AUBC9fDhQ529vGjRIpP2Dh06yHfffacDzQAAIHrU5LgAAAC2wKzlMlRm8cBR3+oAc/dObeTbkYN0e+MGtWXP+t+kVZMPxcnRQRb9MEFmTvgqxs/z6NEj+fXXX+XevXtSsmRJqVChQpQepzLvGjVqpAPMBQoU0IHqjh07SurUqXXAulmzZvo1AAD+/399xYoVegK/0AHmPHnyyMaNG2Xx4sUEmAEAAAAASODMGmQ+c+GyXLh8TTJmSCcj+neXtKlTve5EkiRSIG9umTF+uOTJ6Sy9h34tDx49jvHzpEuXTgc2bt++LceOHZNWrVpF6XEjR47UWdB16tSRkydPyg8//CA///yzHDp0SNKnTy+7d++WlStXxrhfAJCQ3Lp1S598a926tT6pp6hyGH379tX/Q7nEFwCA2Pn000/1AgAAYO3MGmS+ev2mXhcvXFCSJUumohH65+DgYGNwolmjevLsua+s3rAlVkFmdYl21qxZo/yYFy9eyKpVq/TtadOm6VrMBgULFpQBAwbo2ypDGgASM/U/+8cff5Ty5cvLX3/9ZWwvVqyYLjmk/oemSvX6JCIAAIi5+/fv6wUAAMDambUmsw4si4jDmwCuQ4oUev3c18+4TdbMr+t2XrhkWhM5vqmMZz8/P8mdO7eUKFEi3P2NGzeWr776Svbt22fSriYU/Oeff/RtwwfAdevW6bXKiHZ0dHzr81auXDnCdpUFqC4/f/78uSQGauwBWL/z589L7969Zc+ePcY2e3t7XTNSnYxLnjx5ovm/BdgajrWA7TEk43BsBWwHx1vAtiTGfTZVPCWFmTXInDtHdr2+ceuOXufI/jrT+NqNW8Zt7vm8DtQmT25vzq7JhQsX9FoFdiNSuHBhnWnt4+MjT58+lTRp0hjrP8+dO1ffzpkzp14bfnZxcXlnkBkAbEFAQIBMnz5dJk6cKP7+/sZ2VfN+1qxZ+n8kAAAAAABInMwaZC6QN5dky5JJLly+Kk+ePpMihfJLhvTp5OKV6/L7X5ukfOkSsuSP11nARQsVMGfXdODYUGojIilSpNAlNFRZjdBBZhVYNmQux0TYzOiwGc6J7ZLzxPZ6AVvw33//iaurq77iI/S+Onr0aOnfv7+uqw/AdnCsBWyH4RjLfgvYHvZbwLawz8aeWSMDSZMmlZaNG8hL/1eydNV6/fOAHp30fWqyv0oNW8uV6zcld87s0qrph2KtH/JCQkIs3RUAMMtlQx4eHlKxYkWTAHPDhg3Fy8tL3N3dCTADABCPsmfPrhcAAABrZ9ZMZmXEgB56MXBt11JSOznJ8jUb5PGTp1Ki6Pvi0auLpHxTr9lcUqdOrddPnjyJ8P5Xr14Z67QYtgWAhGrbtm3SrVs3uXTpkrEtY8aMumTGZ599puvRAwCA+LVkyRKGGAAA2ASzB5kj0rpZQ71YUv78+fX63LlzkU52pTKYM2TIEGlJDQCwdarO/KBBg+THH380aW/Xrp18//33kjlzZov1DQAAAAAAWCcKab5RunRpXXNZZe2dPXs23ECtX79er9Vl4wCQ0KiTaCtXrtSTn4YOMOfKlUs2bNggv/76KwFmAADM7JtvvtELAACAtUtmqWDGkRPecv7SVfH185OIShyrSQJrVa1gtj45OTlJ48aN5ffff9dZfKtXr5ZkyV4Pz40bN2Tq1Kn6dtu2beOtD+ryc0NJjoCAAF2zGgDi261bt6RXr16yZs0aY5udnZ188cUX+ostJYIAALBc+SoAAABbYPYg87mLV8RtwFdy9sLlt27XtGHdWAWZFy5cKD4+Pvr2rl279Pr48eMyceJE4yR+gwcPNnnMuHHjdMbyunXrpHz58vLxxx/Ls2fPdC20+/fvS9myZXUt0vgyefJkGTNmjPHnnDlzxttzAUBwcLB4enrqyf2ePn1qHBCVzaz+h1auXJlBAgAAAAAA72QXotKKzSQoKEhqNGkvF69cl/Rp0+hAsnO2LGIXwbaFCuSTBnWqxfi5ihcvLqdOnYr0fpUlHBgYGK598+bN0r59e2OA2qBChQo6u9nZ2VnMkcncsGFD3ccDBw5IYvD8+XO9TpUqlaW7AiQKqs68mthvx44dxjZ7e3sZNmyYDB06VFK8Y/JV9lnA9rDfArZHfQdRvLy8LN0VAFHE8RawLeyzNprJfPSktw4wOzo4yOaVP0ou52zx9lyurq5y586dSO+PrBTFBx98IBcvXtTZzGoSQBVoUVnNtWvX1tnP8V2yQy2GYA8AxDVViue7776T0aNHy8uXL43tlSpV0lnNxYoVY9ABAAAAAID1Bpnv3Hug1+VKF4vXALPSr1+/GD9W1R+Nz9rLAGAJhw8f1ifgjhw5YmxTJ7bGjx+vazJTBx4AAAAAAFh9kDlThnR6ncQufjOCAQD/p8rwqHrvagJTVbbIoEGDBjJ37lzJmzcvwwUAgBVavny5pbsAAABgfUFml1LFJFuWTHLizDl58dJfHFK+veYnACB2/vnnH3Fzc9NlgAwyZswo06ZNk3bt2omdXURV8QEAgDXInDmzpbsAAAAQJWZNKU6WLJnMGD9cfH395KsJ0+TVqwBzPj0AJBqPHz/WweU6deqYBJhVKaDTp0/rCU4JMAMAYN3Wrl2rFwAAAGtn1kzmA4eOyY+/rRLnbFnk15Vr5e9/9kix99+TlBFkNFd0KSk9OiWuusi+vr76snbD5FzURwUQE6tWrdI1lkNPfporVy6ZM2eOfPTRRwwqAAA24vvvv9dr5osBAADWzqxB5tt3fWTT9l3Gn30ePJQde70i3DZFiuSS2EyePFnXTTXImTOnRfsDwLbcvn1bvvjiCx1kNlDZyj179pQJEyboSU0BAAAAAABsOshcq2oF2bTcM0rbpk+b+IIhHh4eOvtQadiwIZnMAKIkJCREFi5cKIMGDZInT54Y2wsXLiyenp5StWpVRhIAAAAAACSMIHO6tGmkdNo05nxKm+Lk5KQXxd7e3tLdAWADLly4IN26ddMT/IWufz906FAZPny4pEjBBKsAAAAAACABBZkBAHEjMDBQvvvuOxk1apS8fPnS2F6hQgWdvVyiRAmGGgAAAAAAmAVBZgCwMUePHpWuXbvK4cOHjW2Ojo7yzTffSO/evSm1AwBAAjFs2DBLdwEAAMCyQebd+w/J1Lk/SbUKLjKwZ2eTtqgI/TgAgMiLFy9k7NixepLQoKAg45DUr19f5s2bJ/ny5WOYAABIQOrVq2fpLgAAAFg2yHz/4SPZd/CoZMmUMVxbVIR+HAAkdjt37hQ3Nzc5f/68sS1Dhgzy/fffS4cOHcTOzs6i/QMAAHHv6tWrel2sWDGGFwAAJM4gc/1aVcVr8+/i6JAyXFtUhH5cYuHr6yt+fn76dkBAAJe8A5DHjx/LkCFDZP78+Saj0bp1a5k+fbpkzZqVUQIAIIHq3Pn1lZ1eXl6W7goAAIBlgsxOjg56eVcb/k9dAj9mzBjjzzlz5mR4gERszZo10rNnT7l9+7axLUeOHDJnzhxp3LixRfsGAAAAAABgkMR4Cxbn4eEh9+7d04uLi4s4OztbuksALODOnTvSqlUrad68uUmAuUePHnL69GkCzAAAAAAAIHFkMiP6nJyc9KLY29szhEAiExISIj/99JMMHDhQl8kweP/998XT01OqVatm0f4BAAAAAABYTZD56o1bsmjZajl09KQ8fPxEAgODwm1Tv2YVGTe0ryW6BwBmd/HiRenWrZts377d2JYsWTJdj3nEiBGSMmXiq1MPAAAAAABsg9mDzAcOHZPPug8SX78Xb93u3oOHZusTAFhKYGCgTJs2TUaOHCkvXvz//2L58uV19nLJkiV5cwAASKQ++ugjS3cBAADA+oLM6lLwgaO+1QHm7p3aSL7cOWXI2CnSuEFt+bKPm0ybt1g2bN0ps74dKXWrVzZn1wDA7I4dOyZdu3aVQ4cOGdscHBzk66+/lr59+0rSpEl5VwAASMRUCS0AAABbYNaJ/85cuCwXLl+TjBnSyYj+3SVt6lSvO5EkiRTIm1tmjB8ueXI6S++hX8uDR/+vRwoACcnLly9l+PDhUq5cOZMAc7169eTkyZMyYMAAAswAAAAAAMBmmDXIfPX6Tb0uXrigrjUqdnb65+DgYL22s7OTZo3qybPnvrJ6wxZzdg0AzOLff/+VUqVKyfjx43WpDCV9+vR6wr/NmzdL/vz5eScAAIDWokULvQAAAFg7s5bL0IFldTn4mwmsHFKk0Ovnvn7GbbJmzqTXFy5dM2fXACBePXnyRL788kuZO3euSXurVq1kxowZki1bNt4BAABg4tGjR4wIAACwCWYNMufOkV2vb9y6o9c5smfV62s3bhm3uedzX6+TJ7c3Z9cAIN789ddf0rNnT7l58/XVHIqzs7PMnj1bmjZtysgDAAAAAACbZtZyGQXy5pJsWTLJhctX5cnTZ1KkUH7JkD6dXLxyXX7/a5NcuXZTlvyxTm9btFABSWx8fX3Fx8dHLwEBAcYyIgBs0927d6V169Y6kBw6wOzu7i6nT58mwAwAAAAAABIEswaZkyZNKi0bN5CX/q9k6ar1+ucBPTrp+9Rkf5UatpYr129K7pzZpVXTDyWxmTx5smTJkkUvajKwW7f+n+ENwHaEhITIokWLpEiRIrJixQpje6FChWTnzp26ZEbatGkt2kcAAAAAAIC4YheioiEWtnzNRlm+ZoM8fvJUShR9Xzx6dZGcztkSZSazn9/r+tQNGzbUQfgDBw5IYvD8+XO9TpUqlaW7AsTKpUuXdKby1q1bjW1qXx48eLCMHDlSUr6pSW/r2GcB28N+C9ieli1b6vXKlSst3RUAUcTxFrAt7LMJLMiM8CpXrqzX+/btSxTDw04NWxcUFCTTp0+Xr776yniySHFxcZGFCxdKqVKlJCFhnwVsD/stYHvYbwHbw34L2Bb2WRstl3H4+CnpM+wbWbRsday2AQBrcvz4cX1iaODAgcYAs4ODgy6Bs3///gQXYAYAAAAAALBYkPnajduy4s+Nsu+/o7HaBgCswcuXL2XEiBE6W/ngwYPG9jp16siJEydk0KBBkixZMov2EQAA2K4xY8boBQAAwNpZXfQjIDBQr5MlTWrprgBApHbv3i1ubm5y5swZY1u6dOlk6tSp0rlzZ7Gzs2P0AABArKgJgwEAAGyBWTOZo+Lshct6nTF9Okt3BQDCefr0qfTq1UuqV69uEmBWE/N4e3tLly5dCDADAAAAAIBEJd4zmfd4HZZp837Wt30ePNLrvV5HpFXXvuG2ffT4qZw8c17frlKhTHx3DQCiZd26ddKjRw+5ceOGsS179uwya9Ysad68OaMJAAAAAAASpXgPMvvcfyi79h8ybXvwUC8RcXRwkE5tmsuHdarHd9cAIEru3bsnffv2lWXLlpm0q3IZkyZN0mUyAAAAAAAAEqt4DzLXq1lFdq1dom9v+3efjJ48U+rWqCyjPb4w2U7VL02ZIrlkz5pZklKPGYAVCAkJkV9++UX69+8vDx/+/8TYe++9JwsWLJBatWpZtH8AAAAAAACJIsicyslRCubPo2/7+7+S7p3aSIkihYxtAGCNrly5Iu7u7rJ582ZjmzoBNmjQIBk1apQ4ODhYtH8AACDhW7lypaW7AAAAYB1B5tBeBbySh4+eyLPnvpFuc/j4KVm0bI2ULVlUl81ITHx9fcXPz0/fDggIIKMbsICgoCD54YcfZPjw4cb9USlbtqx4enpKmTLUiwcAAOaRIUMGhhoAANiEJOZ8sms3bsuKPzfKvv+OxmqbhGry5MmSJUsWvRw6dEhu3bpl6S4BicqJEyekSpUqujyGIcCcMmVK+fbbb+XAgQMEmAEAgFmtWbNGLwAAANbOrEHmqAgIDNTrZImwLrOHh4eeYEwtLi4u4uzsbOkuAYmCv7+/jBw5Umcre3l5Gdtr166tA8+DBw+WZMnMeuEHAACAzJgxQy8AAADWzuqiJmcvXNbrjOnTSWLj5OSkF8Xe3t7S3QEShb1794qrq6t4e3sb29KmTStTpkyRrl276klJAQAAAAAAYMEg8x6vwzJt3s/6ts+DR3q91+uItOraN9y2jx4/lZNnzuvbVSpQ9xRA/Hn27JkMGzZMZs2aJSEhIcb2Tz75RGbOnCnZs2dn+AEAAAAAAKwhyOxz/6Hs2n/ItO3BQ71ExNHBQU/492Gd6vHdNQCJ1IYNG6R79+5y/fp1Y1u2bNl0wFkFmQEAAAAAAGBFQeZ6NavIrrVL9O1t/+6T0ZNnSt0alWW0xxcm26lL0lOmSC7Zs2aWpImwHjOA+Ofj4yP9+vWT3377zaRdlcuYNGmSpE+fnrcBAAAAAADA2oLMqZwcpWD+PPq2v/8r6d6pjZQoUsjYFhFfXz85e/GKlC1ZNL67ByARUOUwlixZogPMDx48MLYXKFBA5s+fL3Xq1LFo/wAAACKiJiYGAACwBWad+K94kYJ6icx/R0/Kkj/Wyp8bt0v9WlVk3pQx5uwegATo6tWrujTGpk2bjG3qaomBAwfKqFGjxNHR0aL9AwAAiEytWrUYHAAAYBPMGmSOyP2Hj2TlX3/Lb6vWybmLV4ylM3Jmz2rprgGwYUFBQbrGsprcz9fX19heunRpWbhwoZQtW9ai/QMAAHiXixcv6nWpUqUYLAAAYNUsEmQODg6WHXu8dGD57+27JSAwULeXLFpImjWqJ80a1hPnbFks0TUACcCpU6d0neX9+/cb21KmTCmjR4+WAQMGiL29vUX7BwAAEBVubm567eXlxYABAACrZtYg87Wbt2XZ6g2yfPV6uXnnnm7LlDG93H/wSD7+oJZ4fv+1ObsDIIHx9/eXCRMmyPjx4yUgIMDYXrNmTVmwYIEULBh5uR4AAAAAAABYaZDZ/9Ur2bhtlyxdtU7+3fefnoBLTQbYoVUT6fBpU7l05bp09xita6QCQEzt27dPZy+fPn3a2JYmTRqZMmWKdO3aVZIkScLgAgAAAAAA2FqQ+cChY9K5zzB5+PiJ/rlUscI6uNy8UT1xcno92ZYKMgNATD1//lzXXZ45c6Y+iWXQrFkzXZPZ2dmZwQUAAAAAALDVIPPtuz46wJwhXVqZ9e1IqV2tYnw+HYBEZtOmTeLu7i7Xrl0ztmXNmlUHlz/55BM9iSgAAAAAAABsOMicPl1aSW5vrwPNHXsNkQZ1qkm7Fo2lZpXyXLoeAV9fX/Hz89O3VT1ZSogAEbt//77069dPlixZYtLepUsXXR4jffr0DB0AALB5TZs2tXQXAAAALB9kVsHkozvWyMq//pbfVq2TdZt36CWnczb57JOPpe0nH8Xn09ucyZMny5gxY4w/58yZ06L9AayNKoexdOlS6du3rw40G+TPn1/mz58vdevWtWj/AAAA4pL6zAMAAGAL7EJCFzGNZ4eOnZTf/lgvf27aJs99/XSmbt5cznLxynVp2rCuzJvy/wBrYs9kbtiwoR6fAwcOSGKpq6ukSpXK0l2BlVIlMXr06CEbNmwwtqnJ/AYMGKBPzjg6vq7zDvNgnwVsD/stYHvYbwHbw34L2Bb2WRsNMhv4+r2QPzdukyV/rJVDx07ptmTJkkr1ii7S/KP60qheTUn1ZmLAxKpy5cp6vW/fPkkM2KkRmeDgYJk9e7YMHTrU+HeilCxZUhYuXCjlypVj8CyAfRawPey3gO0xXKW1bds2S3cFQBRxvAVsC/ts3EkiFuDk6CCftfhY1v82T3b++Yu4d2wtaVKnln/2eEmfYd9IiRqNZcaCXyzRNQBW5PTp01KtWjXp3bu38R9/ihQpZPz48fLff/8RYAYAAAnas2fP9AIAAGDtLBJkDu399/LJmCG95ej21TJv6hipVaWC+L8KkFNnL1i6awAs5NWrVzJ27FgpU6aMSTZ/9erV5dixYzqr2d7envcHAAAAAAAgoU/8Fx3Jk9tL0w/r6uX6rTty7uJlS3cJgAXs379fXF1d5dSp16V0lDRp0sikSZPEzc1N12EGAAAAAACA9bCaIHNouZyz6QVA4qHKYYwYMUJmzJghoUvFN2nSRNdkzpEjh0X7BwAAAAAAABsKMgNIXP7++29xd3eXq1evGtuyZMkiM2fOlJYtW4qdnZ1F+wcAAGAJ+fPnZ+ABAIBNIMgMwGIePHgg/fv3l19+MZ3os1OnTjJ16lTJkCGDxfoGAABgaZ6enpbuAgAAQJQQZAZgdqocxvLly6VPnz7i4+NjbM+bN6/Mnz9f6tevz7sCAAAAAABgI5hBC4BZXb9+XddZbtu2rTHArCbzGzBggJw8eZIAMwAAwBtfffWVXgAAAKwdmcwAzCI4OFjmzp0rX375pTx79szYXqJECX0paIUKFXgnAAAAQtmzZw/jAQAAbAJBZgDx7syZM+Lq6mryRSl58uQycuRI8fDw0LcBAAAAAABgmwgyA4g3r169kkmTJsm4ceP0bYNq1arJggULpHDhwow+AAAAAACAjSPIDCBeeHl56ezlEydOGNtSp04t3377rbi7u+s6zAAAAAAAALB9RHkAxClfX189iV/lypVNAswff/yxnDp1Snr06EGAGQAAAAAAIAEhkxlAnNm8ebPOUr5y5YqxLXPmzPLDDz/Ip59+KnZ2dow2AABAFK1Zs4axAgAANoFMZgCx9vDhQ+nUqZM0aNDAJMDcsWNH8fb2ltatWxNgBgAAiKY0adLoBQAAwNqRyWxlZQb8/Pz07YCAAEmaNKmluwS8VUhIiPz+++/Su3dvuXfvnrE9T548Mm/ePB10BgAAQMyoz1lK586dGUIAAGDVyGS2IpMnT5YsWbLo5dChQ3Lr1i1LdwmI1I0bN6Rp06Y6S9kQYFblMPr16ycnT54kwAwAABBLc+bM0QsAAIC1I8hsRTw8PHSwTi0uLi7i7Oxs6S4B4QQHB8vcuXOlaNGisnbtWmN78eLFZd++ffL9999LqlSpGDkAAAAAAIBEgnIZVsTJyUkvir29vaW7A4Rz9uxZcXNzk127dhnbkidPLiNGjJAhQ4bo2wAAAAAAAEhcCDIDeCdVI1yVcxk7dqz4+/sb26tUqSILFizQWc0AAAAAAABInAgyA3ir//77T7p27SrHjx83tqlyGBMnTpQePXpIkiRU3QEAAAAAAEjMCDIDiJCvr6+MGjVK11hWdZgNGjVqpCegyZ07NyMHAAAQj9RVZAAAALaAIDOAcLZu3SrdunWTy5cvG9syZcokM2bMkDZt2oidnR2jBgAAEM+qVavGGAMAAJvAde4AjB4+fChdunSR+vXrmwSY27dvL97e3tK2bVsCzAAAAGacdFktAAAA1o5MZgASEhIiK1eulN69e8vdu3eNI6JKYsybN08+/PBDRgkAAMDM1PwXipeXF2MPAACsGpnMQCJ38+ZNad68uXz66afGALMqh9GnTx85deoUAWYAAAAAAAC8FZnMQCKlJvPz9PQUDw8Pefr0qbG9aNGiur1y5coW7R8AAAAAAABsA0FmIBE6d+6cnthv586dxjZ7e3sZPny4fPnll5IiRQqL9g8AAAAAAAC2gyAzkIgEBATI1KlTZfTo0eLv729sr1Spks5eLlasmEX7BwAAAAAAANtDkBlIJA4dOiSurq5y9OhRY5uTk5NMmDBBevbsKUmTJrVo/wAAAGCqZcuWDAkAALAJBJmBBM7Pz09nLqsMZlWH2eDDDz+UuXPnSp48eSzaPwAAAERMJQIAAADYAoLMQAK2fft2XXv54sWLxraMGTPK9OnT5bPPPhM7OzuL9g8AAAAAAAC2L4mlOwAg7j169EiXxqhbt65JgLldu3bi7e2t1wSYAQAArFujRo30AgAAYO3IZAYSmD/++EO++OILuXPnjrEtV65cujQGX1IAAABsx8uXLy3dBQAAgCghkxlIIG7duiWffPKJniDGEGBW2cq9e/eWU6dOEWAGAAAAAABAvCCTGbBxISEh4unpKR4eHvLkyRNje5EiRXR7lSpVLNo/AAAAAAAAJGwEmQEbduHCBXFzc5MdO3YY2+zt7WXo0KEybNgwSZEihUX7BwAAAAAAgISPIDNggwIDA2Xq1KkyevRok1p9FStW1NnLxYsXt2j/AAAAEHsFCxZkGAEAgE0gyAzYmCNHjkjXrl312sDR0VHGjx+vJ/xLmjSpRfsHAACAuDFv3jyGEgAA2AQm/gNsxIsXL2TIkCFSvnx5kwDzBx98oCf269u3LwFmAAAAAAAAmB2ZzIANUDWXVe1lVYPZIEOGDDJt2jRp37692NnZWbR/AAAAiHtffvmlXs+cOZPhBQAAVo0gM2DFHj9+LB4eHrrOcmht27bVAeYsWbJYrG8AAACIX15eXgwxAACwCQSZrYivr6/4+fnp2wEBAZQ+SORWr14tvXr1ktu3bxvbcubMKXPmzJGPP/7Yon0DAAAAAAAADKjJbEUmT56sM1PVcujQIbl165aluwQLUEHlFi1ayCeffGISYFYBZ1V7mQAzAAAAAAAArAlBZiuiyiLcu3dPLy4uLuLs7GzpLsGMQkJCZOHChVK0aFFZtWqVsb1w4cKye/duXYsvTZo0vCcAAAAAAACwKpTLsCJOTk56Uezt7S3dHZiRmtCvW7du8s8//xjbkiVLpid7GT58uKRMmZL3AwAAAAAAAFaJIDNgQYGBgfL999/LqFGj5MWLF8b28uXL68n+SpYsyfsDAACQSK1fv97SXQAAAIgSgsyAhRw9elRcXV11/W0DR0dH+frrr6VPnz5M/AgAAJDIOTg4WLoLAAAAUUJNZsDMVMby0KFDpVy5ciYB5vr168vJkyelf//+BJgBAAAgS5cu1QsAAIC1I5MZMKOdO3eKm5ubnD9/3tiWPn16XTKjY8eOYmdnx/sBAAAAbcGCBXqtPj8CAABYMzKZATN48uSJuLu7S61atUwCzK1btxZvb2/5/PPPCTADAAAAAADAJpHJDMSzP//8U3r27Cm3bt0ytuXIkUNmz54tTZo0YfwBAAAAAABg08hkBuLJnTt3pFWrVtKsWTOTAHOPHj3k1KlTBJgBAAAAAACQIJDJDMSxkJAQWbRokQwcOFAePXpkbC9UqJB4enpK9erVGXMAAAAAAAAkGASZgTh06dIl6datm2zbtu3/O1myZDJkyBAZMWKEpEyZkvEGAABAlIwfP56RAgAANoEgMxAHAgMDZfr06fLVV1/JixcvjO3lypXT2culSpVinAEAABAtlSpVYsQAAIBNoCYzEEvHjx+XypUry6BBg4wBZgcHB5kyZYrs27ePADMAAABiRM3joRYAAABrRyYzEEMvX76UcePGyaRJk3Qms0HdunVl3rx5UqBAAcYWAAAAMda7d2+99vLyYhQBAIBVI8gMxMCuXbvEzc1Nzp49a2xLly6dfPfdd9KpUyexs7NjXAEAAAAAAJAoUC4DiIanT59Kjx49pEaNGiYB5latWom3t7d07tyZADMAAAAAAAASFTKZgShau3atDjDfvHnT2Obs7CyzZ8+Wpk2bMo4AAAAAAABIlMhkBt7h7t270rp1a2nSpIlJgNnd3V1Onz5NgBkAAAAAAACJGpnMQCRCQkJk8eLF0r9/f3n06JGxvWDBgrJgwQKpWbMmYwcAAIB406ZNG0YXAADYBILMQAQuX76sM5W3bNlibEuaNKkMHjxYvvrqK3FwcGDcAAAAEK+6devGCAMAAJtAkBkIJSgoSGbMmCEjRowQPz8/Y3vZsmVl4cKFUrp0acYLAAAAAAAACIUgM/DGiRMnpGvXrnLw4EHjmKRMmVLGjh2rS2YkS8buAgAAAPP54IMP9Hrv3r0MOwAAsGpEzZDo+fv7y9dffy0TJ06UwMBA43jUrl1b5s+fL++9916iHyMAAACYX+jPpgAAANaMIDMStT179oirq6ucOXPG2JY2bVqZOnWqdOnSRezs7CzaPwAAAAAAAMDaJbF0BwBLePr0qfTq1UuqVatmEmBu0aKFeHt767IZBJgBAAAAAACAdyOTGYnO+vXrpXv37nLjxg1jW/bs2WXWrFnSvHlzi/YNAAAAAAAAsDUEmZFo3Lt3T/r27SvLli0zaXdzc5NJkyZJunTpLNY3AAAAIKyiRYsyKAAAwCYQZEaCFxISIr/++qv069dPHj58aGxXE/qpif3UBH8AAACAtZk5c6aluwAAABAl1GRGgnblyhVp2LChdOzY0RhgTpo0qQwZMkSOHz9OgBkAAAAAAACIJTKZkSAFBQXpzI/hw4eLr6+vsb1MmTLi6ekpZcuWtWj/AAAAgHcZNGiQXs+dO5fBAgAAVo0gMxKckydPiqurqxw4cMDYljJlShk9erQMHDhQkiXjzx4AAADW7/Dhw5buAgAAQJQQbUOC4e/vL+PHj5cJEyZIQECAsb1WrVq69nLBggUt2j8AAAAAAAAgISLIjARh7969OnvZ29vb2JY2bVqZPHmydO3aVZIkofw4AAAAAAAAEB+IvMGmPXv2THr37i3VqlUzCTA3b95cTp8+LW5ubgSYAQAAAAAAgHhEJnMcCQ4Oltu3b0uaNGkkderUcfVr8RYbNmyQ7t27y/Xr141t2bJl0xP+tWjRgrEDAAAAAAAAzIBM5jiwcuVKyZEjh7i4uOgg5yeffCJPnjyJi1+NCPj4+Ei7du3ko48+Mgkwq7IYKnuZADMAAAASgr///lsvAAAA1o4gcywdOXJE2rZtK1999ZXcuXNHrly5ImfPnpUuXbrEzTsEo5CQEPn111+lSJEi8ttvvxnb8+fPL9u2bRNPT09Jnz49IwYAAIAEwd7eXi8AAADWjiBzLE2bNk0KFSokPXv21D9nzpxZRo4cKatWrZLLly/HxXsEEbl69arOXO7QoYM8ePBAj4mazM/Dw0NOnDghderUYZwAAACQoCxevFgvAAAA1o4gcyzt3LlTatSoYdJWs2ZNvd61a1dsf32iFxQUJDNmzJBixYrJxo0bjeNRqlQp8fLykkmTJomjo2OiHycAAAAkPIsWLdILAACAtUvwE/89f/5c9u3bJ76+vpI3b14pXbp0lB6nspDPnz8vKVOmlJIlS0q6dOki3E7VBFb1mENTdZmTJk0q165di5PXkFidOnVKXF1dZf/+/ca2FClSyOjRo2XgwIFcOggAAAAAAABYgQQZZPbz85Pvv/9eNm/erAPMAQEBxonhVN3et7l06ZLebseOHca25MmTi7u7u0yePFkHOQ3U7w0ODtb3h6XaXr58GaevK7Hw9/eXCRMmyPjx443vnaIyxhcsWKDLkwAAAAAAAACwDgkyyHzv3j0ZMWKEvp0qVSrJmTNnlOojq1q/qravqv/r5OQklStXlqdPn8rBgwflhx9+EB8fH1m6dKlxezUJhwo6qyzp0AIDA3WAOXXq1PHw6hI2lbWsgvynT582tqVJk0aXxXBzc9N1mAEAAAAAAABYjwQZsVMB4mHDhuls5IcPHxon5XuXcePG6QBz8eLF5eLFi7JlyxY5cOCAbNu2TQeTly1bpm+HprJq1bahqYB2SEgIGbfRLGsyePBgqVKlikmAuWnTpvpnlUlOgBkAAAAAAACwPgkyyJw5c2b55ptv9AR8Kts4KlT28S+//KJvz549W7JmzWq8r3bt2tKrVy99+8cffzR5XKNGjXQwOnRpjLVr1+paziorGu+2adMmqVChgsyZM0cH55UsWbLIihUrZPXq1eFqXgMAAACJgSrXpxYAAABrlyDLZcTEiRMndNazCm5Wr1493P2tWrWS7777Tv7991+T9gEDBsjixYulY8eOOntaTRY4duxYGT58uKRNm/adz6tKckTk5MmTUqRIEZ3hm5Cp19mwYUOTtvbt2+uTBBkyZAhXigSA9dS+B2Bb2G8B26O+DygJ/TsBkJBwvAVsS2LcZ1OlShUvvzdBZjLHxNmzZ/ValcqISIkSJfT6xo0bJoFPFZTes2ePzlxWwdHp06fr+sEqyIx3U+Pdpk0bfTt37tzy119/6YxmFWAGAAAAEnsijFoAAACsHZnMbzx+/FivM2bMGGmdZxVIVmUxnjx5on82yJcvn85mjol9+/a9NcM5vs4uWBM1qWKuXLlk4MCBJmVKAFi/xPA/Ckho2G8B2zF06FC99vLysnRXAEQTx1vAtrDPxh5B5lA1mfWAJIt8SAz3BQQExMHQwyBTpkwycuRIBgQAAAAAAACwQZTLCHPG4tmzZxEOVFBQkLFOS+rUqc31/gAAAAAAAACAVSPI/IaqB6xcvHgxwoG6cuWKBAcH6wBz+vTpzfcOAQAAAAAAAIAVI8j8RpkyZSRp0qRy5swZuX37driB2rp1q3E7Ozs7875LAAAAAAAAAGClCDK/obKTa9euLSEhITJmzBiTQXr+/LlMmTJF327RokW8vRm+vr7i4+OjF1X3WWVOAwAAAEic2rdvrxcAAABrl2An/tu+fbs8ffpU3z516pReX716VdasWaNvJ0mSRJo0aWLyGBVcVo+bN2+ePHjwQJo1a6ZrNM+aNUsuXLigS2q4ubnFW58nT55sEuDOmTNnvD0XAAAAAOvWpUsXS3cBAAAgSuxCVOpuAlS8eHFjcDkiqjRGYGBguPb58+fLF198oTOJQ8uRI4ds2LBBSpYsKfGZyWyYXLBhw4a6jwcOHJDEQGWLh56AEYB1Y58FbA/7LWB72G8B28N+C9gW9tm4k2AzmevWrSvvvfdepPerAG5EunXrJrVq1ZIlS5bIuXPnJEWKFFK+fHl9mVratGnjscciTk5OelHs7e3j9bkAAAAAWLc6derotZeXl6W7AgAAkDiDzNOnT4/xYwsVKhSuLjMAAAAAAAAAIDwm/gMAAAAAAAAAxBhBZgAAAAAAAABAjBFkBgAAAAAAAADEWIKtyWyLfH19xc/PT98OCAiIdHJCAAAAAAlfyZIlLd0FAACAKCHIbEUmT55sMuFgzpw5LdofAAAAAJYzbdo0hh8AANgEymVYEQ8PD7l3755eXFxcxNnZ2dJdAgAAAAAAAIC3IpPZijg5OelFsbe3t3R3AAAAAFhQv3799NrT05P3AQAAWDWCzAAAAABghY4fP27pLgAAAEQJ5TIAAAAAAAAAADFGkBkAAAAAAAAAEGMEmQEAAAAAAAAAMWYXEhISEvOHI75kzZpV/Pz8pHjx4olikIOCgvQ6adKklu4KgChgnwVsD/stYHtOnDih1yVKlLB0VwBEEcdbwLYkxn22ePHismDBgjj/vWQyW6n06dOLo6NjhPcFBwfLjRs39DomYvr46D4uOtt7e3vrBXH3fiWWfsbn88bl77bEfss+aznst5Ybm7j6/RxrEx/2W8uMja0fa2PyuOhsb2dnpxfE3ftlbnxGTnz7Ld9t427cLYX9Nv7Gh302gVOZzLAt9+7dU9nnem3Ox0f3cdHZvlKlSnpB3L1fiaWf8fm8cfm7LbHfss9aDvut5cYmrn4/x9rEh/3WMmNj68famDyOz8hxg33WcuPDfvt2fLc1z99OfOK7bfyND8fahI1MZgAAAAAAAABAjBFkBgAAAAAAAADEGEFmG6RqNY8aNSrSms3x9fjoPi62/YRtjaOl+hmfzxuXv9sS+y37rOWw31pubOLq93OsTXzYby0zNrZ+rI3J42zlb83a2co48hk5fseH/da2sN9abnys5XjLPpuw2amaGZbuBFC5cmU9CPv27WMwABvAPgvYHvZbwPaw3wK2h/0WsC3ss3GHTGYAAAAAAAAAQIyRyQwAAAAAAAAAiDEymQEAAAAAAAAAMUaQGQAAAAAAAAAQYwSZAQAAAAAAAAAxRpAZAAAAAAAAABBjBJkBAAAAAAAAADGWLOYPBazLmTNnZOPGjXLjxg3JmzevtGnTRjJnzmzpbgF4iyNHjsiPP/4o+/fvl7Zt28qAAQMYL8BKnD9/XpYtWyYPHz6UUqVKSbt27cTe3t7S3QIQicePH+t9dsWKFfL06VP577//GCvABj4Lb926Ve7evSsFCxbU32HTpk1r6W4BiMQ333wj169f17dTp04thQoV0t9jU6VKxZiRyYyEok+fPvoL8LFjx8TZ2VkHmwsUKCCbN2+2dNcARGLs2LHSpUsX/YH60qVLcu3aNcYKsBLqC2/JkiXlypUrkjNnTvn222+ldu3a8vLlS0t3DUAE7t27J0WKFJGjR49Krly55NChQ4wTYOVUQLlq1ar6c3C2bNnkt99+k/fee08OHjxo6a4BiMT7778vpUuX1kvGjBll7ty5+vvs5cuXGTMRsQsJCQlhJGDrmjdvLgMHDpRq1aoZ2z7++GPx9vaWixcvWrRvACL27NkzffZXUR+s1QftadOmMVyAhQUHB0v+/PmlXr164unpqdvu3Lmjv/iOGzdO+vfvb+kuAggjICBAgoKCJGXKlDJx4kQZOnSo8DUPsG5169aV77//Xp/UNRx/K1euLMmSJZM9e/ZYunsAouDFixc68KySMX7++edEP2bUZEaCsGDBApMAs1KzZk19Vtjf399i/QIQOUOAGYB1UeVrrl69Kp07dza2qRNBH374oSxdutSifQMQMVXKRgWYAdiO5cuXGwPMSpIkSfR3WpUoBcA2ODg4SLFixUhufIMgMxKETJkyhWtTZ3/z5MkjKVKksEifAACwRar0lFK8eHGTdvXziRMnLNQrAAAS/nfYvXv36hqvAGzDgwcPdImqWrVqWborVoGJ/xAtavKfbdu26VrHaqI9dRmeqh2VO3futz5OZRP/9NNP+rGPHj3SdZObNWsmn3zySby8A3/++adepk6dGi+/H7AVT548Me6zqsaquuQ9R44ccvbs2Xc+dvfu3XofUhMHvXr1Sn/g7dq1q3Tq1MksfQcQ8XFY7ctqn1b7sToOq0wotV+/jaqlrCbZ3L59u54cTG2vSk2pY3FEz2FnZxdu4qF06dLp3+Pn5yeOjo68PUAUqP0t9HFYTe6lkiBOnTr1zsf++++/+jisvryqchjqclxXV1fp2LEjYw/EI1W2Qu13ar9V+6Gvr680btxYhgwZ8s7HqnrK6pL5c+fO6asLypUrJ926ddNXBL3LvHnz9NVES5YsiaNXAiSushU7d+7U+63af1UJqTFjxuiyNG+jPkv/8ccfOn5069YtXWdZlYxT33mTJ08e4WPU/v3dd9/p8o///POPtG/fXkaNGhVPr8y2EGRGlH399dd6x1EH3dDUl8238fHxkTp16sjJkydN2n/55Rf95fb333/XdadCGz58uD4j9DaNGjWSJk2ahGtXATG1k6vf3a9fvyi8MiDhUnXdwl5ypz4ov8uiRYv0pHyh6zmqSYVU4HnHjh36pJEKQhncuHEjwmBVRB+eXVxcov06AIiMHj1a10QOexxWH6rfRgW11HH49OnTJu2LFy+WFi1ayLJly0yOw+pyXbXvqyX0fm74f6DuBxA1FSpUkPPnz0f7OKzqoavAVNjj8K5du/SX6IULF/IWAPHg9u3b+soddcI1tMKFC7/zsWqS3LD10NeuXavnHFm/fr3+XB6ZLVu2SO/evfV+/9lnn8XyVQCJy+rVq6Vt27bhSqWqWNTbqEQq9Vl43bp1Ju0qRjV79mx9klgFncNKlSqVnvjv6dOn+tistlfJG9WrV5fEjiAzokxlQKqsJnUmqH79+voAGvbgG5EOHTroALPKdh4xYoSeTEid4VVB6zVr1uizS+pLc2hFixbVZ4XeJnv27OHa1BdoVTOyUqVK+kszX4SR2KVJk0YHfz/44APJmTNnhCdmwlK1WLt3764/IPfo0UNPqqkOpCtXrtS3VXaG+h/Qrl0742MyZ86sZ9Z9Fy7/A2J3HFbZxIbjsIeHh75a4V3UvqqOj3nz5tUncdXay8tLvvnmG525odahsy+yZs2q1/fv39f7dugP6up/CnVfgahTn53VF091HFaZjOr2u6g5RXr16qWPw1988YWebFNdPbBixQq936urEtTva926NW8FEMdUkEpdgaAykNV+pjIbVfLFu6grFb788kt9293dXe/rKgA1ffp0XcZRfR5XJ5zUcTSsffv26e1VsGvOnDm8p0A0qQRFFftR+6xaVCxIJR++y8iRI3WAWc0VpGJVKhnqwoULOj6lysepbGZ1oigsdWW++r6sDB48WO+7Ku515coV3rsQIIru3LkTEhQUZPw5a9as6hRtiLe3d6SPOXDggN7G0dEx5NKlSyb3/fnnn8b7nj17Fuv34eLFiyHOzs4hNWrUCPH19Y317wMSguDgYOPtEydO6H0uR44cb33MoEGD9HaNGjUKd9+kSZP0fWXKlInTfqr/J3379o3T3wkk9ONwxowZ9f54/vz5SB+zZ88evU2qVKlCrly5YnLfH3/8Ybwv9HHz2LFjun3jxo0m23/wwQchderUidPXBCSm4/CRI0f0vpUnT563PqZfv356uyZNmoS7b/z48fq+8uXLR/r4CRMm6G0ARN/Lly9D7t+/b/x58uTJen/q2rXrWx9XvXp1vZ2Hh0e431e8eHF9n/ocHZb6v5AuXbqQZs2ahQQEBPCWATHw4MEDva8ZNGjQQO9zS5cujfQxT548CUmZMqXe7u+//za57+zZsyEpUqTQ9x0+fPidz//tt9/qbV+G6kNixfWOiDKV2RTdzGB12YLSpk0byZcvn8l9KqNSzcKpym2oujmxcfPmTZ3ZpbKl1aVI1IoEXgt9qXtUqX1IUVlUYanMDHVZ/ZEjR3RmBwDbOA6rS29VHdjQ1LwIqsbr8+fPdQaWgZrpXmVyqMt7DaU5jh8/ri8ZVGV0AFjuOKyuMEqaNKm+KlBdogsgbqlJ4yO6PP5t1JU+qqScOkarrMawv09dCRj6mGyg5lZQWZdVqlTR8yuELSEJIGoyZMig97Xo2Lhxo55rpGzZsno/DHv1bcuWLcPttypjWu3roal4liqXUaZMmWj3ISEiyIx4dfjwYb2uWbNmhPcbZuBUAavYUJcCq0sT1CXAgwYN0pcuGJZ31XYGYHqJoJrIQFFlZ8JSl/ipk0PKiRMnYjV0agIydSmiWtR+unTpUn27atWqvCWAhY/Dat4ENTFZxYoV9eV/NWrUkM6dO1MnEohn6suqulQ3suOwKpljqA0b9jj80Ucf6ePozJkz9c+GY+yqVat434B4dPToUV3eRn1GzpQpU6THWnX5feh6zU2bNtWfgVVpqj59+ph8hw0MDOQ9A6zsM7I6ETR27FidjKE+H6tAtEriUEkZTNj5GqfKEK/UZGBK2CxmA0O7YbuY6tmzp86WjkhkM4ICiDgTQ83E6+DgoM8IRyRXrlz6Q7KaTCw21NneiOo4U0sdsPxxuEiRIjrDSmU4q/kXBgwYoPdZAPFLZSerIJSqDxlR7VbDcVidBAp7HJ4wYYKexCissFcxADDvsVZdbauuQFAnkdQx1ZApreY4imzy3phcBQEgfj8jq3kW1FX43t7e+uSSvb29ruWsJgHEawSZEa8Ms2c7OTlFeL+aTExRl+rGxqeffhqrxwN4zfBB920Te6kAtKI+KMdG+vTpdYYVAOs8DqvSU1GZLBSAdRyHVakbANZ3rFUJFGq/VcdatRiCzJ9//rlZ+wkgbj4jq2QMtSA8ymUgXqkzO0pkl/sEBAToNdnGgHUwfKlVZTMio2pXhf6SC8B6cRwGbAvHYSDhHWsVvvcC1oXPyPGDIDPilcpUVCKbmMTQbtgOgGWpOnLq8jyVHfXkyZMItzFM+KfqxwGwbhyHAdtiOLY+ffrUmGUVFsdhwLaOtWp/Vgkc6jO2qqsOwPL4jBw/CDIjXhkuIVD1WyNiaDdMYALAslR2coECBfTt//77L8LLeE+ePKlvGyYABGC9OA4DtkVdnqsmso7sOKwCz6dPn9a3OQ4D1nWsVZNxhp7YL+x3XlWbmSsBAevAZ+T4QZAZ8ap27dp6vWLFinAH3Pv37+sJhZQ6derwTgBWokGDBnrt6ekZ7r7FixfrTAx1UGYiIcB2jsPLly8Pd5+aNGz79u0m2wGw7uPwokWL9GX3JUqUkBw5cligdwDCUid8smbNqif1U5OChbV06VK95jsvYD0Mn33//vtvefz4scl9wcHBxs/O7LfRQ5AZ8eqTTz7RExscP35cvvzySwkKCtLtz549k44dO+pL8qtUqSJFixblnQCsRK9evfQM2MuWLZOxY8fqyQ7UvvvHH3+Ih4eH3qZPnz6W7iaAKGjZsqW+HPDIkSMybNgw43FYXbqrjsOqxnqNGjXk/fffZzwBK/HFF1/o4/Cvv/4q33zzjc5eVvvu77//rj9PKxyHAeuhJvbr0qWLvt2zZ0+5ePGi8T71+Xn+/Pn6tqurq8X6CMBU6dKlpXz58jo2pSbhNEzwp2qrDxw4UM6ePStZsmRhEuxosguJ6HoOIAIHDhzQO5uBl5eXzqQoW7as8bKf9u3bS/fu3U0e99tvv0m7du30bbWTqsuEzpw5o3didUngrl279A4OIO4NHz5cpk+fbjwjq8pdqHpwjo6Oxm3WrVsntWrVMnnc5MmTZfDgwfq22l59eDYEpxo1aiR//fWX/gIMwHz27t1r3C8Nx2X1QdjFxcU4WZj6kOzm5mbyuF9++UUHlBWVaZUrVy7jcTh16tSyZ88enRUJIO4NGTJEZs2a9dbj8MaNG6V69eomj5swYYI+MRTRcbhx48ayZs0a3QYg7qlj5qVLl/TtmzdvypUrV/Tx87333tNtyZIlkx07dpg8Rp28rVixoj6+qvuLFy+ug1eGgLO7u7vMnTuXtwuIB+oqgiZNmhh/PnXqlM5OVkkUas4hpVKlSjJlyhSTxx06dEgnW6jkxzRp0kihQoXk6tWr4uPjo4+9Kunq008/5T2LhmTR2RiJ26NHj/QX0bAOHz5svF2tWrVw93/22Wd65k6VAal2WMOECOXKlZPZs2cTYAbikSptEXbiIHVuMXRbRDNhq/01f/78MmnSJL2Pqy+2qlZz165dZdCgQQSYAQt9gI7oOKw+IBuEPWGkdOjQQZInT64D1NeuXdNlMpQKFSrInDlzCDADFj4OG4LHoQ0dOlQHtNRJX3UlggpQq59VJqRK+iDADMQf9dlXBalCU8dOw/EzokQLFaD6559/9JUI6iTQ0aNHdXvatGmlf//+MmLECN4yIJ68evUqws/IKhtZLYpKcAxLJWqo0nHqCgS13xvmQsiXL59MnTpVmjdvznsWTWQyI8rUmSDDhF+RUdlRkdVpVR+oL1y4oH+Ps7MzdeQAMx1w1fI26kqEt2Ulq31XfQFWWRkALHuyN+yX3rDU1UJqiQjHYcD8OA4Dtked2Al7cig0leFYtWrVtx6vVSZ0ihQpdGakOtELIP6oK+zVFX5vo8rHvW3C3OvXr8udO3ckQ4YMOrkKMUOQGQAAAAAAAAAQYxTyAgAAAAAAAADEGEFmAAAAAAAAAECMEWQGAAAAAAAAAMQYQWYAAAAAAAAAQIwRZAYAAAAAAAAAxBhBZgAAAAAAAABAjBFkBgAAAAAAAADEGEFmAAAAAAAAAECMEWQGAAAAAAAAAMQYQWYAAAAAAAAAQIwRZAYAAAAAAAAAxBhBZgAAgHeYMH2ezFjwS7TG6aW/v3z93RyZv3hFghvfmIyHNT6HNbOm13/t5m39t3zo2ElLdwVx6PZdH/2+/v7XJpsa1wuXr+l+n/A+Z+muAACAUOxCQkJCQjcAAADYOhXgnTr7J1Efc2pVqSDVKrnE6vflKFlTsmTKIEe2r47yY548fSbvV24o77+XT3b+aR3BwrgSk/GwxuewZtb0+l37j5B/dh+Qg1tWSoZ0aY3t0+b9LM99/SJ9XJrUqaSPW4dw23fv1EYyZUgf5ef3f/VKvA4fl9NnL8rjp88kbepUer+qXL60pEyRItLH/bFus3ifu2jSliJFcsmeJbNUqVBG8ufJJYnZ0ZNn5MPWrvJhneqy6IcJYitevQqQyg1bS9YsmWTD0vmW7g4AAHgjmeEGAABAQrF+y075wfNXfXv3gcOyafmCWP2+oX27iZOjg0lbcHCwjJ82T9KmSS29XdtLQhGV1xXReMS1uHoOW32frOVv7r+jJ2Xd5h06WBw6wKwsXPKH+Dx4GOljs2fNbBJkNmzfulmjKAeZf1nxp3w701PuP3gU7j7Vn4E9u0jXdi0ifOyGrf/K+i07Iv3dn3xUX74b9+VbA9WInfsPH8ncRct0QP+zFh/HyXAmT24vvd06yJfjpsqfm7ZJ0w/r8jYBAGAFCDIDAIAEZ8nKtXpdIG8uOXrSW2czFilUIMa/74uu7cK1qYDfzIVLJKdzNpsKXr5LVF5XROMR1+LqOWz1fbKWvzn1fHZ2dtLx06aRbuP+eWvJlD5duPZUqZxi9dzDvvlefvztD307Ty5nqV21omTOmEEePXkiO/celPOXrsrw8d+L97kLMmXMkEh/z0f1akrp4oX17SfPnuvA+f5Dx2TV+i26j5NGDopVPxG5R4+f6r+h6pVc4izIrLRq8qGMnTJbZv34G0FmAACsBEFmAACQoFy5dlP2/XdUKpUrLR1bNZGeQ8bKkj/WytdD+1m6a4DN1ezdsnOvVCpXSge2I9O+ZRMpmD9PnD738jUbdYBZBbiH9HbVQfWkSZMa71elcBb+9oeMnDhDfl25VkoWe186ftoswt9Vp3oladeysUnbd3MWyaSZnrJs1XoZ7fGFODqkjNP+I36pLP8P61TTJwqOnTojpYq9PokAAAAshyAzAABIUH5btU4HoNq1+Fg++qCWZJgwXf5Yu1m+GthTUiRPHq5285RZP0qWTBmlW8dPxefBI9myY4/cuH1XCubLLc0/qm+chM3J0dF46f/h46d0SQ5D7WU1CZVBrhzZ5fPW4YNdDx49lk3bdsnNO/ckQ/q0Ur9GZcmTK8db+3Pn3n3ZvGO33PV5IDmyZ5XGH9SW1G+yQ1VWq8rmVJNfqddbrWJZcSlVPNJxuXrjluza95/cvucjye3tpUjB/FKrakV96blBVF9X2PEI6/qtO7L7wCG5dfueODqmlEIF8krNyuUlWbKof/SM6DnCjs+7xjS671NUxigm/Qjt+OmzOrv+3v2Hkj5tWp1tr7I8QwdQI3r973otKpD687LVkf79KRevXJOlq9bLe/nySJvmjd75HqzesEWCgoKkYZ0aYk6BgYEyedZCfdu1XUvp5/55uG1U8Fnd9/DRE/luzk8yZdZPugxH2H08Mq7tW+og86uAALl6/abJlQ7qJJW6+kG9r1kzZ5T3C+STii6lohWcX7hkpa4brTJu1bhv37Vf15POncNZGtSuKunSpon08d7nL8m+g0f0/yMVTC1drLCuIZ0kSZK3Po+aoFE9z91793V/a1WtINHxrn6qv92/Nm3XAf0mDepE+DtUlvim7bukQpkSkiRpUtm07V/dfvnaTZO/2Yh+R1Rft0HDujV0kHnlX38TZAYAwAoQZAYAAAmGCoit+HOjpE2TSj7+oLYOOKngy7zFy2Xj1n+lWaN6Jtv7+7/Sl3KrIE2mDOlk4OhJ8uLFS31f4wa1jUHmmQt/05OwGQJ+J7zP68u0lWfPffXvMFDBlbBBvg1bd0qfYd+YTJI2etIPMmmUh3z2yccR9idzxvQyYOREefHS33j/hGnzZeWP0yVd2tTSqfdQOXLC2+R5+nbrIEP7upu0+b14qUsKqMxQFZgOLUe2LDJ3yhgpX6ZEtF5X2PEw8PV7ISMmTIvwuVQm7JI5k/Vri4qIniP0+OR0zvrOMY3q64nOGMWkH8rTZ8/1BHr/7vsv3GtVY/Pj9G+kZNH3I33973ot7Vs2ltUbtspdn/vSoHY1yZYlU7jnmfPTUp31O/2b4VF4B0T2HTyq1y6lioo5HTp2Sm7cuqMD/f26hw8wh9arc1tZ8MsKuXf/ge5vVAOrQUGh3mc7O+PJkc69h8rJM+fDba/e62Xzv9N1pt9FnRRS74+aUO/m7bsyaeZCk7+r9GnTyKxvR+oTA2HrF/cbMUG27twb7ncWLVRAFnw/TgrkzR3h89y56yMTf/DU/wMV9XcTnSCzmpTxXf1Uf6cqqO3o6KD/xiIK6E+YPl/2eB2Wv36ZLRu2/av/3hT1fob+m/20aUNjkDm6r9ugbMnXf5d7Dx6J8usEAADxhyAzAABIMLbu3Kezf7t81kIcUr6ezKt9qyY6yKwynMMGmUNnBPYdPl7y5ckp1SuVk2yZM8p7b7n836VkMT0xmwqoqID2F13+Xz/XOXtWk23v3PORHh5jJH/eXFKtQllJmTKF7NzrJcdPn5Oh476TutUrSdbMmSLsT+FC+aVqhbI6U1lNvqYCNR6jJ0lIiOh6tCobNXvWLDqbWQVofvBcIi0+bqAzhw26DRyp78uYIZ3Ur1lFnLNllRcvX8rBIyd01mG7Hh7yz+qfdaZ0dF5XWKqPXfsOlx17vXSWaa0qFXT/k9glkbMXL+vXrAJuUQ0yv01UxzSqryc6YxSTfijT5i3WAeY0qVPpDMxcObLJs2e+cv7yVfl330G5ev2WSZA5rHe9FpUJ3bntJzpb9Jff/xSPXl1NHq+C3KvWb9XZ180j2Q/CUq9dZZEWL1LordvN+3lZhJm5n7dpLrneUmYjMoaTJ6oEQsYIaj2H5uTkqE8AqAzcIydORzmwOuvH1wHPlCmSS77cr7POR307QweYVfZygzrVJWumjDqb+YzKsP3vqDx4+DhKQWaDg0dP6Kze0sWLSJXyZXQGvOrnles3pWu/4bL59x+NZUbUyaTWrv3l1NkLOpirArvqJIP6G1H71OlzF6VNt4Gy889fwpX2MDyPCrqqsVD1sV1KF4/zfqqJFlt8/IEOHK/9+x9p2biBye85d/GKDjCr31OhbEl5FRCo/y/M+3m55MudUz775CPjtoXfZI7H5nWr/VHtsyoDWp14MVzlAQAALIMgMwAASDBU7WVFZXUaqOCIqs+8a/8hfTl57hzZwz1OBeBaNmkg08YNjVJJh+JFCkrhgvl0wC91qlTSO5KyEcqTp8918O+bYf2Ml32rYGHLLn11Bt7mf/ZIhzCTqqn+uHdsLaMHf6EDtobMxMoNW4vXkRM6S3X3ut9MslW/HDdVFi1bLWs2bpPBX7wOMG7esUcHT2tWKS8/zZgQLkgzY8EvMn7aPPFcslJGDeoVrdcV1oat/+qgULo0qeWX2ZNMMn8NWaJJ3ryW2IrqmEbl9UR3jGLSD8X7/EW9VtncYcdGBd8D32SgRiYqr0X93U+d85P8+vtf0q/b52Jv//+/5eVrNojfixd6QsGw5T8iorK7Hz15qt/Pd5WgMGSrhqUC9jEJMqvArpIje5YobZ/zTfD//sPXjwtr/dadcvnaDX376XNfOXzslDFbWQXCU6Z4fULK+9wl/T5u/n1huBM/Zy9clkwZ00fvdTx8HG4/VuPauc9QXepm+oLFMnPCV7r9lxV/6kBr208+kimjB4crn6Kuavjtj3Wycu2mcLWn1fP0795J166Oiej007VDK/1+/7R0Vbggs/r/o7h3/FSvVQkfFbBXQWaV8R/R32xsXreiJoJU/VcnFwkyAwBgWQSZAQBAgqDKBGzfvV/KlCgiRd9/z+S+Dq2ayP7/jup6tBEFYlRgZeyQPtGqGRxV6pL/UR69TOqKqtuqHIcKRKrAd0SPGdbf3RjwUVQWYfkyJXVAtGfnz8KVQ2hUr4YO8ly7ecvYprKfFZU9O2P+YgmREP2zyoQ2BLMVFXSLLVUSROnTrUO4IKoSk2BjXI5pZGIzRtHpR+GC+eWf3Qd0sDLs+ITNkI4plU2sysMsXr5GNmzbKU0/rGu8b/GKP3XWbsfWpic0IvPwTaD3bbWDDdw/b62zZ8NS9aFj481b8E6GEg+RncNQWblqCU0FM1VQfkT/HsY2FcRXwejzF6+GCzLHJANf7bND+3Uz2Y/VSQz1v6Zm0w6y/d//92nd5n/0OlnSpDJ55sJwf4eGMj6Hjp0OF2xVgdaBPTpFu38x6Wfh9/JLjcrldFa+qtFsyL5XpXJ+/2uTOGfLov/+oyo2r1tJny6N8cREQYnbyScBAED0EGQGAAAJgqqnGxgYpAN/oSeYUl69CnizzQbx6NUl3ERSKjCiAi3xIXfO7MZMydAyZUhvrO8b0WMiyh419PG9fOHrk2ZI9zrI9+TJM2Pb5auvszfVpe1v8+RNIDU21KR5SiWX0hLfYjKmkYnNGEWnH/26dZQTp8/JoNGT5Lu5i6Rc6eJSvHBBXZ7ApVQxkwBfbKjJ8FR26E9LVxuDzKochyqv0q5FY2Pf3sXQH0PQ723at2xiLPsQF1TQVLkexZMFN27dNXlcWB/VqymlixfWt5MnTy7ZsmaSyi6lJUvmjCbbjR7cW67duC0tu/bVEzKWKVlUShQupIOqoScGjKpC7+WL8O9DlbNxdHCQh4+f6OCsmuTu0ptM619+/+utv/Pps//v36ED4LE5QRadfiqu7VvpILPKZv5+3FDdtnLt37pkhbriIjp9ic3rVkKCX/99xs3eAwAAYoMgMwAAsHmq7qfKUlYOHD6ul4jcunNP/tlzQOpWr2zSnsrJMd76Fvby74j6Ht3HJEsW+f2hf1twyOsMz46tm0mut2TLZoxi4DEqQt48Z3yKyZhGJjZjFJ1+pE2TWk/aeNL7vOzcd1BOnTmvywCoUhwqgPnT9PGS901t4NhQgcGalcvr0iWqVm2RgvmNZQzcOraK8u9RtW6Vx0+eirkZJnRTQXmf+w8lc6aIg8eGTHNVQsZQtzoiqs5vu1AldCKTJ6ezbFn5o65FvfvAYV3GYe7Py2TUpB+kcvnS+j2KSma3QUiYSSRN7nvzd2cI5ge/CZb2d/88XMmW0PJHMAFebP9/RaefhjIo+fPklDUbtuoSMmpMfl62WhwcUuqrRqIjNq9bUSVd4vp/GAAAiBmCzAAAwObt8TqiL3NXAbZWYeqEhq4JrEoG/PbH+nBB5pgwZnpGI6Bpbmoiw0PHTkneXM66xEZ8vq78eXIZg3MupaI+6Vh8e9frickYxYaqrawWgy0790qHnoPFY8wk+X3h9Dh5b1QwWQWZFy1dJX27ddR1p/VEjO/lj3I/VWarqkGs6t2q+rxvCwDGNVXyJk8uZz0Z4qSZnjJ59OBIt50+f7GuNa2uRqjoUirWz62uclCT1qnFwPPX32XEhOn6hMCkUR5R/l1nLlwyyQA2OH32gp7wTmVeG8ZVBW1ViZKSxd7XE0OaU3T6afg77NKupYwYP02Wrd6g3y81QV+nNs3DBeH//zcb8XPH9nXf83mgT/ZkD1M+CAAAmJ/ptaIAAAA2aOmqdXqtghxqcqmIlnFD++q6u5v/2S0+Dx7F+jlVYMMhZQodIPF/FfXyDOZkKJcwZdZPOvgbkWOnzoj3udeT0sXmdTX5sI5xorxtu/ZFGMgylNQwp3e9npiMUUxs3PavPHr8NMIgm6KCdO8S1femTrVKuqSKKmEw+6ffdBmZbm8mY4uOimVL6YC2qr1rTup1Du3rbiyj8M33c8O93sDAQB1gnv3TUv3zkN5uJhMdxoSaNFMF1MPKmzvq71HYiSHHTJ4pQaEmdVSZ18MnvD6ZUK/m/092NX2z/wz9+judgR6Weh/2eB3WJ8viWnT6adCmWSM90Z7Kkv9x6SodTHbr0CrSLOvbd+9F+Nyxed1Xr9/Umcyq7IxTPF6NAgAAooZMZgAAYNOePH0m67fs0CUkDIHOiKgaxypTTtVlXrl2k/To1DbWz60mGFRZsC0695GyJYpK8uT2erKzz1uHn6DKEtRl7WpM/tq0XVp26SOlixeRIoXy64zF23d8dOD34pXrMnXMEJOaszF5XfVqVNa1b9dv3SntunvokgdFChaQJEns5Mz5y/LfsZOyZM5kXZLA3N72emI6RtE1ccYCXf/ZpXQxyZ3DWdKlSS13fO7ryQDfVuohOq/FJNP0sxYy7JvvxfPXlVIwf16pXa1itPtctUIZvW+p56sUB1nCBvN+XhZp2QmV0dqkQR1p1rCuLinyg+evelEZs6o2ssquVsH6PQcOyc07rwOX3Tp8Kq2bNYx1v/oO+0b/H1E1snM5Z9d/A2ryxh17ovceGWTNnFEHyff9d0wquZSUF/7+snv/Iblz774OvvZz/9y4rSrXooLcaqzrNP9cKpcrretC29vby83bd+Wk9zn9ev/4aUacTqIZ3X4aqPa2zT+S+b+skCvXb+r9qEAEJS3U71alV9Q+1LbbAHm/YH49yZ/hfY7N6z58/LReV61QNk7HAwAAxAxBZgAAYNNWrt0sL/1f6SDauyY1a96ong4yq5IZcRFkHtSzi3TuM1SXiVCLUqFMCasJMiuzJo6UfLlzyPxffpejJ731ElqpYoXDBU9j+rrmTB4tY6fOkp+XrdEBIEMQSFHPoUogWMK7Xk9Mxii6GtWrqevW7jt4VC+hA8KqZrAKYsfFazFo3ayRfPvDAp2l2q1DqxhNLNi0YV0ZM3mWbNi6U3p1ibtSIr+uXBvpfZ82baiDj8rw/t2laKECMn76fD0J4B/rNptsq0pkqAzmuAgwK80a1ZN1m//Rk9qFpgLPLZs0kCF93KL1+8qUKCrVKpaV0ZNnyvlLV4zt2bJkkrlTxpiccFEnwZYv+F5GffuDLP9zg+w9eEQvoct4qGBqzjgOMEe3n6F1bddCPJeslODgYHHv2DrCbdTf3dA+3WTw2Cnyzx4vvYR+n2PzutUJLaVVk4hLJAEAAPOyC7HmQoIAAADvsPbvf+TKtRtStaKLccKwyKjLwecsWqYnuvq8TXNJkSK5zP95uZ406rMWH0f6uJkLl+isxs5tP4mwJuiuA4fk3v0HEhgQKM7Zs0qLjz/Ql/e/7XdfuHxNNm7dKaVLFJHqlcrptnc9RtXvPXPuojT7qH64rD5VAmTZqnX60v7GDWqHe6y6/H3/oWM6M1PJkS2LrtGrahJHJLLX9a7xMPRl78HDcufufUmTJpW8XyCvlI1mFmhEzxGTMY3K64nuGMW0HwEBgXLo+CldP/z5c1/JkjmjlCpaOMIJ/2LyNxdWlUZt5PGTZ3Jo2ypdZiMmug8apTNN929cHq6fC5f8IX5+ftK+VVNJn+7dE+IZtn+bwoUK6KzY0FQQ89ips7pkiXqPVJmGwgXz6eCoCkK+rUTJhUtXpW6NyjoDPCpUuYxDx07qetD+rwJ0Jm75MsUla+ao1/w9evKMfNjaVT6sU10W/TBBbt/1kZ17D+qrLnLnzC41q1R4a41rtf8cOHRMT1SqMtVVML1EkUKSPWvmcH8H6qSZmhTvo/o1o9y/yB4f3X6qOs4lazbRQejtq39+63Op0hYqU/rBo8cSHBQU4fsc1detqL8D9dzFixSSdUvmRvu1AwCAuEeQGQAAAEhgfvtjnQwYOVG6d2ojoz2+iPHvOel9Xj74tKu4tW8lY4b0jtM+JlRhg8wJlaqVrUqZfDtykNmv3pj383IZNekHWTxzonxQu5pZnxsAAESMchkAAABAAnD2wmX5/a9Nutbznxu2SXJ7e+narmWsfmfxIgV1lvTiFWt0yQyVfY3ES2X6b9mxR2fjb9j6r6633LKxectVvHjpL7N+/E0qly9NgBkAACtCkBkAAABIAC5dva7LbBhq4Y4c1DNOJolTtZEL5c8jt+/5EGRO5A4fP6UDvIp9smQyccRAXdbFnO7c9RG39i2lQZ3qZn1eAADwdpTLAAAAABJIkHn95h3i6OgoFcuW1FnIML/Y1kq2Zmoyzz0HDknatKmlesVykdZ0BwAAiQ9BZgAAAAAAAABAjEU+HTMAAAAAAAAAAO9AkBkAAAAAAAAAEGMEmQEAAAAAAAAAMUaQGQAAAAAAAAAQYwSZAQAAAAAAAAAxRpAZAAAAAAAAABBjBJkBAAAAAAAAADFGkBkAAAAAAAAAEGMEmQEAAAAAAAAAMUaQGQAAAAAAAAAQYwSZAQAAAAAAAAAxRpAZAAAAAAAAABBjBJkBAAAAAAAAADFGkBkAAAAAAAAAEGMEmQEAAAAAAAAAMUaQGQAAAAAAAAAQYwSZAQAAAAAAAAAxRpAZAAAAAAAAABBjBJkBAAAAAAAAADFGkBkAAAAAAAAAEGMEmQEAAAAAAAAAMUaQGQAAAAAAAAAgMfU/fNfrbuTcdnkAAAAASUVORK5CYII=", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "Find out whether memory or arithmetic sets the speed limit" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Arithmetic intensity (FLOPs/byte):** 5\n", "- **Peak arithmetic (GFLOP/s):** 1000.0\n", "- **Memory bandwidth (GB/s):** 100.0\n", "- **Ridge point (FLOPs/byte):** 10.0\n", "- **Attainable ceiling (GFLOP/s):** 500.0\n", "- **Share of peak (%):** 50.0\n", "- **Limited by:** memory bandwidth" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "At 5 FLOPs per byte the kernel can reach at most 500 GFLOP/s, 50% of the arithmetic peak. It sits left of the ridge at 10, so memory bandwidth is the limit: faster arithmetic units would not help. Reuse data (blocking, fusion) to move right. The roofline is a ceiling, not a prediction; measure the kernel against it." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(21,5,5)\n", "buffer=io.BytesIO()\n", "figure.savefig(buffer,format='png',dpi=140,bbox_inches='tight',pad_inches=.16)\n", "display(Image(data=buffer.getvalue(),alt='Find out whether memory or arithmetic sets the speed limit'))\n", "plt.close(figure)\n", "display(Markdown('\\n'.join('- **'+str(k)+':** '+str(v) for k,v in metrics.items())))\n", "display(Markdown(interpretation))\n" ] }, { "cell_type": "markdown", "id": "ch21-cell16", "metadata": {}, "source": [ "**Use the idea:** Use rule 21.3.1 when its stated conditions fit. Compare the calculation with your own decision threshold; retain the relevant error or uncertainty.\n", "\n", "**Assumptions and limits:** Idealized roofline; caches, latency and instruction mix omitted. A ceiling, not a measured speed.\n", "\n", "
A kernel does 1 FLOP per byte. Will a chip with twice the arithmetic peak make it faster?\n", "\n", "No. At 1 FLOP/byte it is capped at 100 GFLOP/s by memory bandwidth, far below either peak. Raise its data reuse or the bandwidth.\n", "\n", "
\n", "\n", "**Book source:** [Rule 21.3.1: Know whether a kernel is compute-bound or bandwidth-bound](source.html)." ] }, { "cell_type": "markdown", "id": "ch21-cell17", "metadata": {}, "source": [ "## Continue with the chapter workbook\n", "\n", "The original decision worksheet, additional calculation, exercises and solutions follow." ] }, { "cell_type": "markdown", "id": "ch21-cell18", "metadata": {}, "source": [ "# Chapter 21 notebook: Scientific Computing: Precision, Performance, and Reproducibility\n", "\n", "**Goal:** Distinguish arithmetic accuracy from speed and set a measurable computational contract.\n", "\n", "**Start with:** Rules 21.1.2, 21.2.2, 21.3.2. Use a calculator or the optional Python lab. Programming is optional for the workbook; the Jupyter version requires a Python 3 kernel. All lab numbers are constructed practice inputs, not observed data.\n", "\n", "**Source:** [Finished Chapter 21](source.html) from *Mathematical Rules of Thumb*. Numbered rules, classifications, and the decision path come from the book. The lab, exercises, answer key, and worksheet prompts are companion additions.\n", "\n", "## 1. Frame your decision\n", "\n", "Write a question in which an answer would change something you do. Gather: Precision and data scale; permitted absolute/relative error; reproducibility contract; profile; data movement; processor count or failure spacing.\n", "\n", "- My question and intended decision:\n", "- Known inputs and units:\n", "- Required accuracy or threshold:\n", "- What I expect before calculating:\n", "- What I still need to find out:\n", "\n", "Use the lab as a worked starting point if you do not yet have your own problem. For notation or prerequisites, ask the chapter skill to explain only the concept blocking the next step.\n", "\n", "## 2. Choose a route\n", "\n", "- **Is the claimed accuracy close to machine precision?** Combine unit roundoff with conditioning and algorithmic error; do not equate `eps` with final accuracy.\n", "- **Does an expression subtract nearly equal values?** Search for a stable equivalent such as `log1p`, `expm1`, compensated summation, or a scaled formulation.\n", "- **Do parallel runs differ?** Quantify the discrepancy, rule out races and undefined behavior, then choose a tolerance, deterministic tree, or reproducible accumulator consistent with the contract.\n", "- **Are tests flaky?** Derive absolute and relative tolerances from expected error and units, including explicit policies for nonfinite values and arrays.\n", "- **Is the program too slow?** Profile the complete representative workload before changing code, then reprofile after each intervention.\n", "- **Is a hot kernel limited by arithmetic or data motion?** Measure arithmetic intensity and hardware ceilings before choosing vectorization, blocking, fusion, or traffic reduction.\n", "- **Will more processors help?** Measure strong scaling and use the effective serial fraction to bound the gain.\n", "- **Can the run outlive reliable hardware?** Estimate checkpoint cost and job-level failure spacing, calculate a starting interval, and test actual restart.\n", "\n", "**Chapter-specific stop check:** Do not promise bitwise reproducibility from a tolerance check. Avoid reading machine epsilon as guaranteed final accuracy or a theoretical ceiling as measured performance.\n", "\n", "## 3. Work the lab\n", "\n", "For x=1e-12, compare log(1+x) with log1p(x); forming 1+x loses relative information before the logarithm is evaluated. Separately, if 10% of work is serial, Amdahl's idealized speedup on eight processors is 1/(0.1+0.9/8)≈4.706, with an infinite-processor ceiling of 10. These are mathematical ceilings under the stated model, not measured speedups.\n", "\n", "Predict the sign and scale before running the code. Then change one input and explain why the result moves. The code checks the constructed example; it does not prove the rule for every possible input. Code assertions may describe the example's chosen regime, so inspect them before changing that regime." ] }, { "cell_type": "code", "execution_count": 7, "id": "ch21-cell19", "metadata": { "execution": { "iopub.execute_input": "2026-10-03T00:58:21.407351Z", "iopub.status.busy": "2026-10-03T00:58:21.407274Z", "iopub.status.idle": "2026-10-03T00:58:21.409509Z", "shell.execute_reply": "2026-10-03T00:58:21.409456Z" }, "jupyter": { "source_hidden": true }, "tags": [ "practice-lab", "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log(1+x): 1.000088900581841e-12; log1p(x): 9.9999999999949996e-13\n", "Difference relative to log1p: 8.89006e-05\n", "Ideal speedup: 4.705882; ceiling: 10.000000\n" ] } ], "source": [ "import math\n", "x = 1e-12\n", "naive, stable = math.log(1+x), math.log1p(x)\n", "serial_fraction, processors = 0.1, 8\n", "assert 0 < serial_fraction <= 1 and processors >= 1\n", "speedup = 1/(serial_fraction+(1-serial_fraction)/processors)\n", "print(f\"log(1+x): {naive:.17g}; log1p(x): {stable:.17g}\")\n", "print(f\"Difference relative to log1p: {abs(naive-stable)/abs(stable):.6g}\")\n", "print(f\"Ideal speedup: {speedup:.6f}; ceiling: {1/serial_fraction:.6f}\")\n", "assert speedup <= min(processors, 1/serial_fraction)+1e-14" ] }, { "cell_type": "markdown", "id": "ch21-cell20", "metadata": {}, "source": [ "**My prediction, observed result, and explanation:**\n", "\n", "_Record your work here._\n", "\n", "## 4. Practise without the answers\n", "\n", "### Exercise 1\n", "\n", "Using |a-b|<=atol+rtol × |b|, compare a=1e-10 and b=0 with atol=1e-9, rtol=1e-6.\n", "\n", "**My approach, assumptions, calculation, and check:**\n", "\n", "_Write your attempt here._\n", "\n", "### Exercise 2\n", "\n", "If a fraction 0.5 of runtime can be made twice as fast, what is the ideal total speedup?\n", "\n", "**My approach, assumptions, calculation, and check:**\n", "\n", "_Write your attempt here._\n", "\n", "### Exercise 3\n", "\n", "Two parallel reductions differ in their last few bits. Is that alone proof of a race?\n", "\n", "**My approach, assumptions, calculation, and check:**\n", "\n", "_Write your attempt here._\n", "\n", "**Coaching prompt:** “Use the Chapter 21 skill to help me with Exercise 2. Ask for my attempt, give one useful hint if I need it, and help me check the assumptions before showing the answer.”\n", "\n", "## 5. Answer key and reasoning\n", "\n", "Read this after attempting the exercises, or use it immediately if you prefer a complete walkthrough. An answer is complete only when its assumptions and stopping point are clear.\n", "\n", "### Answer 1\n", "\n", "The difference is 1e-10 and the threshold is 1e-9, so the comparison passes. A purely relative criterion at zero would be unsuitable.\n", "\n", "### Answer 2\n", "\n", "1/((1-0.5)+0.5/2)=4/3≈1.333. Speeding up one component by two does not double end-to-end speed.\n", "\n", "### Answer 3\n", "\n", "No. Floating addition is order-dependent. Measure the discrepancy and compare with the error contract, while separately checking races and undefined behavior.\n", "\n", "## 6. Build the complete chapter toolkit\n", "\n", "The new lab samples the chapter; the following checklist covers all 8 rules. Study one thematic group at a time. A large group can take several sessions.\n", "\n", "- **Spend a Finite Precision Budget Deliberately:** work with rules 21.1.1, 21.1.2.\n", "- **Make Reproducibility an Explicit Contract:** work with rules 21.2.1, 21.2.2, 21.2.3.\n", "- **Model Hardware Limits and Failure Costs:** work with rules 21.3.1, 21.3.2, 21.3.3.\n", "\n", "For each selected rule, read its equation, explanation, and worked use in the source. Reproduce that example; change one input; then change one assumption so the rule is no longer justified. Record the result and what check catches the failure. Historical examples remain labeled and qualified as in the source.\n", "\n", "Read each complete numbered profile in the [chapter reference](source.html) before applying it. The cues below abbreviate the graph metadata; they are not complete conditions. Change the status only after doing the practice described below.\n", "\n", "| Rule | Book role | First assumptions to inspect | Practice status |\n", "|---|---|---|---|\n", "| 21.1.1: Budget binary64 as about sixteen decimal digits | Independent | representative workload; floating point execution | new |\n", "| 21.1.2: Use log1p and expm1 for small arguments | Independent | representative workload; floating point execution | new |\n", "| 21.2.1: Expect parallel floating reductions to change low bits | Independent | representative workload; floating point execution | new |\n", "| 21.2.2: Compare floating results with absolute plus relative tolerance | Workflow | meaningful absolute scale; meaningful relative scale | new |\n", "| 21.2.3: Profile before optimizing scientific code | Workflow | representative workload; representative build configuration | new |\n", "| 21.3.1: Know whether a kernel is compute-bound or bandwidth-bound | Workflow | representative workload; floating point execution | new |\n", "| 21.3.2: Use Amdahl's law to bound strong scaling | Independent | representative workload; floating point execution | new |\n", "| 21.3.3: Set checkpoint interval from checkpoint cost and failure rate | Independent | independent exponential failures; fixed checkpoint cost | new |\n", "\n", "For a completed row, record: **rule number / my new input / mathematical claim type / verified assumptions / calculation / check / valid use / rejected use / next step**. “Practised” means you worked an example. “Demonstrated” means you can explain a valid use, transfer it, and reject a misuse without the answer key.\n", "\n", "## 7. Apply it to your own problem\n", "\n", "Return to your opening question. Choose the smallest rule set that can settle it. Use the book's independent/workflow/specialized classification separately from the claim type (exact, approximate, bound, diagnostic, or heuristic).\n", "\n", "- Selected rule number(s) and reason:\n", "- Assumptions that hold, fail, or remain uncertain:\n", "- Substitution with units:\n", "- Result and error, uncertainty, or bound:\n", "- Independent check or limiting case:\n", "- Decision this supports:\n", "- Stop here, do a named next calculation, or gather missing information:\n", "\n", "## 8. Transfer and continue\n", "\n", "Useful nearby chapters: Chapter 7: linear algebra; Chapter 19: optimization; Chapter 20: numerical methods. Bring the question, units, assumptions, result type, and uncertainty to the next chapter. Choose a bridge only when it supplies an operation you actually need.\n", "\n", "**Completion check:** Explain this chapter's lab in your own words; solve one changed-input exercise; reject one invalid use; and produce a decision record for your own problem. If one check fails, revisit that part of the chapter rather than marking every rule complete." ] } ], "metadata": { "book_companion": { "calculation_sha256": "221161ba9a522041cf179f6a7f727cf915bbab1c2c633f469e54196e069a2d89", "chapter": 21, "example_data": "constructed", "execution": "All cells executed in order in a fresh process with a new in-process Python kernel. This is not socket-based Jupyter execution.", "reader": "reader.html", "source_sha256": "5a1868d45ebbd4be6bbea59ef12972c95c080a07e70ae9a3e777e334919016b0", "version": "2.0.0" }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.14.4" } }, "nbformat": 4, "nbformat_minor": 5 }