{ "cells": [ { "cell_type": "markdown", "id": "ch07-cell00", "metadata": {}, "source": [ "# Linear Algebra: Choose Stable Matrix Methods Before Computing\n", "\n", "*Mathematical Rules of Thumb · Jason Karpeles · Chapter 7*\n", "\n", "Choose Stable Matrix Methods Before Computing\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": "ch07-cell01", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:57:36.351770Z", "iopub.status.busy": "2026-10-03T00:57:36.351655Z", "iopub.status.idle": "2026-10-03T00:57:36.400316Z", "shell.execute_reply": "2026-10-03T00:57:36.400251Z" }, "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": "ch07-cell02", "metadata": {}, "source": [ "## C07-D01: Solve a sensitive system and inspect both errors\n", "\n", "Does a small residual guarantee accuracy relative to unperturbed inputs?\n", "\n", "The condition number κ measures how much the matrix can magnify a small input error. Nudge b by one part in 10⁸ along the direction the matrix shrinks most, and the solution moves κ times as much. The residual still looks perfect, because it only checks the equation you actually solved.\n", "\n", "$$\n", "A=\\operatorname{diag}(1,1/\\kappa),\\quad A x=b,\\quad\\delta b=(0,10^{-8})\n", "$$\n", "\n", "**Symbols and inputs:** Condition number κ. Binary64 solve of a constructed diagonal matrix. Worst-case amplification depends on perturbation direction.\n", "\n", "**Predict:** Does a small residual guarantee accuracy relative to unperturbed inputs?" ] }, { "cell_type": "code", "execution_count": 2, "id": "ch07-cell03", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:57:36.401276Z", "iopub.status.busy": "2026-10-03T00:57:36.401219Z", "iopub.status.idle": "2026-10-03T00:57:36.747230Z", "shell.execute_reply": "2026-10-03T00:57:36.747131Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABZkAAAKJCAYAAADZQidKAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjExLjIsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvgI3uAAAAAAlwSFlzAAAViAAAFYgBxNdAoAAA7ehJREFUeJzs3Qd4VFX6x/FfeqWEXkLvLZR0K4qi2BEL1br6V1m7WV1dXVnXssLu2vvaKAqKBRV7wZZOCb333iEJ6fk/50BiwgQIKVOS7+fhPncy587MmXNvLpl33vser+Li4mIBAAAAAAAAAFAF3lV5EAAAAAAAAAAABJkBAAAAAAAAANVCJjMAAAAAAAAAoMoIMgMAAAAAAAAAqowgMwAAAAAAAACgyggyAwAAAAAAAACqjCAzAAAAAAAAAKDKCDIDAAAAAAAAAKqMIDMAAAAAAAAAoMoIMgMAAAAAAAAAqowgMwAAAAAAAACgyggyAwAAAAAAAACqjCAzAAAAAAAAAKDKCDIDAAAAAAAAAKqMIDMAAAAAAAAAoMoIMgMAAAAAAAAAqowgMwAAAAAAAACgyggyAwAAAAAAAACqjCAzAAAAAAAAAKDKCDIDAAAAAAAAAKqMIDMAAAAAAAAAoMp8q/5QAADgaq9PnqFvfvpN/Xr10CP33aa6qLbf49Mv/E+p8zJ0aswg3fV/19b483tqX2rL0pVr9MhTz9rbr//nMTVu1NBjjiVX9r066sNxhdrBseM+jnf+qsy5befuvZo28zNlLFmhg5mZKi4u1pDT43XLdSM16+sfNHnGp2oa1livTJogZ/PUcysAoDyCzAAAVNPfn35eS5avsrevH3W5LjjnTKeN6co16/VLUrrqstp+j2bfmedvEta41l7DE/tSWw4cOFi6P/Py8j3qWHJl36ujPhxXqB0cO+7jeOevE53bTBB3xPV3aM/efeXub9e2tV1v2rLNPr51y+ZyBU89twIAyiPIDABANezYuVv/m/qhCgoK7c+5uXk1EmR+/vXJ+jkpTQP69tJDd9/CPnJj7CsAgDt7+MlnbYC5basWuvP/rlH7tm3k7e2lVi1cE1QGANRNBJkBAKiGGbO+sgFmHx8fFRYWKmXeQq1et0FdOrav1rguW7XWZvX4+vgcd7ubxl2li4YOVljjRqqr3P09VnZfwfXc/VgCgJo+tx3MzNJvKXPt7YfvG6/Lhg1x2OaS885W357dFODvzw4AAFQZQWYAAKph+iez7XrMFRfruzm/a8u2HXr/49lOyz7u1rmDXeqy+vAe4RwcSwDq27lt4+attv6y0aNLxwq3CW/Tyi4AAFSHd7UeDQBAPZY2f5Gtg2iMvGyYLr/wXHv7g1lf2axmAAAAV8rJzS29HRgQ4NK+AADqNjKZAQCoovc//sKuu3Zqr0ERfRQaEqIX/jdV23bs0k+/p9hZ20+WuaT1mVff0fJV6+zPCxYv15U33llum+EXnKvRIy464YzyT7/wP6XOy9CpMYN01/9dayfTmfnFN/Y19u0/qDatWujioYN1elxUucft2rNXt/1lgs18uvOma3RaXOQx+5uZla0/3fU3FRYV2st1hw4+tVLv8+i+mQ/BH8/+TsnpC7R9xy6dFhel8TeMPuF7LFsb25QuyViy3L7Pju3bauTwC9Sza+eTnrW+suN0svuqKirbl7KysrI1JzFV8xYu1dYdO7Vn736FhgSrR5dOOv/s09SnZ7djPraqx8zRdu7eqxmffqkFi5c57I+aYo7TWV/9oPmLlmn33n02eNKqRTP7+3jRuYPVvFkTh8dU5liqqb6nzluo739O1Or1G5WVfUhNwxordlCELrvgHLs/qmtuxhL98GuSVq1Zr4NZ2WreNEwd27W1NeG7HyNb0dOPq5r6PXe3feMOY1tZZrzM1TpzMxbbMgztw1vr4qFnKTayf6UeX1tjX5NjmH0ox54DzBfJWdnZ9vi6YfSIcueUoqIizf7uZ/30W7K27dyt1i2aafiF5+qU6IGVeo3qjmNlzm2zvv5Bk2d8qoOZ2aXb3fHg4woMPHZJDLM/Xpk0oVb2nzP+XwAAuBZBZgAAqsB8CP30qx/s7SsuPs+uTfAgok8PZSxervc++qJKQeadu/aUmyF+z779DjPG9+/Ts1Izyi9Zvsq2NQlrbAPfY265T4uXryq3zbvTP9G4Ky/RxEf/UnpfsyZhyi8oUGLqfBu4O16Q+cPPvrYB9cAAf736739U+n2W7dv6jZs1+pb7tHrdxtL2pk3DKvUejS++naM7H3rcBrzLevWd6fr7feM1sF+vSs9afzLjdLL76mSdTF9KfPzFt7rrb08qNy+vwuec+OL/dPVlF2ji3xPk7+9XY8dMWd/8+Ktuf/Cf2n8g85j7o7o++/pH3f3wkw77vMTfnnxWkyb8RaOGX1ju/hMdSzXRdzNu4+//R2kN1LLMVQ5PPveaXnjyYZ11WqyqYuv2nbrjwX8e83089dzruvX6Uba/dem4qonfc3fcN+4wtpW1Zv1Gjbz5Hm3YtLXc/W9M+VBXXTpM//nH/fL19XX62NfkGK7ftEUjb7pHazdsKm3/8vtf9MbUD/Xhm8/ac/qBg5kad9tflDw3o9zzTP5glu697XoljL/xuK9RnXE8lorObZu2bHO4L3X+wuM+T+uWzWtl/znj/wUAgOsRZAYAoAq++PYnm33k5eVVGmQ2zAdEE2T+5sffbNCxyUlOMGaynGa88V89/8YU++HQfKB96O7/K7dNuzatT+o5zcSE1/75AZt19GjCn9WlU3vt23/AZjiZiQrNB+OYQRG68pLzSx9zw6gRNsj8/S9J9oPqsWo1mucwLjl/yEm/VyM/P1/X/PkBG9Q22Vfdu3SSv5+vWjRvWqnHm8znm+99xJYnadm8qf405gr16NZZ2dmH9PWPv2rCpBd1503jamWcamNfVbUvZTPFgoMCNfzCc9SrWxe1atlMgf4B2rJ9h778/mf9nJhm64ibjLPHH7yrxl/fZOXdeNff7P5s1jTM7o/ePbraLMMvvpujRye+oLtuvkbVYYJAf37gMRtQMjVITfDIZIn6+fra97lq7QYbhN61a89JPW9N9N2M/4WjbtbmbTvsBFpXXnKePU4aNgzV+o1b9M70T7R81VpdM/5+ffLuC4rs3/ek+mgCPReMutkGM729vXXBOWdoyBnxat60iXbt3mu/sDF9NRm/dem4qonfc3fdN64e25M5V1/757/Kx9tH/7j/DnXu2E47d+/RzM++0a/J6TZDNcDfr8JAdm2PfY2NYX6Brr/9rwoI8NeTf7tH7dq21oZNW+wVSma+hRvueFCJX07XDXc+ZDN5H7jjJnuOMEHn/0390GZR//ult2zWeNwxMpKrM44nq2QyvxVr1utvTzxj73vuiYfsFR9HM+dMc4xUpLr7zxn/LwAA3EQxAAA4acOv/XNxy96nFl9+3e3l7t+1Z29xeMSZtu31yTOqPLK3/WWCfY6RN9193O0SHn3abnfFDXc4tF375wdsW7v+g4svHnNLcWZWdrn2vLz84qFX3mi3OfeK68u15efnFw846zLb9tSzr1X42qnzFtp2s8zNWHJS76+kb2asTB8yM7Oq9B4HX3aNbYs578riHbv2OLRP+WBW6f4wy/Ydu2p0nE5mX1VGdfuyc/ceu82xTJ35mX1s24gzirdu31njr3/OiOtt26Ahl1f4/K++M/2E++NEXnn7ffvYPqdfVHzgYGaF2xQUFNixOJljqSb6fsOdD9m2jpFDihcsXubQfignp/iqP91ltzl7+LXFJ2vMrQn2sR0GnlX8c2LqMbc7um+eflzVxO+5u+4bV49tTZyr//rP/5SOfdr8hU4f+5oaQ/MezbkhJze3XPuqtetLj6+xtyZUeI7Iyj5UHD30CrvNTfc8XCvjeLzz1/HazHOVPO+adRsrHKMX35xq283/+zW9/5zx/wIAwD0w8R8AAFXIpExMm29vH50VZuoTnn16nL1t6i26A5M99N9//lUhwUHl7vfz89Wfxl5hby9curLcZejmUt1xV15qb0/76HMVFBQ4PK/JXjIG9O1V5UtdTd/+9ch9CqlCLU6THbV0xWp721xua+qeHm3MFRcrsn+fWhun2lLVvphSJ2abYxl9+UU2i81kPVZ02XN1Xt/URl64dIW9bbLSK8qWu/maq9Svd3dVx6GcHLsOb91KDUJDKtzGx8fHjkVl1UTfTabq7O/m2NsP3fV/iujdw2EbU37m6Ufus1dAmJIG5nVP5nL47+b8bm/fe+v1x62xe6wrATzxuKqJ33N33jeuHNuTYZ5/4qMJFZ6r/54wXi2aHX5f786Y5dSxr8kxLCwq0qRH/2Kzdcvq0rF9admob+f8XuE5wmRSX3Hx4b8HktIW1Pg4ukp195+z/l8AALgHymUAAHCSTPDYTIoXFBRoJ1Q6mgk8m0u4Fy1baT9c9evl2g9PfXp0tR+SK9L3SN/M+9m8dbt6dO1U2mZqeJqJ7bbv3K2vf/xNF557ZmmbuQz7s68P16S+ftTlVe6bmexoQN+q1S0uqYdpAgLnnnnsCQcvGjpYSenH/tBf3XGqDdXpi7k/ZW6G5iSmac26DTqQmWUv0S5hyrwYGzdvrdHXTzryxYu/n5+GnX3GMZ/70vOH2InRqspcZm3MX7TUHp/m+GvUsIGqoyb6biYdM2NiXHzeWcd8jg7t2qpT+7Zas36T0uYvrPTxb57fMIGc0VdcrPpyXNXE77m77xtXje3J6NQ+vMIAY8m+MZPrvTvjU1vaxJljX9NjaPpRkZ7dOuvHX5Pl6+ujoYNPq3CbHl0PT+q4Y9duWxe8ovrPVR1HV6nu/nPW/wsAAPdAkBkAgJNgPmyZmonGBUPOqDAbaejgUxXWqKH27j9gA9KuDjKbQO6xNCyTCWpqeZbVvFkTG1j+ePZ3enfGJ+WCzNM/+VI5uXm2DvOlw86uct+6dT78obwqtm7badftw9scN4utc4d2tTpOlfHQE89oxeq1Fba9/fxTDtmHVe2LqRt60z0PK33B4hP26Xjvoyqvb1675LEVBVdKdO1ccSCssuN07pmn6KxTY/Tjbyl2IrVJL71pgzYD+/VW9IC+GnxqjBo3aqiTURN9X7ths12bINRdDz1hbx+JzRy+reLSc8iuPfvs7R0nUTe6JDhmahKbKyaqwhOPq5r4PXfnfePKsT0Zpsbz8XTt1KHc75Kzxr4mx7Bd24rnHjAahBweQ7N/gwIDKtzG1Hwu+zoVnUuqOo6uUt39VxPnVgCA5yDIDADASTATCJlMMCNjyXJdeeOdx93+o8+/sZeIHn35rTP5+R37g53JvCtRXFzk0H7D6BE2yGze97oNm9Wx/eEsr8kfHJ7wb9TlF9pLZavq6ODqycjJy7NrM1Hg8fhXcuyrM04nMm/hkmNmaVVUiqQqfTHPM/bWBC1ZsdpmjZmJx6IHRqh1y2YKCgyUj8/hKmkJEybayZpKstMqUpXXL9kfJzrWA/wDqjVO5vXfeeFfemf6x3rvoy/s+zWPMYuZfMu895HDL9Aj940vF/Q5nprou5mE7nA/C20AvFKvm5Nbqe3KbmsmJasqTz6uqvN77q77xtVjezJO9LtREkDMy8+3EzSakjXOGHvnjWElttEf41x0jHGu6ji6SnX3X02cWwEAnoMgMwAAJ+H9j78oV4fTLMdjsplN6Qwzy7snih7Yz2Zim7IfJrD88L236dfkuVq1doO8vb11zdWXVev5ywY/TlbjIyUS9uzbf9zt9uw7nF3lSo8/eLcOZmbWeKC9LLNfTKDFmPrKxGPWhS3Idwxq14SS/bF77/HHe9eevdUeJxOIuWncVXYxrzdv4VKlz19k66WaMjXmcvONW7bpvVf/7bS+N250+DmaNmmsl5/+e6Vet23rlqqsJkcyZHft3quioiL7++cM7nJcVef33F33javH9mSc6Hdj95EsVlMnvWxgtLbH3pPGsDrj6CrV3X81cW4FAHgOgswAAFTS/gMH9eX3P9vbY0ZcfMIyERMmvmgnwTHZlicbZK5O8LWmmZq39zzylN7/ZLbuv/0mm0FqDDk9Th3C27isXz2P1BXdun2nNm3ZpvA2FV/qnDZvUa32ozL7qqoTI56MZSvX2HXbVi2OGWgxWfiba+ky7F7dOtv1th277OSYxzo2TN3Umhwnc/n6OWfE2+X+O27Sk8++qmdfm2zrp27YvFXt27Z2St8jeh+uQbp33wF179KpwgmuqqN/nx6ll+GbsgDmCyBncPVxVRO/5+66b1w9tidj4ZLlOpSTe8xSEanzFtp17+5dnDr2njSG1RlHV6nu/quJcysAwHM4JwUCAIA6wJSNMHWIS2ZDPyM++riLmQDQmPN7qg2QnAwzU3116mfWpOEXnmuzkUyG1dvvf6yvvv+l2hP+1YQzTom2l0cbr707o8JtTPbjh599Xav9cJd9VXJZuHnPZtKpivz75bdq7fXPPDVGgUfKBbz81nsVbrNj5+5a3x9nnRZXenvvCbJfa7Lvpha0yWg1mawTX/ifapoJoJVkzD757Gv2derDcVUTv+fuum9cPbYnw5zf3p3+SYVti5au1M9Jafb2eWef5tSx96QxrM44ukp195+7/L8AAHAOgswAAFSSyUguyTDqcSS77nguHTbEZrmaD2clkwVWVknt40XLVp10gLqmmYyrkZdfaG//498vKr+gQB3btdVZp8W6tF/NmoRpzBUX29uvT/lAL701zdawLGGyWMfd9hc7gWFtcpd9Fdm/r12bLLn7H5tULuidmZWth598Vl9+97PatGpRK69vJoG85qrD5VPMlxHPvvZuuXrTa9dv0phbE9S6ZfNqvc470z/RlA9mVTjWO3fv1bOvvmNvBwUFqmvH9k7ruynn8fC9t9rbU2d+pjsefNxm3h4tNy9PP/ySpL/+8z8nFSg2z//AHX+yt39Pnadx4++3ddLLMn3+5sdfNfXDz1RXjqua+D13133j6rE9Gd06d9BTz71mJ30tW9fYlKq59vYH7Hi1aNbUXuXjzLH3pDGszji6SnX3n7P+XwAAuAfKZQAAUAlLV67RgsXL7O3hF5xTqTEzH5piI/srKW2+pn8yW3fefE2lx/qCIWfqyWdeU/ahQzrlgpH2MtWGDQ7Pbj/8gnM1esRFTt1v148cbrMIzeQ/xnUjh7tFSY+/3X2L0jMWK2Pxcv1j0kt64Y2p9kO8CTSYOp2mNuQ/H7jTfng3vI9kvdUkd9lXgyJ66/yzT9dXP/xivxD5/Juf1LXT4SDr0hWrlV9QqFcmPqpnXn1HW2rp0vEH7rzZ7g9TMsBkdL7y9vvq3qWjDfaY3yET6Hn8r3eV7o+qMJdVz/z8m9IARssWzdSoYQPt23/A1kg3AUhzbD6a8GeFVHLiv5rq+6jhF2rnrj166rnX7RdLH8z6yn4hY/poJsPauWu3duzaY7+oMR574I6Tqq1sgjVm8rIX35ym739OtEuXju3UvFlT7d6z1wZ/TLBtxEVDSwOzdeG4qonfc3fcN+4wtpXVu0dX29c7H3rclqTp2D7cvq+SeQlMtupL/3rE/i46c+w9aQyrO46uUt3954z/FwAA7oFMZgAAKuH9I1nMxqWVDDKXDUivWb9JSekLTio79sWnH7EfvkxgwgS4f0lKt8ua9Rudvs86lMlctpnNwy+QOzBBxJlvPmdLd5jMVXPJdPLcDFsL29SM/mzKy3aSuBJmMqWa5k776uWJj+qG0SNsoOJgZpbNjjNL5w7tNO2VSbr4vLNqvXTIjNf/q5vGXqngoCA78aXZHyYQaC67NvujZCKpqjJfcFxz1aU2sGj2twkkmS9yTG1Wk0EXOyjCTvh37UlOSllTfb/jpnGaNfklnXfWaQrw99PaDZts/+YvWmrrwvr6+mjIGfF64qG7qzSxl5l80+xL8z5NIGf1uo32+U2QynwJZAJYNRVgdpfjqqZ+z91x37h6bE/GQ3ffor/dc6sNLJa8LyNqQF99/M6LOi0u8piPrc2x96QxrO44ukp19p8z/l8AALgHr+Ky1+kAAIAKzc1YosysLPn7+ysusn+lRykrK9tm8BgmY6kyk5CVZf6bNtlx23buUn5+vv25XZvW6tQh3LabD6dbt+9QWONG6tere7nHLlm+ys7YbjLpSibfqegS1+Qjwe+B/XofNwh75Y132sCpycz9zz+ql3FUmb6VON57LCv7UI5Wrlmn/PwCGxRv3jTM3v/y2+/ZSRjNhEXzf3SshVlT43SifVUZNdUXMxbLV621/WjdqoXalZksbW7GYptBVlHfavKYMQH3FatNHwrsZE8l5QwOHMy0gQkjLnJAueDgyTKTUW3bsdMGLcxl3SaodLxjuLLHUk313YzVmnUbte/AQRtoMZfBm+PS19e3xiYjXbdxs+1vy2ZN1bpVcwUGBNTp46qqv+fuum/caWwrUtHz5+Tm2rGzfWrb+qRLHdTW2NfmGJqyLOs2bLL7MGZQRIXbmC8/Fi1dYW/HRw2Un98f7+e62/9qs61NGa1XJ02o0jge7/x1vLbDgfcl9nb0wIgKJx00mfbmS9EAf397BVZt7T9n/L8AAHAdgswAAOCEFi9bqSEjrre3v/3wzeMG6NyJ+TA85PLrtGrtBl02bIheOfLhHkDdwe853F1FQWYAAOoaymUAAIATZoc98Nh/7O1TYwa5XYDZTCS0bNUah/vNhELXjn/ABphNjV5zOTUAz8TvOQAAgHtj4j8AAFChkTfdo5y8PC1fucaWIzB1Fk0dSXdjZqw3kwmFNWpo6/SGhoZo+45dtmZkibtuvuaYlzgDcH/8ngMAALg3gswAAKBCvySnq7Cw0N5u2qSxHrv/Dg3s18vtRuuu/7tW77z/sZ1EyATDS5js5X69u+v2G8e63cRPAE4Ov+cAAADujZrMAACgQr8mpatYxWrSuJG6dGp/3Emr3IGZ3Gjr9p3avXefggID7aRCYY0burpbAGoQv+fwRCcz2S0AAJ6KIDMAAAAAAAAAoMqY+A8AAAAAAAAAUGUEmQEAAAAAAAAAVUaQGQAAAAAAAABQZQSZAQAAAAAAAABVRpC5DrnpppvsAgAAAAAAAADO4uu0V0KtW7RoUb0Z5czMTLsODQ11dVfg4TiWwLEEd8N5CRxLcEecm8CxBHfDeQkcS+6FTGYAAAAAAAAAQJURZAYAAAAAAAAAVBlBZgAAAAAAAABAlRFkBgAAAAAAAABUGRP/ebisrCxlZ2fb2/n5+fLx8XF1lwAAAAAAAADUI2Qye7iJEyeqRYsWdklPT9eWLVtc3SUAAAAAAAAA9QhBZg+XkJCgHTt22CUyMlJt2rRxdZcAAAAAAAAA1COUy/BwISEhdjH8/Pwq9Zi8vDxt3bpVubm5KioqkicqLCy0a8qDgGMJ3t7e8vX1VYMGDdS0aVP7MwAAAAAAcB6CzPWMCTBv2LDB1m82vLy85IkIIoFjCWW/dDKL+eJs3759at++vQICAhggAAAAAACchCBzPWMymE2A2WQ/t23b1mMzgclkBscSSpgrMkyAefv27Tp06JB27dplz28AAAAAAMA5uKa4njGBGMOTA8wAcPSVDUFBQQoPD7c/Z2ZmMkAAAAAAADgRQeZ6mPFnSmQQYAZQ15i6zOb8Vlxc7OquAAAAAABQrxBkdpHffvtNMTEx8vf3V/PmzXXPPffYeskAAAAAAAAA4EkIMrvAqlWrdN555+nss8/WgQMH9P333+uDDz7QHXfc4YruAAAAAAAAAECVEWR2gf/85z82e/mJJ55QYGCgIiIiNGHCBL3xxhvatm2bK7oEJ1qzfqO+/P5nZWVl18rzfzvnd83NWFz684bNW+3r7T9wUO7o99R5+jV5rqu7USf9nJiqpPQFTn1N9icAAAAAAPUPQWYX+O6772wWs5msqsS5556rwsJC/fjjj67oUp2ybsNmG1Tdsm2HQ9u+/Qdsmwm+VSRt/iLbnpeXX2v9++Kbn3T9HQ9qy/adtfL84+//h557fUrpzz/+mmxfb+2GzXKVX5PSbfCxIo9OfEF//9dzqm+ONyY15S8TJumJ/75S48/L/gQAAAAAAGX5lvsJpdauXausrCw1adJEbdq0qdTI5ObmavPmzTY7uXXr1nYCqmM999ixY8vdFx4eboPOpg3Vs3bDJhtUvevma/TAnTeXa/vyh19099+elL+fn5YlfqngoMBy7bckPKqc3FwtnDOrzuyG9m1b6/yzT1fjhg1c1oeHnnxGAQH++mbG/xzaTokeqKLCItU3xxsTd8f+BAAAAAAAZRFkPsJMuvfxxx/rm2++scumTZvs/TfeeKMtY3E8e/fu1V/+8hdNmzZN2dmHSyC0bdvW3nf77beXCzbn5+eroKDABqLLMtsEBASUPh5VFzMoQn6+vhVmif6eMk/NmoZp1+69Spu/UGfER5e2rd+0RZu2bNMl5599zC8IPNFZp8XaxV09mvBnV3cBNYj9CQAAAABA/UOQ+YgtW7Zo5MiRpQPToEEDHTx44hq2Jih8zjnnaO7cwzVlO3bsqMzMTJvRfOedd2rjxo2aOHFi6fZ+fn52ycnJKfc8RUVFNhM6ODi4pvZtvRUSHKQBfXtp3sKlyj6UUy5bOTFtvkZcOFSffPmdfkuZWy7IXBKUPjVmkMNzLlu1Rpu3blfD0FBF9OmhAH//Cl/blONYuWa9srIPqXuXjmrTqkWl+33gYKbtU3BQkM485Y9+HY+pszx/0TIFBvhrYL/e8vf3c9jG1GRevGylzRhudCSb2dSFXr5qrc6Ii1JISLCWrlitjVu22edo3jTMbmPGbuGS5crMzlaH8Lbq2qn9Mfths7+XrFBmVra6dGpvs6eN4uJiffXDL/b+3Nw8W4qkxJmnxNh9Y8a9qKhYp8U6jvvOXXu0dOVqFRdLvbp1VovmTR22MaVP/P39FRfZ3477/EVL7fYD+/Wyx0Jl/JyUpqDAQPscZj9kLF4uH18f+xyBAQEVPqYy43N03zKWLNehQznKzcs77ph88+Ovatmimfr36Vnu+bZu32nfX9SAfqX7qaLXyMnJdfhiobLva/3Gzba0iulHv949FBT4x3aesj8BAAAAAIBzEWQ+wgQ1rrrqKg0dOtQu06dPV0JCwgkHcNKkSTbAbDKXP//8cw0YMMAGYt58803ddNNN+ve//22D15GRkaWP6dy5s9atW1fueUww2gSau3TpUtP7uF46JWaAUucvVOq8haUB25JM5fjoAdq2c5d+T5nvkOVsHxs9sPQ+8/h7HvmXVq75Y381CWuspx6+R5ecd3bpfeZ5J0x6UbO/+9nW1i5x6bAh+u9jf3Uoy3G0bTt2afT/3attO3drykv/qtR7fPv9jzVh4gs6lJNrf27dsrneeu5Jh+1MTeb7/zFJX01/QwP69iytC/34M6/q43de0JPPvKqUeQvt/VNfmaizT4vTf195R8//b4oNiJYwQb9XJk1QqxbNSu8zx+wzr76rF/43VdmHDpXef0Z8lJ59/CEbCDWlS0qUvZ3yzQc2GG1qMhcWFOr7j94ubTPvyfT5g1lf2d8nw2SXj7h4qJ5+JKHceJq6wy2aNdFd/3etbvvLBO07MsFhk8aN9MYz/yy3P4/lr4/9xz7HTeOu0l1/e8IGN42mTRrrxace0eBTY0q3Nf2p7PiU9O22G0brzoce1/4DmWrZvKm279x93DG56Z5HdNHQwXrxX4+U62dy+gJb0mXaK5N09ulxx3wN04f5P35S+rjPvv7xhO/r829+0tMvvKEVq/841hs1DNVjD9ypqy4dZn82x7Yn7E8AAAAAAE5GyWdVVB0T/x1h6i6bwLIpj9GuXbtKH4Cvvfaavf3iiy/aAHNJ8MQ8z3XXXVdumxIm8/n7778vF4w0JTp8fHx01llnVWN3okRJNvLvqYczzA/fnmf3Teyg/oqPGmAzJEuCbiVZzi2aNVW3zh3szya796o/3WUDzB3btdVZp8bYDOm9+/br1oQJdpLAEguXrrCBvGZNGtsgWFzUAIWGBOvTL7/XPya9eNwdY4J6F47+Px3MytZnU17SoIg+J9yRP/ySpAce+7cN3pmM6dNiI21m6Y13Pqj8goJKHwh/mTDR9j16QD9bt7lZkzA98cyrNthoSrsMiuht33fbVi2UlL5A4277S7nj9h//fsluawLMph8moN8+vLV+Tkyz42fqjJvnNWNhApbmdsliMoeP5d5HntKMT7+0ZU8i+/dR1IC+to72h7O+toHUo5lJFP9098M209X0oUO7Ntqzb7/+/MBjtjxNZWzetkN3PPhPW7vaBMnD27TS7j37dP2dD9rJJEuczPiUPO+tCY8qJDjYZhebwG5VxuREfT/6NU72fb3/yWyb4d6tc0f7nvr06GoD1nf97UmbLW940v4EAAAAAOBEVm7foSe/+lYXvPiaCo76PI+TQyZzNSxdutSWxWjUqJEuuugih/Zx48bprbfe0nfffVfu/nvvvVfvvvuu7rvvPv3973/XypUr7fq2225TixYnLq8QHx9f4f2LFi1Sr169bLmOYzEBMBMoOjoQ5mlMBu3xmECtCWL9mjy39L3+ljxXPbt1VsMGIYodFGGDsSYz1ASxNmzaarORLxs2pHT7J599TQUFhXpl0qO6eOgfwf+5GUs08uZ79Nzrk/XWc0/Y+0xZjHdf/JeGHMkuNQ5mZuma8ffr/Y+/0N/uubW07EDRkW/HiooKlZQ2X9fd/le1bdNSU1562ga5K7Nvnn3tXbv+z2MP6OojWaamhMFN9zyszYlp9suNkucpGSvzeqX3HemDGYM5n05W29YtSzOqX3n7ffXu0VXvvvCUzY42zOOeeOY1vfLO+/rmp980dPCptnzI65M/UMMGoXr7uScUG9m/tH+/JKXbLGbTj/8980+dPfw6O8mduV2W7U+x/VfatzXrN+mjL761Gb/TX/+PDXoaq9au11V/utsG85csX6UeXTuVPo/Zd7f/aaz+8ucbS4/vWxImaPZ3c5S2YLGiB/Q95lia8SlWsX0/140crn/cf7v9wsfc/9h/XtZr786w7/vxB+86qfEpYZ73htGX21rF5nlLHHdMjnyJdfSx8Me+LCrXVtFrlLRX5n0Zl5x3lp548K7SY8Ewvx+j/u8+vfP+x+o34S/2Pnffn2bczHs83nmwtlBTHxxLcDecl8DxBHfEuQkcS3C17Lw8zV60VNPT5yp1/cbS+z+bO1/n9uqhui40NLRWnpcgczUsWbLEriMiIsoFj0oMHHj4su61a9faGswlk/116tTJBp5NkDk8PFyNGze2Wc8TJkyQK/V+5J/Kzs+TOwn289eSf/ztpB9nArqmhqsJCGdnH1JwcJDNNB06+BTbbrJuTdauyW42QebEtPKlMky2pKnTa+rsmuxLU4e2LJPtnLbgj0zmvj272cUEIVet3WBfs6i4yAYjTSkKkw0d0bv8ierL73/RM6++o+iB/fTGf/9ps0NL7N1/wAb4yjJ96dqpg/Ly85WesdgGyksCzIZ5/GMP3KEzL72m0uN09/9dWy6oaDKQTeD51JiBWrB4mV1K9Ox2OAiYvmCxDaL+mpxug3933nxNuQCzcXrcH+VhTlbikdrYJshYEpA0zHu/46ZxeuiJZ2zWedmgpNmXJQFJw/w+XnnxeTYouXnLtuMGJUs0CA3Rw/feWvq7bJ7rr3ferA9mfa3E1PknPT5ln/ehu2+p8BxRU473GpV5X8aIi4ba/bl4+Spt37HLvk8TsDWZzxlLl3vc/gQAAAAAoIT5fLtoy1a9nz5PsxYs0sHcw6VHy/pt9dp6EWSuLQSZq2HPnj123bLlH0G6skzwOCAgwE7ot2/fPrVq1aq0LSYmRj///MekWScjMTHxuBnOx/tGoiTQVFEw6lB+ng7l5cudeB2jryWO13ZqbKSS52bYzMfOHdvZ7MhTYyJLHxMX1d8Gt8zPiWmHA7qnx0XZn/fsO2AnT1u6co1uvKviILcpvVHyXCZb9Pa//rN08sCjmazm0iCfl3lX0r9fessG0SY9+pfSCflKrF67weF1773teiWMv1GZe/fbDGuTlX30++/epZPN4C7bt5JAnbe3j0Mf+vToVu45duw6XCvYZCib5ViTG5rH7Ny91/5s6jyfMIBqXs7rGPvLq/x+NmURbN96lu+b0a9Xd7vetWdfubaO7dvaCTXLahLWyK7zCwpP2D8vedmSKKbcRFlBPj7q0rGd1m7YZJ/jZManRKcO4Q7Pe8IxOer4KvHHvvSu3GuYsanE+zI+mf2dHn7qOe3cffi8VpYJNJfrixvvz5Jxq61vZivDla+NuoVjCRxLcEecm8CxBHfDeQnHsy87Wx+mz9OUxBQbZHY4fgICdElEX42MGqj47t3sZ0pUDUHmasjLO5z1e3QwpCzTZoLMJpO5NmRlZZVebmRqxFYnWzLIz1/upjp9Mtmm/3n5LRv4NRP92XrMkRGl7fFRA/X3p59TVla2DTabkhcmWGcEHyltYWrt9jsqA7kidzz4uH0dM+Fa5w7tbFaxCQSazGZT+9kEhY/27OMP2izOK/90l2a+9bzatfnjS4iwxo1snduyunU6XCs68EjfSoJ3RwezTaZzZZmSB2WV1NU1WdKmDxUx2dllty0JNteUkuc1dYOPtnvvvnL7p0RJ0Lw69hx57oruL+nTyYxPiUD/kz+G/fx8lXvk/FLW7r2O+/xEr1GZ97V63QaNf+Ax+81u7+5dbGkLMxmq+Z0xGfvVKa/jqv0JAAAAAKifTAnF31av0dSkVH22YKFyK5jbJ65zR42Ni9HF/SNUfOSqfgLM1UOQuRqCj2QHHqumlAnYHDp0qFa/WZs4cWK5Mhum/EZVLX/876pLzORigQH++i1lrg32lpTIKHFK9AAb/P3gs69tlvMVl5xX2hYSEmxLYuTk5um5Jx6ydYePtmXbjtKTlwlSmxIR77/2n3KB/r8//bwNMlfEBK8/fPNZXfmnuzX82j9r5pvPqkO7trbN9PXt55+s8HGm/EG7tq3t5H9bt+8srQtsvDvjU1WHyUo2BvXvo7/fN96h3dR9LqkLXLLtG1M+0EXnnilf3z9OJ/n5BXYywJIMbVNyxGSGV0bvHl3seuqHs3ThuWeWnuTN79O70z85vE3P8oHcmmAmyPvx12Q7cV4J88WBqSlcUv7iZMbnRI43JmafLlq60gZ3S44n87wfz/62Vt5XcnqGfa0X//WILZtRwnwBc+pFo0+q7+6yPwEAAAAA9cu2/Qf0fkqapianau2RK5HLahYaoqujI21wuVvLP+ZEy3Sz0rGeiiBzNbRtezgguH79+grbN23aZAM3phZzkyZNVBvMZIFXX321vT1q1Khygb76LsDfX5H9+yp57gJt2rJdF5xzRrl2U26iSeNGev71yfbnU2MGlWu/9fpRuufhp3TOFdfriovPV6f2bW1gbO2Gzfry+59tjWUTgDYZy2aSu/mLltnJALt0aq+DB7M0JzFV3/7023H7aEoIzHzrOV15450aft3tmvnmc6XZ1Mcz8rILNPHF/+mCUTfrpnFX2gkDTQ3n6Z98KV/fqmezxwyKUPSAfnr5rfe0fNVaDTk9Xs2aNtau3fu0bOVqffLl93aCQlOD2Wzbv09Ppc1fpLMvv04jh1+g1i2a2/GZ/ulsPfnQPTr7yESILVs0s4FOM9adO7aXt7eXzjwlRsFBh7NcyzJ1sTu1D9ePv6XoihvutJMxmsCkeW1TB9oE2M+Mj1ZNM19I3HDXQ7p53JXq0aWTVq5Zr9cmz7Bto0dcdNLjcyLHG5PI/n30/sez7aSQl5x/trKyD+mDWV/ZCfJq4321aN7Urt+cNlOHDuWoQYMQbdy8TdM/mW3Lfxydte0J+xMAAAAAUPcVFBbqu6XLNSUpRd8uWabCoxK/zOfPIT27a0xcjM7r00v+xM1qDRHJaujf/3AgadGiRbbmsqnBXFZJzeV+/fqV1lKtaS+99FKNZTLXRSZwbDKZTS3d+OgB5dpKymeYCfhKti1r9OUXae36TXrhf1Nt2Y2jDStTzsJMava3J5/Vv55/o/S+pk0a667/u1ZPPvvacfvYq1tnffz2C7rihjs0/Lo/68M3n7OT/B3P+BtH65ekNDuZ4T8mvVR6//23/0kvv/2+quP1/z6msbcm2Exps5RlyoA0LFM/+rV/T9DIm+/VitXryvXD1IVu3Khh6c+XnHe2vv85UY8/82rpfSnffKD2bVs7vL7J3H1l0qMadfO9dt+ZpURYo4Z6ddKEWvkyxXxp0Kplcz372uEvHUqMGXFxudIlJzM+x3O8MTET4n329Y/6ds7vdjFMCYt7brmu3PY19b7OiIuyXxiYSQvNUuKioYMV3rqllq1aW+m+u8v+BAAAAADUXSZTeVpyql22Hzjo0B4e1lhjYqM1KjZK4WF/XNWO2sMn+2owE/mZCfxSUlL0zDPP6NFHHy1tKygo0H//+197+9JLL1VtSUhI0Pjxhy/bHzZsWLVqMtdFphxAxpLl9vYpUQMd2kdcdJ6Kiw+XoKgoQPbQ3bfo8gvP1ayvf9Ta9RvtRI4mo3nYkDPUo2un0u3+NPZK+/Ps737W3n371bVzB4294hJbhsME8po3+yOT3WR+mvtMQLKEKc3x8Tsv6PH/vmqzTP9x/+0KDChfp7Ys0/bB/57Vex9/rqS0Bba28vlnna7zzj7NZqqaLO0S5n2Z12tcJvhZUR9KmLrSX01/3QbfTaapqf1sApy9u3e1WbVlH2PKe/z4yTv6ePZ3SpmbYUsomEzuqy4dVm48r75smH3c978k2szYoqLi0lq9JtO1qLD8N40m4PnL51P13kdf2OxdWyu4R1eNuvzCciVPjDNOiS733o6ua22CpJX18tN/t1m1JRNCmuPHlHio6vgcq28nGhNT1/vrGf/T5BmfauuOnerSoZ2uGzVc6zZsdjiejvcaJW3my4fjvS9/fz998u6LmvLBp8pYskI+Pt46LTbSHvv/feUdtW7VotJ9d6f9CQAAAACoO3Ly8/VFxiJNSUrVLysdr/T18/HRBf362HIYZ3TvKp9aSvhExbyKzad9WKtWrSqdoO/tt9/Wv//9b11++eWlmcIm87VPnz7lRmvWrFk2iGwCNybge9lll+ngwYP2sV999ZXCwsLs89ZWuYyy4uPj7ToxMfGY2yxbtsyue/Y8XFvWU5VMREZQHTVxLJ164Wi1aNZEs6a8zIB6OFee4zIzM+2a2a3BsQR3wXkJHE9wR5ybwLGEk7V4y1ZNSUzRB+lztS/78NxnZfVo1VJj46J1ZdQgNavCnGicl2oGmcxlmADx4sV/XCpufPTRR3YpCWiaDOWyLrnkEj3wwAN66qmnSpeyEwNOnz69VgPMWVlZpRMP5ufnE3QFAAAAAACARzuYk6OZ6fPtJH7zNmx0aA/x99dlA/vbrOWoju1LJ5mH6xBkLqNbt27HH6xj1A198sknNWTIEL311ltasWKFLakQHR2t22+/XZ07/1G2oDZMnDiRmswAAAAAAADwaKbYQsra9XYSv0/nL1B2Xr7DNpEd2tusZRNgbnCkbCPcA0HmMj7++OMqD+Q555xjF2ejJjNQfafHRdqavwAAAAAAwLl2HszU9NR0TU1K1codOxzaw4KDdVX0IJu13Kt1K3aPmyLI7OFCQkLsYvj5+bm6O4BHeurheyk1AwAAAACAkxQWFemn5Stt1vKXCxeroKj8BPKGmbxvXFyMLojoq4BjVBeA+2APeThqMgMAAAAAAMATbNyzV9OSUzUtOU2b9+1zaG/dqJFGx0ZpdGy0OjStvTnOUPMIMns4ajIDAAAAAADAXeUWFOirRUs0JTFFP61YaWsvl+Xr7a3z+va2tZbP7tlDPt7eLusrqo4gs4c72ZrM3t7eKiwsVFFRkb0NAHWF+UPFLJzbAAAAAMD1lm/bbsthzEidq91ZWQ7tXZo309j4GF0dHakWDRq4pI+oOQSZ61lNZl9fXxtkzs3NVVBQkBN6CADOKx9kBAQEMOQAAAAA4AKZubn6dF6GDS6nrlvv0B7k56dLBkRoTFy04jt3kpeXF/upjiDIXM9qMjdo0MAGmLdv367w8HAbdAYAT2ayl825cNu2bfbnhg0burpLAAAAAFCvPpPNXb9Rk5NS9PG8+crKzXPYpn+7thobF6MRgwaoIUmPdRIRxnpWk7lp06bat2+fDh06pJUrV3rsN0Yl9Xs8tf9wHxxLnq9sPS9zZUfjxo1d2h8AAAAAqA/2ZGXpg7R5Nmt56dbDST9lNQwM1JVRg2zWckR4W5f0Ec7jVXx0tW14bCZzSU3m5OTk4z7GZDLv2rVLmZmZDsXWPYUp+WGcKHMb4Fiq+8yXTaZEhslgNgFmV9VkNudUIzQ01CWvj7qDYwkcS3BHnJvAsQR3w3nJNcwcX7+uWq3JiSn6ImOR8o7EZ8o6pUtnW2v54oh+CvI/cWlXV+NYqhlkMtezmsyGCca0bevZ3yBxAgDHEgAAAAAAzrF13369l5KmqcmpWr97j0N7iwahGhUTrdFxUerSvDm7pR4iyAwAAAAAAACgnPzCQn27eKmttfz90uUqOupqeG8vL53Tu6ettXxu757y42rzeo0gMwAAAAAAAABr1Y6dmpqUqumpadpx8HBZwLI6Nm2iMXExGhkdqdaNGzFqsAgy16GazPn5+dQoBgAAAAAAwEnJzsvT5wsW2qzlxNVrHdoDfH11YURfm7V8WtfOLpsLB+6LILOHmzhxoiZMmFD6c3h4uEv7AwAAAAAAAM+wYOMmTUlK1Yfp83QwJ8ehvXfrVhoXH6srIgcqLCTYJX2EZyDI7OESEhI0fvx4e3vYsGFkMgMAAAAAAOCY9mVna2b6fE1JTtHCTVsc2kMDAjQicoAtiTGwXbi8vLwYTZwQQWYPFxISYhfDz8/P1d0BAAAAAACAmykuLtbvq9fYrOXPFmQoJ7/AYZvYTh01Ji5alw7or5AAf5f0E56LIDMAAAAAAABQB23bf0DTU9M1JSlFa3ftdmhvFhqiq6Mjba3lbi1buKSPqBsIMgMAAAAAAAB1REFhob5ftlxTElP1zZKlKiwqKtduyl+c3aO7xsbH6Lw+veTvS3gQ1cdRBAAAAAAAAHi4dbt2a1pyqqalpNkM5qOFhzXW6NhojY6NUnhYmEv6iLqLILOHy8rKUnZ2tr2dn5/PxH8AAAAAAAD1RE5+vr7IWGRrLf+ycpVDu5+Pjy7o10djYqN1Zo9u8vH2dkk/UfcRZPZwEydO1IQJE0p/Dg8Pd2l/AAAAAAAAULsWb9mqqUkp+iBtnvYeST4sq3vLFrbO8lXRg9QsNJTdgVpHkNnDJSQkaPz48fb2sGHDyGQGAAAAAACogw7m5OijufNt1vK8DRsd2oP9/TR84AAbXI7q2N7WXgachSCzhwsJCbGL4efn5+ruAAAAAAAAoIYUFxcrdd16TUlM0SfzFyg7L99hm0Ht29lJ/IYP7K8GgYGMPVyCIDMAAAAAAADgRnZlZmp6arqmJKZq5Y4dDu1hwcG6KmqQxsRFq3eb1i7pI1AWQWYAAAAAAADAxQqLivTT8pW21vKXi5Yov7DQYZszune1k/hdGNFXgVzRDjdCkBkAAAAAAABwkY179mpacqqmJadp8759Du2tGjW0geVRMVHq2KypS/oInAhBZgAAAAAAAMCJ8goK9NWiJZqSlKIfl6+0tZfL8vH21nl9etlJ/M7u2V2+Pj7sH7g1gswAAAAAAACAEyzftt0GlmekztXurCyH9s7Nm2lsbLSujolSy4YN2CfwGASZAQAAAAAAgFqSmZurWfMzbHA5Ze16h/ZAP19d0j/CTuJ3SpfO8vLyYl/A4xBk9nBZWVnKzs62t/Pz8+XD5RMAAAAAAAAuZcpfzNuwUZOTUvTx3AU20Hy0fuFtNC4uRiMGDVSj4CCX9BOoKQSZPdzEiRM1YcKE0p/Dw8Nd2h8AAAAAAID6am9Wtj5Im2uzlpds3ebQ3jAwUFdEDbQT+fVvRwwHdQdBZg+XkJCg8ePH29vDhg0jkxkAAAAAAMCJioqK9OuqNTaw/EXGIuUWFDhsE9+lk81avqh/PwX7+7N/UOcQZPZwISEhdjH8/Pxc3R0AAAAAAIB6Yeu+/XovJU1Tk1O1fvceh/YWDUJ1dXSUrbXctUVzV3QRcBqCzAAAAAAAAEAl5BcW6tsly2zW8ndLlqmouLhcu7eXl4b06mGzls/t00t+zJ2FeoIgMwAAAAAAAHAcq3fu1NSkVL2fkqYdBzMd2js0baLRsdEaFROpNo0bM5aodwgyAwAAAAAAAEfJzsvT5wsWakpSqn5fvcZhfPx9fHRhRF+Ni4/RaV27yNvbmzFEvUWQGQAAAAAAADgiY9NmWw7jw7R5OpCT4zAuvVq30ti4GF0ZNVBNjsyTBdR3BJldICcnRx9//LHeeecdrVu3Tm+88YZOO+00V3QFAAAAAACg3tuffUgz587T5KQULdy0xWE8QgL8NXzgAF0TH6OB7dvJy8ur3o8ZUBZBZhc499xzFR4ervPPP1933323MjMda/kAAAAAAACg9hQXFytxzVpNSUzRrAUZyskvcNgmplMHjYmN0aUDIxQaEMDuAI6BILMLfPvttwoMDNT8+fNd8fIAAAAAAAD11vYDBzU9Nd2WxFizc5dDe9OQEF0VPciWxOjRqqVL+gh4GoLMLmACzAAAAAAAAHCOgsJC/bBshQ0sf7N4qQqKisq1m/IXg7t309j4GJ3ft7cCfAmZASfDt75c/lBYWGhn+WSmTwAAAAAAgPph/e49mpacqmnJadq6f79De9vGjTU6NkqjY6PVrkmYS/oI1AW+dTWonJGRoW+++cYuv/76q51s78Ybb7ST7B1PQUGBnn32Wb311ltauXKl/P39FR0drfvvv1/nnXee094DAAAAAAAATl5uQYFmZyzSlKRUzVmx0qHdz8fHZiuPiY3WWT27y8fbm2EGqqlOBpnXr1+vAQMGnPTjTLbz5Zdfrs8++6z0vry8PP344492eemll3TrrbeWe8zUqVP12GOPHfd5AwICtGDBgpPuDwAAAAAAACpn6dZtdhK/GWlztTc726G9W4sWGhsfrauiItW8QSjDCtSgOhlkNnV0IiIiNHToULskJyfr4YcfPuHjXnvtNRtgbtCggb09fPhwHThwQE8//bQmTZqku+66y2Yzd+7cufQxF154oSIjI4/7vJToAAAAAAAAqHkHc3L0ybwFNms5ff0Gh/Zgfz9dOqC/ncQvplMHGzMCUPPqZJC5Q4cO5TKHK5tFbMpkGP/5z380cuRIe7t58+aaOHGili5dqi+++EIvv/yy/blE48aN7QIAAAAAAADnlElN37BRM9Ln6/OFi5WVl+ewzcD27TQ2LlqXDxqgBoGB7BagltXJIHNVrFmzRsuXL1dQUJDGjRvn0H7LLbfYIPPs2bPLBZldIT4+vsL7Fy1apF69eikzM1N1XXYFl70AHEtwJc5L4FiCu+G8BI4nuCPOTaiOPVnZ+mh+hqanz9PKHTsd2hsFBWr4gAhdHTlQvVq1PHxnQUG9iJOg6urbeSk0tHZKxRBkLhOgNfr3729rKB8tNjbWrlesWKH8/Hz5+flVedBN6Y4PPvhAubm59uebbrpJISEhOuecc/TCCy9U+XkBAAAAAADqkqKiYv26eo0NLH+zdJnyC4sctjmlc0ddHTlI5/XuqUA/Ql2AK/Cbd8SOHTvsuk2bNhUOlCmbYQLLJsC8d+9etWjRosqDPn78eI0ZM8bhflMLujISExOPm+FcW99IuKP69F5RuziWwLEEd8N5CRxLcEecm8CxBGfZvHefpiWnalpymjbu3evQ3rJBA105qL+uPf1UdWrWlB2DauP/uOohyHzEoUOH7LqiLOYSgYGBNshc3TT6Vq1a2aUmZGVllfbH9M3Hx6dGnhcAAAAAAMCZ8goK9PXipZqSmKIflq+wtZfL8vH21tDevTQ2Plqx4eHy9fEmMAi4CYLMR5hazEZJCYuK5OTk2HVwcLDchakPPWHChNKfw8PDXdofAAAAAACAk7Fy+w5NSUrR9NR07crMcmg3mcrj4mJ0VXSkWjVqaO+jzjLgXggyH9Gy5eGC8Js2bTpmOQ2TKezr66uwsDC5i4SEBFt+wxg2bBiZzAAAAAAAwO1l5eZp1vwMG1xOXrvOod3UVr4oop/GxcfolC6d5eXl5ZJ+AqgcgsxH9OvXz64zMjJsxrIpjVFWUlKSXffs2bNak/4BAAAAAADUR6b8xbyNm2w5jI/mzldmBVeT92vbxgaWRwwaqEbBh686B+D+CDIf0bFjR/Xq1UtLly7VW2+9pVtvvbXcQL300kt2fcEFF8idUC4DAAAAAAC4s71Z2fowfZ7NWl68ZatDe4PAQF0ROVBj46LVvx1lQAFPVGeDzIWFhaUF4ouKiuza/FxQUGBvm8ssjp4k7+6779bNN99sS1CYusuXXXaZDh48qH/961/6+uuv7aSAt912m9wJ5TIAAAAAAIC7MbGYX1etsYHlLzIWKfdIPKas+C6dNDY2RhcP6Kdgf3+X9BNAzaizQeb+/ftr8eLF5e5788037WKYAHNJwLnEjTfeaIPJM2fO1HXXXVeuzQSlX3zxRXXo0MEJvQcAAAAAAPA8W/fv1/sp6ZqalKJ1u/c4tDcPDdXImCiNjo1St5YtXNJHADWvzgaZzQR9R2cqH91+NG9vb82YMcOWxjAlM1asWGGzl6Ojo3X//fdr8ODBcjeUywAAAAAAAK5UUFiob5cus7WWv12yTEVHriwv4e3lpSG9emhsXIyG9uklv+PEawB4Jq/ikpoS8EhZWVnKzs62t4cNG2YD68nJyarrMjMz7To0NNTVXYGH41gCxxLcDeclcCzBHXFuAscSKrJm5y5NS07Veylp2n7goEN7+yZhGhMXo1ExkWrTuDHnJbgl/o+rGXU2k7m+CAkJsYvh5+fn6u4AAAAAAIA67FBevj7PWGhrLf+2ao1Du7+Pjy6M6Ktx8TE6rWsXe9U4gLqPIHMdymTOz88/bokQAAAAAACAqli4aYsNLH+YPk/7Dx1yaO/VupUth3Fl1EA1OZIMB6D+IMjs4ajJDAAAAAAAasOBQ4c0c+58G1xesHGzQ3tIgL+GDxygcXExGtShnby8vNgRQD1FkNnDJSQkaPz48eVqMgMAAAAAAFSFmborac06TU1K0afzM3QoP99hm+iOHWzW8qUDIxQaEMBAAyDI7OmoyQwAAAAAAKprx8GDmp6arimJKVq9c5dDe5OQYF0VFamxcdHq2boVAw6gHDKZAQAAAAAA6qHCoiL9sGy5piSl6utFS1RQVFSu3ZS/GNy9m8bGx+j8vr0V4EsYCUDFODt4OCb+AwAAAAAAJ2PD7j2ampyq91LStGXffof2No0baXRstEbHRKl90yYMLoATIsjs4Zj4DwAAAAAAnEhuQYFmZyyyweU5K1bZ2stl+Xp722zlMXHROrtnD/l4ezOoACqNILOHY+I/AAAAAABwLEu3btOUpBR9kDZXe7KyHdq7tmhuJ/G7KnqQWjRowEACqBKCzB6Oif8AAAAAAEBZB3Ny9Mm8BZqalKq09RscBifIz0+XDoiwtZZjO3W0tZcBoDoIMgMAAAAAAHg4U/4iff0GTU5K0SdzFygrL89hmwHtwm3W8uWD+qthUJBL+gmgbiLI7OGY+A8AAAAAgPprd2aWZqSl26zlZdu2O7Q3CgrSlVEDNSY2Rv3C27ikjwDqPoLMHo6J/wAAAAAAqF+Kior088pVmpyYoi8XLlZeYaHDNqd162Kzli/s11dB/n4u6SeA+oMgs4dj4j8AAAAAAOqHzXv36b2UNE1LTtWGPXsd2ls0bKDRMVEaHRutzs2buaSPAOongswejon/AAAAAACou/ILC/X1oiWakpSiH5atUFFxcbl2H29vndu7p8bERevcXj3l6+Pjsr4CqL8IMgMAAAAAALiZldt3aGpyqqanpGtnZqZDe6dmTTUmNlpXx0SqdaNGLukjAJQgyAwAAAAAAOAGsvPyNGt+hqYkpSppzVqH9gBfX13Uv6+ttXxql87y9vZ2ST8B4GgEmQEAAAAAAFykuLhYCzZt1pTEFM2cO18Hc3IctunbprXGxsfoisiBahwc7JJ+AsDxEGT2cFlZWcrOzra38/Pz5UPtJQAAAAAA3N6+7Gx9mD5PU5NStXDzFof20IAAG1Q2weX+4W3l5eXlkn4CQGUQZPZwEydO1IQJE0p/Dg8Pd2l/AAAAAADAsbOWf1u1xk7i99mChcotKHDYJq5zR1sO4+L+EQoJ8GcoAXgEgsweLiEhQePHj7e3hw0bRiYzAAAAAABuZtv+A3o/Jc1O5Ld2126H9mahIRoZE2Un8uvWsoVL+ggA1UGQ2cOFhITYxfDz83N1dwAAAAAAgKSCwkJ9t3S5zVr+dskyFRYVlRsXby8vnd2zu8bExei8Pr3k70uIBoDn4gwGAAAAAABQQ9bs3KVpyal6LyVN2w8cdGhvFxamMXHRGhUTpbZhjRl3AHUCQWYAAAAAAIBqyMnP1+cZi2zW8q8rVzu0+/n46IJ+fTQuPkZndOsqb29vxhtAnUKQGQAAAAAAoAoWbd5iA8sfps/TvuxDDu09WrXU2LhoXRUVqaahh0tdAkBdRJAZAAAAAACgkg4cOqSP5i6wweX5Gzc5tIf4++uyQf01Li5GkR3ay8vLi7EFUOcRZAYAAAAAADiO4uJiJa9dpymJKfp0foYO5ec7bGMCyiZr+bKB/dUgMJDxBFCvEGQGAAAAAACowM6DmZqemm6zllft2OnQHhYcrKuiB2lsXIx6tW7FGAKotwgye7isrCxlZ2fb2/n5+fLx8XF1lwAAAAAA8FiFRUX6cdkKG1j+atESFRQVOWxzZvduNmv5goi+CvAltAIAnAk93MSJEzVhwoTSn8PDw13aHwAAAAAAPNGG3Xs0LSVN05JTtWXffof21o0aaXRslEbHRqtD0yYu6SMAuCuCzB4uISFB48ePt7eHDRtGJjMAAAAAAJWUW1CgLxcutlnLc1assrWXy/L19tbQPr00Lj5GZ/fsIR9vb8YWACpAkNnDhYSE2MXw8/NzdXcAAAAAAHB7y7Zu05SkVM1IS9eerMMlKMvq0ryZxsbH6OroSLVo0MAlfQQAT0KQGQAAAAAA1HmZubn6dF6GzVpOXbfeoT3Iz0+XDIiwk/jFde4oLy8vl/QTADwRQWYAAAAAAFAnmfIXc9dv1OSkFH08b76ycvMctunfrq0NLI8YNEANg4Jc0k8A8HQEmQEAAAAAQJ2yJytLH6TNs1nLS7duc2hvFBSkK6MGakxsjPqFt3FJHwGgLiHIDAAAAAAAPF5RUZF+WbnaZi3PzlikvMJCh21O7dpZY+JidHFEPwX5M68RANQUgswusm/fPi1atEjBwcHq2bOnXQMAAAAAgJOzZd8+TUtO07TkVG3Ys9ehvUXDBhodE6XRsdHq3LwZwwsAtYAgs5Nt3rxZ9913nz755BNFRkbaYPO2bds0adIkXXfddc7uDgAAAAAAHie/sFDfLF5qs5Z/WLpcRcXF5dq9vbx0bu+eGhsfo3N79ZSvj4/L+goA9QFBZiebN2+eFi5caNcmg9l4+umndcMNNygiIkKDBg1ydpcAAAAAAPAIK7fv0NTkVE1PSdfOzEyH9o5Nm9hyGCOjI9W6cSOX9BEA6iOCzE7WpUsXzZkzR02bNi2974477tADDzygr7/+miAzAAAAAABlZOfl6bP5C23WctKatQ5jE+Drqwsj+mpcfIxO7dJZ3t7ejB8AOBlBZifr1auXw307duxQcXGxmjdv7uzuAAAAAADgdsxn5AWbNmtKYopmzp2vgzk5Dtv0bt1K4+JjdUXkQIWFMM8RALhSnQ8yL168WD///LOysrJsOYqhQ4ee8DEFBQX66aeftGLFCgUGBioqKso+trY8+OCDCgoK0vnnn19rrwEAAAAAgLvbl52tmenzNSUpRQs3b3FoDw0I0IjIAbYkxsB24fLy8nJJPwEA9SDIvH//ft1111369ttv7UR7JW688cYTBpmTk5M1atQorV1b/hKcYcOGacqUKWrSpEm5+9etW6dFixYd9zl9fHzs4yvyzDPPaOrUqXrttdcUHh5eiXcHAAAAAEDdylr+bdUaW2v5swUZyskvcNgmtlNHjY2L0SUDIhQS4O+SfgIA6lmQee/evXr77bft7d69eys4OFhpaWknfNz69ettNvG+ffvUqVMnnXfeeTpw4IBmzZqlL7/8UsOHD7cZzmW/KTWZ0q+88spxn9ff37/CIPPkyZN1zz336NFHH9VNN91UpfcKAAAAAIAn2rb/gKanptus5bW7dju0NwsN0dXRkTa43K1lC5f0EQBQj4PMjRo10ptvvmmzltu2batJkyZVKsj8yCOP2ADz4MGDNXv2bFvCwli2bJni4uJs2Y2ZM2fqiiuuKH3MhRdeaJeT9cknn+iGG25QQkKC/v73v5/04wEAAAAA8DQFhUWas3KVPpy/UN8sWarCoqJy7Sap6+we3TUmLlrn9+0tf986GbYAgDrHqWfr3Xv3aeWa9WrSuJG6d+lYa68TFham66+//qQek5OTYwPIxrPPPlsaYDZ69uxpM45NMNiUzCgbZK4KU8Zj5MiRGj9+vP71r39V67kAAAAAAHB363bt1rTkVE1NStX2gwcd2sPDGmtMbLRGxUYpPCzMJX0EAHhIkPmXpHTdct/fdemwIXp10gS5kwULFtjJAdu1a1fhJH+XXHKJDTInJiZW+3Uuu+wy9ejRQ+ecc44+//zz0jZToqNPnz4nfI74+PgK7ze1oXv16qXMzEzVddnZ2a7uAuoIjiVwLMHdcF4CxxLcEecmVIWprfz1kmWanj5Xv69Z59Du5+Otob166urIgTq1Syf5eHvb++vDZ1pUH+cl1JT6diyFhoZ6fpA5rFFDuz50KEfuZtWqVXZtgrQVMdnM5rKdHTt22DrNDRsefi8na9euXTrrrLPs7aNrOV900UWVCjIDAAAAAOCulm7brulp8/Txggztr+Dzf+emTTQ6JlLDB0SoaUiIS/oIAPDgIHP/Pj3k5+ur5avXyt3s37+/tNRGRQIDA+1y6NChagWZhwwZYpfqKJtNbbKvS75xMZMLmkB4bX0j4Y7q03tF7eJYAscS3A3nJXAswR1xbsKxHMzJ0Udz52tKUqrmbdjo0B7s76fhAwfo8v59NahduBo0aMBggvMS3Ar/x3lQkLlxo4a69fpReu71yXpz2kzdMHqE3I0J0h6L95FLd4qLi+UuJk6cqAkT/ig9Eh4e7tL+AAAAAADqB/PZOGXtek1NStEn8xcoOy/fYZtB7dtpbHyMhg/srwaBgZTCAIA6yqlB5nUbNqtNqxZ20r8HH/+vvp3zu2IG9lOTsMYO23Zq31ZnxEc7rW8l36KWZDQfLS8vrzRj2J2+cU1ISLATCJZkMvv4+Li6SwAAAACAOmznwUzNSEvXlMRUrdyxw6E9LDhYV0UN0pi4aPVu09olfQQA1OEg8/xFS/XAY/8u/fnHX5PtUhEzOaAzg8ydO3e26+XLlx+zZrP5lrZJkyZq3NgxKA4AAAAAQF1VWFSkn5avtFnLXy5aovzCQodtzujeVWPjYnRBvz4K9PNzST8BAPUgyNyrexfdf/ufKrVtj66d5Ez9+/dXQECA1qxZo5UrV6pbt27l2mfPnm3XMTExcieUywAAAAAA1JaNe/ZqWnKqpiWnafO+fQ7trRo11JjYaI2KiVLHZk3ZEQBQTzk1yGwCx84OHp9Mce+LLrpIM2fOtCUozLqk9MSWLVs0adIke3vkyJFyJ5TLAAAAAADUpLyCAn21aImmJKXox+UrHeYl8vX21tA+vWzW8tk9u8uXso0AUO85NcjsTG+//bZ27dplb8+ZM8euFy5cWBosNpP43XPPPeUe89hjj9mM5U8//VSxsbG6+OKLdfDgQU2ePFk7duzQgAEDNHbsWBe8GwAAAAAAatfybdttYHlG6lztzspyaO/cvJkNLF8dHamWDd1nriIAgOt5FR/9laQTbd66XWvWb1Refr5at2iunt062+BvTejbt68WL158zHaTpVxQUOBw/5dffqlx48Zp9+7d5e6PjIy0wee2bdvKnTz66KOaMGFC6c/h4eHauHGj6rrMzMzSDHSAYwnugPMSOJbgbjgvgeMJlZGVm6dP5y+wweWUtesd2gP9fHVJ/wiNjY9RfOdO8vLy4twEt8D/c+BYci8uyWROm79If3vyWTsRYFktmjXVPbdep+tGDq/2a1x//fXaunXrMdtLSmEcbdiwYVq9erVmzZqlFStW2DrN0dHROuecc475GFeiXAYAAAAA4GSYXLN5GzZqSlKqPpo7X5m5uQ7bRIS3tVnLIwYNUKPgIAYYAOBeQebEtPm66sa7lF9QoKDAAPXo2lkhwUFavnqtduzarQce+7e2bt+hv975f9V6nXvvvbfKj23UqJHNZvYEISEhdjH8mL0XAAAAAHAMe7Oy9UHaXJu1vGTrNof2hoGBujJqkMbERdsgMwAAbhtk/suESTbAfNZpsXr2nw+qRfPDs8+a0hUv/G+qnnrudT3/xlRdcfH56ta5g7O753GysrKUnZ1tb+fn57tltjUAAAAAwDWKior066o1NrD8RcYi5VZQNvKULp01Ni5aF/ePUJC/n0v6CQDwbE4NMi9duUYr16xTo4ahevnpv6txo4Z/dMTXV3f937Wat3Cpvv7xV33x7U/2ZxzfxIkTHWoyAwAAAADqt6379uu9lDRNTU7V+t17HNpbNAjVyJgojY6NVtcWzV3SRwBA3eHUIPP6jZvtOqJ3j3IB5rLOiI+2QeZ1R7bF8VGTGQAAAABg5BcW6tvFSzUlOVXfLVmmouLicgPj7eWlc3r31NjYaJ3bp5f8uBIWAOCJQWYvHZ6FtrCw6JjbFBYW2rW3t7fT+uXJqMkMAAAAAPXb6p07NTUpVe+npGnHwUyH9g5Nm2hMbLRGxUSpdeNGLukjAKBuc2qQuUun9nadsWS5du7eq+ZNwxy2+fG3ZLvu3KGdM7sGAAAAAIDHyM7L0+cLFmpyUooSV691aPf38dGFEX01Lj5Gp3XtQiIXAKDuBJm7dmqvvj27adGylbr53of13BN/U7s2rWxbTm6u/v3SW/rx12T5+vro4qGDndk1j8XEfwAAAABQf2Rs2mwn8fswbZ4O5OQ4tPdq3Urj4mJ0RdRANQkJcUkfAQD1j1ODzMbER/+iy6+/XYmp8xU/7Gp1CG+jkOAgrV63UVnZh+w2999+kzq0a+vsrnkkJv4DAAAAgLptf/YhzZw7T1OSUm2Q+WghAf66fNAAG1we2L6dvLwOl6oEAMBZvIqLj5oJwAmWrlitf0x6UT8npZfWYC7JdL7vtht02QXnOLtLdSKTediwYfLx8VFy8uGSI3VZZubhOmOhoaGu7go8HMcSOJbgbjgvgWMJ7ohzk/OZj+qJa9ZqSmKKZi3IUE5+gcM2MZ06aGxcjC4ZEKHQgAB5Ao4lcCzB3XBe8tBMZqNX9y5677X/6GBmltZt3KyCgkK1atFMrVs2d0V3PBoT/wEAAABA3bH9wEFNT0nTlORUrdm5y6G9aUiIro6J1NjYaHVv1dIlfQQAwKVB5qT0BXr+jSmKGxSh228apwahIerXq7szuwAAAAAAgFspKCzUD8tW2FrLXy9eqsKionLtpvzFWT262azl8/v2lr+vS/LFAAA4Jqf+z7Rn7z59/3OiQkOCnfmydRoT/wEAAACAZ1q3a7emJafqvZR0bd2/36E9PKyxRsdGa3RslMLDwlzSRwAA3C7IHN6mlV1v277TmS9bpzHxHwAAAAB4jpz8fM1euNhmLf+8YpVDu5+Pj4b17W2zls/s0U0+3t4u6ScAAG4bZDalMczkfguXrtS2HbtsHWZUT0JCgsaPH19u4j8AAAAAgHtZsmWrpialakbaXO09Mnl7Wd1atNDY+GhdFRWp5g2Y4BwA4FmcGmQ2daRenvioRv/ffbr+jr9q0qN/UZ+e3ZzZhTqHif8AAAAAwD0dzMnRx/MWaEpiiuZu2OjQHuzvp8sG9NfY+BhFd+xgPzMDAOCJnBpk/ubHX/XgE8+ooKBA8xYu1ZAR1yskOEhhjRs5bDt08Kl64qG7ndk9AAAAAACqpbi4WGnrNthyGJ/MW6CsvDyHbQa2b6cxsdEaETlADQIDGXEAgMdzapA5+1CONm3ZVu6+rOxDdjna7r37nNgzAAAAAACqbldmpmakztXU5FQt37bdob1xcJCuihqkMXEx6tOmNUMNAKhTnBpkvnTYEF00dHCltvVmcgMAAAAAgBsrKirSnBWrbNaymcwvv7DQYZvTu3XV2LhoXRjRV4F+fi7pJwAAdSrInJ9foAOZmfL381NDJjIAAAAAAHigTXv3alpymt5LTtPGvXsd2ls1aqjRMVEaHRutjs2auqSPAADU2SDz7O9/1i33/d1mNL86aYIzX7rOysrKUvaRmYnz8/Pl4+Pj6i4BAAAAQJ2TV1CgrxcvtZP4/bB8ha29XJaPt7fO69NLY+KiNaRnD/ny2QwAUI84NcjcIDS4NBiKmjFx4kRNmPBHwD48PJyhBQAAAIAasmLbdk1JTtWM1HTtysxyaO/UrKnGxcXo6pgotWzYgHEHANRLTg0y9+nRTV5eXlqzfpMzX7ZOS0hI0Pjx4+3tYcOGkckMAAAAANWUlZunWfMzbK3l5LXrHNoD/Xx1Sf8Im7V8SpfO9nMuAAD1mVODzK1aNNOIi4fqw1lf67ufE3XOGfHOfPk6KSQkxC6GH5NIAAAAAECVmPIX8zZusuUwPpo7X5m5uQ7b9GvbRuPiYzRi0EA1Cg5ipAEAcEWQeefuvRp+wTnKWLxcN9zxoK4bOVzRA/upSVgjh22bNQlTj66dnNk9AAAAAEA9szcrWx+mz7NZy4u3bHVobxAYqCsiB2psXLT6t6M8IQAALg8y/5acrlsSHi39+bXJM+xSESYHBAAAAADUhqKiIv26ao2mJqfo8wWLlFtQ4LBNXOdOttbyxQP6Kdjfnx0BAIC7BJnbtW2lERcNrdS2kf371Hp/AAAAAAD1x9b9+/V+SrqmJqVo3e49Du3NQ0M1MiZKo2Oj1K1lC5f0EQAAT+TUIHNk/752AQAAAADAGQoKC/Xt0mW21vK3S5apqLi4XLu3l5eG9Ophs5bP7dNLfj4+7BgAANw5yAwAAAAAgDOs2blLU5NS9X5qmrYfOOjQ3r5JmMbExWhUTKTaNG7MTgEAwBODzGbm3pVr1mv33n1q0rgRk/wBAAAAAKrlUF6+Ps9YaCfx+23VGod2fx8fXRjRV+PiY3Ra1y7y9vZmxAEA8NQg88dffKt//Pslbd2+s9wkfybofMt9f1f3Lh318sQ/JgjEsWVlZSk7O9vezs/Plw+XdgEAAACoZxZu2mIDyx+mz9P+Q4cc2nu1bqWxcTG6MmqgmoSEuKSPAADUZU4PMs/8/BuNv/8fCgoMUJ8eXbV4+arStm6dOyj7UI4++fJ7PXj3LWrXppWzu+dxJk6cqAkTJpT+HB4e7tL+AAAAAIAzHDh0SDPnzrfB5QUbNzu0hwT46/JBAzQ2NkaDOrSTl5cXOwYAgLoQZM7PL9CEiS/a228//5T27tuvWxLKZywPOSNOb0z5UF//+Kv+NOYKZ3bPIyUkJGj8+PH29rBhw8hkBgAAAFBnmbKLSWvW2cDyrPkZOpSf77BNdMcONmv50oERCg0IcEk/AQCob5waZF64dLl27Nqtnt0668xTom3G8tHatWlt1ytWr3Nm1zxWSEiIXQw/Pz9XdwcAAAAAatyOgwf1fkq6pialaPXOXQ7tTUKCdXV0pA0u92jVkj0AAEBdDjJv3X74j4GO7dradUVXKzVq2MCus7Md62gBAAAAAOqHwqIi/bBsuaYkperrRUtUUFRUrt2UvxjcvZvGxsfo/L69FeDrsnntAQCo95z6v3BgoL9d5+TkHnObbTt2lgs2AwAAAADqj/W792hacqqmJadp6/79Du1tGzfWqNgojY6JUvumTVzSRwAA4MIgc48unex66crVKioqqnDihR9+SbLrvr26ObNrAAAAAAAXyS0o0OyMRTZrec6KlQ7tvt7eGtavjy2HMbhHN/l4e7uknwAAwA2CzOFtWil2UISS52bo/Y9nKzQ0uFz7m9NmKmXeQoUEB+mCIWc4s2sAAAAAACdbunWbpiSmaEbaXO3NznZo79aihcbERdt6y80bhLJ/AABwU04vWvXk3+7RRWNu1X2PPq1O7Q/XZp6bsUTnjLhei5Yd/sZ6wl9ur9PlMho3bmzXJpO7SZMm6t+/vx566CFFRka6umsAAAAAUKsO5uTok3kLbNZy+voNDu3B/n66dEB/m7Uc06lDhVfAAgCAeh5k7t2jqz6d/KLu+/vTWrB4mb1v4+at2mhmBG7cSI/cN14jh1+gumzdunWlt7dt26bHH39cZ5xxhpKTk9W3b1+X9g0AAAAAalpxcbENKE9OStEncxcoKy/PYZsB7cJt1vKIQQPUMCiInQAAgAdxyfS7/Xp119cz3tCK1eu0bNUa5ebmqXXLFooe2FcB/ocnB6zLSjKZS26/+eab+vjjj/Xee+/ZgDMAAAAA1AW7M7M0Iy1dU5NStWzbdof2RkFBuipqkA0u923bxiV9BAAAHhpkLtG9S0e71Hd+fn7y9/dXbm6uq7sCAAAAANViJnn/eeUqTU5M0ZcLFyuvsNBhm9O7dbWB5Qv79VWQvx8jDgCAh3NpkNlZ9uzZo+zsbIWEhCgsLOykHhcYGKjg4PITFNYkE1h++umnVVBQoBtvvLHWXgcAAAAAatPmvfs0LTlV05LTtHHvXof2lg0baHRstF06NWvKzgAAoA6pk0FmE7D9/vvv9c0339hl0aJF9n4TxH3jjTeO+9isrCw9+uijeuutt7R79257X69evfTAAw/ommuuqbE+vvzyy/rrX/+qgwcP2uD3lClT7OsAAAAAgKfIKyjQN4uXakpSir5ftsLWXi7Lx9tbQ3v30tj4aA3p2UO+Pj4u6ysAAKg9dTLIvGnTJp1//vnlylHk5+dXKqvYPO7XX38trZeck5OjpUuX6tprr7UT9j3yyCPlHvP6668rISHhuM9rsqHNBH9l3XDDDRo1apR27dplA8xXXHGF3n//fV1++eUn+W4BAAAAwLlWbt9hA8vTU9O1KzPLod1kKo+Ni9HV0ZFq1aghuwcAgDquTgaZfX19NXTo0NLl66+/PmEg2HjuuedsgLl58+aaMWOGBg8erLy8PD3//PO677779I9//MMGgfv27Vv6GBN8vvLKK4/7vF5eXg73BQQE2MUEsk3mdEpKip566imCzAAAAADcUnZenj5LTtPU5BQlrVnn0B7o56uL+0doTGy0Tu3aucLPQQAAoG6qk0Hm8PBwG1guUfb28bz44ot2bYLKJsBsmAn57r33XqWlpdlM41dffdW2lzDtZqmJwHhlsq0BAAAAwFlM+Yv5GzfprV9+16yMhcrMzXPYpm+b1hoXH6sRkQPUuBbnswEAAO6rTgaZq2L58uVav369GjRooBEjRji0m/IWJshc2YD1sZjHz50719Z3btu2ra0B/c477+iLL77Qf//730o9R3x8fIX3m9rTpq5zZmam6jozkSPAsQR3wnkJHEtwN5yXUB37sg/pkwUL9X76PC3btt2hvUFAgC7p31cjIwfaILPNWi4qqhefRVA9nJtQUziWwLFUNaGhoaoNBJmPWLx4sV1HRETYrOKjRUZG2vXq1att7WZT6qIqTj31VJsVfcYZZ2jLli32j7E+ffro7bff1rhx46q+JwEAAACgGoqKipW0bp2mp83Tl0uWKq+g0GGbmA7tdXXUQF3Qp7eC/P0YbwAAYBFkPsJMwGe0atVKFWnSpIkti2FqNO/du/eY21Xm24KHHnrILlUNVicmJh43w7m2vpFwR/XpvaJ2cSyBYwnuhvMSOJbgLFv379f7Kemalpyqtbt2O7Q3Dw3V5QP66crIgRrQqSM7BjWC/+dQUziWwLFUx4PM3/z4qx584pkqP37o4FP1xEN3y1lMwNc4Xn1lExA2QeacnJwaec2qZkOXZcptlFwiYmo6+/j41EDPAAAAANRlBYWF+nbpMk1JTNF3S5ersKioXLu3l5fO7tVDY2OjNbRPL+XV0GcgAABQN9VakDn7UI42bdlW5cfv3rtPzhR8ZIKKQ4cOHXPCi5K2kJAQuYuJEydqwoQJ5SY9BAAAAICKrNm5y2Ysv5eSpu0HDjq0twsL05i4aI2KiVLbsMal9ztO9wcAAOCEIPOlw4booqGDHe7fsHmrrv3zX5WZlaWH7r5F8VEDFBIcpCUrVuvpF/6njMXL9ezjD+rCc8+UM7Vp0+Zw/zZsqLB969atKigosNnHpnSGu0hISND48ePt7WHDhpHJDAAAAKCcQ3n5+jxjoaYkpei3VWscRsffx0fD+vXRuPgYndGtq7y9vRlBAADgHkFmM6FdRRPo3ZLwqNZt2KSvZ7yh3j26lt5/SvRATX/9Pzrvqj/pjgf/qYje3dWhXVs5i5nwz1i4cKEOHjyoBg0alGv/9ddf7bp3794EcgEAAAC4vUWbt9jA8gdp87S/gis2e7ZqqbFxMboyapCahrrP1ZoAAMDzOPUr6kVLV9pM5X69u5cLMJcI8PfX5Reeq0M5ufrws2+c2TW1bdtWAwcOtHWNX3755XJtRUVFeu655+ztiy++WO7ElMto0aKFXdLT07VlyxZXdwkAAACAixw4dEhv/ZaoIf9+VoMnPqM3fvm9XIA5xN/flsP46q7x+uX+e3TL4NMJMAMAAPfNZK7Ixi1b7TqscaNjbhPWqKFdr99UvWDp9u3bbcDY2L9/v12bCfI2bdpUmmltAstl3X///Ro5cqT+9re/2RrMl112mc1qNoHc3377zc5Yetttt8mdUC4DAAAAqN/MZ5fktevsJH6fzs/QoSOfg8qK6tBeY+NjdOmACDUIDHRJPwEAQN3l1CBzgyMT5i1etlL5+QXy83N8+bkLl9h1wwbVu1xryJAhWrx4cbn73nvvPbsYPj4+tsZyWVdffbV++uknvfLKK3rggQfsUsLPz0+TJ09Wy5Ytq9UvAAAAAKgJOw4e1PTUdE1NStWqHTsd2sOCg3VV9CBbEqNX61YMOgAAqBtB5sgBfdWoYai27dilvz/9vB5N+LP8/f1K27/8/mdN/+RLe3vI6fHVeq1WrVpp3759x2yvqF60YUplmAD1W2+9pRUrVtiJ/qKjo3XPPfeoX79+cjcmy3rChAmlP4eHh7u0PwAAAABqT2FRkX5ctsLWWv5q0RIVFBU5bDO4RzeNiY3WBRF9FXCMzz0AAAA1yavYXFvlRB/M+kq3//Wf9nZ4m1aK6t9HQUGBWrZyjeYtXGrvv2joYL3x38Pb4PiysrJsGRBj2LBhNkM7OTm5zg9bZmamXZsSJgDHEtwB5yVwLMHdcF6qWzbs3qNpKWl6LzlNmytIpmndqJFGx0ZpdGy0OjRtUuOvz/EEjiW4G85L4FhyL07/WvvKS85XcFCQHp34gjZu3qpNW7aVtpn7/zT2Ct132w3O7pbHCgkJsUtJSQ8AAAAAdUNuQYG+XLjYZi3PWbHK1l4uy9fbW+f37W3LYZzVs7t8vJ06rzsAAEApl1w7deG5Z2rYkNO1cOkKrVm3UQWFhWrVopkG9eutkJBgV3SpTmQym4kOTSYzAAAAAM+1bOs2TUlK1Yy0dO3JOvy3flldmjezk/hdHR2pFg0auKSPAAAALgsyr1q7QV//+Ku6dmyv884+Tf379LQLqo6azAAAAIDny8zN1SfzFmhKYorS1m9waA/y89OlAyJscDm2U0d5eXm5pJ8AAAAuDzIvWbFKj/37JV06bIgNMqP6EhISNH78+HI1mQEAAAC4P1P+In39Bpu1/PG8+crKzXPYJiK8rcbFx2jEoAFqGBTkkn4CAAC4VZC5RbOmdr1//0FnvmydRk1mAAAAwLPszszSB2lzba3lZdu2O7Q3CgrSlVEDNSY2Rv3C27ikjwAAAG4bZB7Yr5caNQzVouUrlZObq8CAAGe+fJ1ETWYAAADA/RUVFemXlas1OSlFszMWKa+w0GGbU7t2tpP4XRTRT0H+TOoNAAA8h1ODzAH+/nryoXv057/+Uw89/owef+guAs3VRE1mAAAAwH1t2bdP05LTNC05VRv27HVob9GwgUbHRGl0bLQ6N2/mkj4CAAB4VJB5bsZi/fR7qjp3CNfUmZ/pu59/V7/ePdSkcSOHbQdF9NZ1I4c7s3seiZrMAAAAgHvJLyzUN4uX2qzlH5YuV1Fxcbl2by8vndu7p53E79xePeXLvCoAAMDDOTXIvGHTVs349MvSn7fv3K3tc36vcNvcvDyCzJVATWYAAADAPazcvkNTk1M1PSVdOzMzHdo7Nm2iMXExGhkdqdYVJNoAAAB4KqcGmU+NGaQZb/y3Uts2PzJJIAAAAAC4q+y8PH02f6HNWk5as9ahPcDXVxf172trLZ/apbO8vb1d0k8AAIA6E2Ru3qyJXQAAAADAky3YuElTklI1M32eDuTkOLT3adNa4+JjNGLQQIWFBLukjwAAAHUyyIyal5WVpezsbHs7Pz9fPtRzAwAAAGrFvuxszUyfrylJKVq4eYtDe2hAgEZEDrBZywPahcvLy4s9AQAA6gWCzB5u4sSJmjBhQunP4eHhLu0PAAAAUJcUFxfrt1VrbK3lzxZkKCe/wGGb2E4dbdbyxf0jFBLg75J+AgAA1Lsg885dezR15mdKW7BYe/buU0FhocM2Z50ao7/e+X+u6J5HSUhI0Pjx4+3tYcOGkckMAAAA1IBt+w9oemq6zVpeu2u3Q3uz0BBdHR1ps5a7tWzBmAMAgHrN6UHmBYuXadTN92rPvv3H3a5TezJyKyMkJMQuhp+fX43sIwAAAKA+Mskv3y1dbgPL3y5ZpsKionLtpvzFkJ7dbWB5aJ9e8vflwlAAAADD6X8V3fW3J22AeewVF6trpw56dOILOv/s03XHTeP03OuT9UtSmp59/CGdER/FHgIAAABQ60ym8rTkVLtsP3DQob1dWJhGx0ZpVGyUwsPC2CMAAACuDDKvXLNeS1esVuOGDfTEQ/do9ndz7P0BAf4aFNFbbz77uM68dJz+MmGi5sya4syuAQAAAKhHcvLz9XnGIpu1/OvK1Q7tfj4+uqBfH1tr+YxuXeXt7e2SfgIAAHgCpwaZ16zbaNcRfXrI39/PXG9mfy46chma+cPt8gvP1b+ef0OfzP5WN427ypndAwAAAFDHLd6yVVMSU/RB+lztyz7k0N6jVUuNiY3WVdGD1Cw01CV9BAAA8DRODTJ7eR8OKgcHBdl14JGZl7PK/HHXplVLu16+aq0zu+axsrKylJ2dbW/n5+cz8R8AAABwlIM5OZqZPl9Tk1M1b8PhxJeyQvz9ddnA/rbWclTH9rb2MgAAANw0yNw+vLVdb9m23a5bt2xu1xs3byvdZteevXbt7ePjzK55rIkTJ2rChAmlP4eHM2EiAAAAUFxcrJS16205jE/nL1B2Xr7DoER2aK+xcdE2wNwgMJBBAwAA8IQgc9eO7dWsaZhWrt2gzKxs9e7eVY0ahmrlmnX65sdfFTmgr97/eLbdtmfXTs7smsdKSEjQ+PHj7e1hw4aRyQwAAIB6befBTE1PTdfUpFSt3LHDoT0sOFhXRQ3SmLho9W5zOAkGAAAAHhRk9vX11eUXnKvXJs/QjE+/1A2jR+jPN4zR48+8qmv+/EDpdq1aNNPVl13gzK55rJCQELsYfn5+ru4OAAAA4HSFRUX6aflKm7X85cLFKjgy50tZZ3bvZrOWh/Xro0D+bgYAAPDcILPx8L236d7bri8NiP75T2MVGBig6Z98qb37Dyiid3c9dPetCgk+XLcZAAAAACqycc9eTUtO1bTkNG3et8+hvXWjRhodG6VRMVHq2KwpgwgAAFBXgsx+fr5q5Neg9GczqcZN466yCwAAAAAcT25Bgb5atERTElP004qVtvZyWb7e3jqvb2+btXx2zx7y8fZmQAEAAOpSkDkvL1/+/pR0AAAAAHBylm/bbsthzEidq91ZWQ7tnZs309i4GF0dHamWDf9IagEAAEAdCzLP/m6OJkx6UWfER2vwKdE645RoNQ1r7MwuAAAAAPAQmbm5+nRehqYmpyhl7XqH9kA/X13SP0Jj42MU37mTvUoSAAAAdTzI3KhhA+3dt1/TP5ltF/NHYL9e3XTmKTE6Mz5aMYMiyHQGAAAA6jFT/mLeho2anJSij+bOV1ZunsM2/cLbaFxcrEYMGqBGzOUCAABQv4LMZ50Wq2WJXyo5PUM//Z6iOb+laOHSlcpYskLPvzFFQUGBio8aoMGnxGjo4FPVsX1bZ3YPAAAAgIvsycrSB2nzbEmMpVu3ObQ3DAzUFVEDNSY2Wv3bhbukjwAAAHCTif8CAwJ05inRdtF947Vj527NSUzVnN9T9XNimn74Jcku6RmL9eqkCc7unsfJyspSdna2vZ2fny8fHx9XdwkAAAColKKiIv26arUmJ6boi4xFyissdNjmlC6dbTmMiyL6Ktjfn5EFAABwQ04PMh+tRfOmih7QT1nZh3QwM0vf/Zyowgr+uETFJk6cqAkT/gjGh4eT1QEAAAD3tnXffr2Xkqapyalav3uPQ3uLBqEaGROl0bHR6tqiuUv6CAAAADcPMptg8q/J6frptxSbwbxu42Z7f0hwkC2pYSYFPHfwqa7omsdJSEjQ+PHj7e1hw4aRyQwAAAC3lF9YqG8XL7W1lr9fulxFxcXl2r29vHRO754aGxejc3v3lB9X6AEAAHgMpwaZM5Ys18NPPmtLYRQUFMrb21t9e3XTHTeNs+UzYgZGyM/P5cnVHiUkJMQuhp+fn6u7AwAAAJSzeudOTU1K1fspadpxMNNhdDo0bWIzlkfHRKl140aMHgAAgAdyakR3zbqNSp6boaDAAN163Sjdct1INQ1r7MwuAAAAAKhl2Xl5+nzBQpu1nLh6rUO7v4+PLurfz2Ytn9a1s00+AQAAgOdyapC5WZMwhTVqqL37D+j5N6Zo+idf6oxTonTWqbE6Iz5azZuGObM7AAAAAGpQxqbNmpKUog/T5ulATo5De+/WrWxg+YqogWpy5Go8AAAAeD6nBplPi4vU4l8/14LFyzXn9xT99HuqPp39vT6c9bW8vLzUt2c3DT41RmeeEqOYgf3k70/5BwAAAMCd7c8+pJlz59ms5YWbtji0hwYE6PJBAzQ2PkYD24Xbv/sBAABQt3gVFx8144aTZWVl67eUuTbgbALPq9dttPcPv+AcvTzxUVd2zePEx8fbdWJiouq6zMzD9fxCQ0Nd3RV4OI4lcCzB3XBegiccS+YjxO+r19hay7MWZCgnv8Bhm9hOHW3W8iUDIhQS4F/jfYBzcW4CxxLcDeclcCy5F5fPshccHKSWLZqpVYtmatG8qdZt3KLCwkKH2abrqqlTp+r555/X2WefrSeeeMLV3QEAAACOafuBg5qekqYpyalas3OXQ3vTkBBdHROpsbHR6t6qJSMJAABQT7gkyLxtxy799FuKzVz+OSlNu/fsK21r17a1zoyP0oiLz1Ndt379et1+++32ksHw8HBXdwcAAABwUFBYqB+WrbC1lr9evFSFRUXl2s3fsmf36G7LYZzXp5f8fV2exwIAAAAnc+pfgOkLFunevz+tZSvXlN4XGhKsoYNPtXWYB58arS4d26s+MJcYXn/99frTn/6kH374wdXdAQAAAMpZt2u3piWnalpKmrbtP+AwOuFhjTU6NlqjY6MUHsYE3gAAAPWZU4PMGzdv04rV69S/T08bUDaB5egB/eTnV/+yHZ555hlt2rRJX3zxBUFmAAAA1KhDefmat2GTsnJz1ahhQw1oF66gSkyqnZOfr9kLF9us5Z9XrHJo9/Px0bC+vW2t5TN7dJOPtzd7DgAAAM4NMp8aG6lFv3ymJo0b1euhX7p0qf72t7/pyy+/VFBQkKu7AwAAgDpi6779ennOL5qWlCp/HZ7jZMehHDUOCtLouGjdOvh0tW7k+Lf4ki1bbWB5Rtpc7cs+5NDerUULjY2P1lVRkWregImXAQAA4MIg8/4DB/X1j7+qa8f2Ou/s02r1tTZv3qxvvvnGLj///LOysrJ0zTXX6LnnnjvhY9955x299dZbWrFihQIDAxUVFaX77rtPMTEx1e5XQUGB7ce1116rM844o9rPBwAAABgLN23RVa++oZ0HM+3PLYICSwdm36FDeunHn/VB2lzN+L8/qV94Gx3MydFHc+dralKq5m7Y6DCIwf5+umxAf1trObpjB1t7GQAAAHB5kHnJilV67N8v6dJhQ2o1yLxhwwZ16NDB4f7s7OwT1km+7rrr9O6775a7f+3atfroo480efJkjRo1qlzbhx9+qEmTJh33eQMCAjRnzhx7+8knn9T27dv1r3/96yTeEQAAAHD8DOayAeZjMe3DX3pVg3t00zeLlyo7L99hm0Ht22lMXLQuHzRADQL/CFQDAAAAbhFkbtGsqV3v33+wVl+nqKhIbdu21bnnnquhQ4cqIyNDTz311AkfZ4LIJsBsspcnTpyo4cOH68CBA/a2yWw2k/SZ7GPz3CVOP/10hYeHH/d5vcvUqjPBZpPNbPpWYtmyZTaQHRcXp9dee00RERFVfu8AAACof0yJjBMFmEuYchifzMsod1/j4CBdFTVIY+Ji1KdN61rqJQAAAOoqpwaZB/brpUYNQ7Vo+Url5OYqMCCgVl7HZDGbSfXKls6ojJKMZBOQ/vOf/2xvm4Dy//73P61bt04//vijXnrpJT3++OOlj2nZsqVdKuv555/X/v37y913/fXXq3Xr1nriiSfUqVOnSj8XAAAAYCb5MzWYK7pKL6+o6LgDdEb3rhoTG60LI/oq0O/EEwMCAAAALg8yB/j768mH7tGf//pPPfT4M3r8obtqJdBclXpxGzdu1MKFC21pi5tuusnh+UzQ2QSZP//883JB5pPVq1cvh/tCQkLUpEkTm8lcGfHx8RXev2jRIvv8mZmVy2LxZCcqfQJwLMHZOC+BYwmuMm/DJjvJX0kN5sKiYuUUFmpvbp4Kig9P/leWucYu0NdH/7lyuM7v09veV5Cbq8zcXKf3HZ6D/+fAsQR3w3kJHEtVExoa6vlB5rkZi/XT76nq3CFcU2d+pu9+/l39evdQk8aOM1wPiuit60YOd1rfTEkNo1+/fgoODnZoP+WUU0pLW5hyF76+Th06AAAAoEJZubk2azm3qEg5BYXHzF729/ZWkK+PXZskilD/2rmqEAAAAPWPUyOlGzZt1YxPvyz9efvO3do+5/cKt83Ny3NqkHnbtm123a5duwrbW7VqZQPLeXl52rt3r5o3b15jr/3222/bDOrKSkxMPG6Gc219I+GO6tN7Re3iWALHEtwN5yVUxopt2/VhxiLtzKk4C9nHy0uFR7KZTfA5L++PAHTjRg05zsC5CS7D/3PgWIK74bzkQUHmU2MGacYb/63Uts2PTBLo7MsszKR/xxIUFKSDBw8qKyurRoPMffv2rfJjTV9K+p6fny8fH58a6xcAAADcT1ZunmbNz9CUpBQlr113zO0a+/vLz9urwgB0WHCw+p9g8moAAADALYPMzZs1sYs7Kgkum0zlY8k9UqfOBJvdxcSJEzVhwoTSn8P5sAAAAFDnmHIY8zZu0pTEFH00d36l6if7+5jqyxUbHRulIH8m+gMAAEDNoLDwESWZyVu2bKlwoHbt2mUD0CZTOCwsTO4iISFB48ePt7eHDRtGJjMAAEAdsjcrWx+mz7NZy4u3bHVobxgYqBGRA3V+317687QZ2nnwxBNAt2jQQLcMPr2WegwAAID6yGVB5v0HDmpOYqrWrNuovPwCtW7RTKfHRalj+7Yu6U9JyQozAaApO+HnVz6zIzU11a67du0qf39/l/QRAAAAdV9RUZF+XbXGBpa/yFik3IICh23iu3TSuLgYXdS/n4KP/G064//+pKtefeO4gWYTYJ5xy41q3chx4m0AAADAo4LMb06bqSeeeVWZWYdrCZcws1xfcfF5eurhexUS7NySFCZ43LlzZ61Zs0bvv/++xo0bV679jTfesOvzzz9f7oRyGQAAAHXD1v379X5KuqYmpWjd7j0O7S0ahGpkTJRGx0arawvH+UH6hbfRD/fdqVd++kXTklNNjY1yNZhNiQyTwUyAGQAAAB4fZJ4283M9+Pjhyf96dutsJwM0AeXFy1fph1+S9MGsr5SZlaW3nnvS2V3T7bffrrvvvlt33nmnmjRpogsuuMBOqjdp0iR99NFH8vX11a233ip3QrkMAAAAz5VfWKhvlyyzWcvfLVmmojKBYcPby0tDevWwWcvn9uklvxNM8mwCyBMuvUgPDDtP6atXKzMnV40bNbST/FGDGQAAAHUiyJyfX6DHn3nF3r7lupF65N7b5O39x4QkPyemavQt9+nL739RUvoCxUX2r/JrnXLKKVqyZEm5CfsmT56sDz/80N42AWNTZ7ksU9v4888/1/fff6+LLrrIlsUoKCiwlywaTz75pHr06FHlPgEAAADG6p07NS0pTe+lpmnHgYMOg9KhaRObsTw6JkqtG598aQsTUB7QLtzeDg0NZdABAABQd4LMGUuWafeefWrdsrn+dvct5QLMxhnx0Ro1/EJN/mCWzWquTpD5wIED2r9/f7n7zMR9ZjHMBH5HM3WYv/jiCxtMfuutt7Rhwwa7XVRUlB544AGNGDFC7oZyGQAAAJ7hUF6+PstYqCmJKfp99RqHdn8fH10Y0Vfj4mN0WtcuDn8rAwAAAO7KqUHmbTt223XvHl1tJnFFInofzhTeun1ntV4rMTFRhYWFx2w39Z8rEhAQoEcffdQuJgPa9LOigLS7oFwGAACAe8vYtFlTk1L1QdpcHcjJcWjv1bqVxsbF6MqogWoSEuKSPgIAAAAeE2QOCgyw6z179x1zm737DxzeNiiwWq/VoEEDVZcJOLu7kJAQu5RkYgMAAMD19mcf0sy5822tZRNkPlpIgL8uHzTA1loe2L7dMRMgAAAAAE/g1CBzn55d7XrR0pVaumK1enXv4lCz+ZPZ39nbfY9si+PLysqykxMeHr98t866BgAAqMuKi4uVuGatLYfx2YKFOpSf77BNdMcONmv50oERCvWAhAYAAADA7YLMLZs307lnnqJv5/yusbf9RRP+crtOix1ks5aXrlijp559TUtWrFbDBqG65Lyzndk1j0VNZgAAANfafuCgpqema2pSilbvLD+xtNEkJFhXRUVqbFy0erZu5ZI+AgAAALXJq9ikXDjRth27dNk147Vu4x+XDZrLA0u6ERjgr9f/+08bjMbJZTIPGzbMZjInJyfX+aHLzMy0a2ZLB8cS3AXnJXAs1S8FhYX6YdkKWw7jm8VLVVBUVK7d/H07uHs3jY2P0fl9eyvgGPOR1CbOS+B4gjvi3ASOJbgbzks1w+l/7bZq0UzffPA/vfrudM3+7metWbfR/pHesnlTnRYbqT/fOEbdu3R0drc8FjWZAQAAnGf97j2alpyqaclp2rp/v0N728aNNTo2SqNjo9WuSRi7BgAAAPVCrQWZ52Ys1tvvf6JBEb113cjh9r6s7EPavXefgoMClTD+RrsAAAAA7iwnP1+zFy7W1KRUzVmx0qHd19tbw/r1sbWWB/foJh9vb5f0EwAAAKhzQeYNm7ZqxqdfKjcvrzTI/O1Pv+mWhEd16bAhenXShNp66XqFif8AAABqx5ItW21geUbaXO09Up6srG4tWmhsfLStt9y8QSi7AQAAAPVWrQWZ/fz87PrQoZzaegkw8R8AAECNOpiTo0/mLdCUpFSlr9/g0B7s76dLB/S3WcsxnTrY2ssAAABAfVdrQeYundrZdVL6AqUvWKQ+Pbup6MiEKGaSv4KCguM+3tvb2y44voSEBI0fP77cxH8AAACoPPO3adq6DXYSPxNgzsrLc9hmYPt2GhsXrcsHDVCDwECGFwAAAHBGkLln184afEqMfvo9RReOvqVc26yvfrDL8VBSo3KY+A8AAKBqdmdmaUZaus1aXr5tu0N7o6AgXRU1SGPiotW3bRuGGQAAAHB2kNl487kn9Oo77+v7X5K0feduZWZmae/+AwoKDFDjRg2P+9iwE7QDAAAAJ8tcWTdnxSqbtWwm88svLHTY5vRuXW1g+cJ+fRXkf7gEHAAAAAAXBZmDgwJ19y3X2cX4ZPZ3duK/oWedxsR/NYSJ/wAAAE5s8959mpacqmnJadq4d69De8uGDTQqJkpj4mLUqVlThhQAAABwlyDz0Vq3bK7zzz5dA/r2dObL1mkTJ07UhAkTSn8ODw93aX8AAADcRV5Bgb5evFRTElP0w/IVtvZyWT7e3jq3d087id85vXrIl7ktAAAAgCrxKj76r214bCZzycR/ycnJqusyMzPtOjQ01NVdgYfjWALHEtwN56XqW7l9hy2HMT01XbsysxzaTaayCSxfHR2pVnW4RBvHEjie4I44N4FjCe6G85IHZjKj5jHxHwAAgJSVm6dZ8zNscDl57TqHIQn089VFEf1scPmULp3k7e3NsAEAAAA1hCAzAAAAPJK5IG/+xk02sDwzfb4yc3MdtunbprXGxcdqROQANQ4Odkk/AQAAgLqOIDMAAAA8yt6sbH2YPs8Glxdv2erQ3iAwUCMGDdCYuGgNaBcuLy8vl/QTAAAAqC8IMgMAAMDtFRUV6bfVa2xg+fMFi5RbUOCwTVznThoXF6OLB/RTsL+/S/oJAAAA1EcEmevQxH/5+fl24j8AAIC6Yuv+/Xo/JV1Tk1K0bvceh/bmoaG6OiZSY2Kj1a1lC5f0EQAAAKjvCDJ7uIkTJ2rChAmlP4eHh7u0PwAAANVVUFiob5cu05TEFH27ZJmKiovLtXt7eensXj1s1vLQPr3kx5fsAAAAgEsRZPZwCQkJGj9+vL09bNgwMpkBAIDHWrNzl6Ylp+q9lDRtP3DQob1dWJitszwqJkptwxq7pI8AAAAA3CjI/NNvKfolKU279+7TgL69dN3I4TqYmaX1G7eoQYMQdQhv46queZSQkBC7GH5+fq7uDgAAwEk5lJevzzMW2lrLv61a49Du7+OjYf36aFx8jM7o1lXe3t6MMAAAAFDfg8xZ2Yf0p7se0o+/pZTedygn1waZTdt5V/9JLZs3Vdq3H/IhAgAAoI5atHmLDSx/kDZP+w8dcmjv2aqlxsbF6MqoQWoaevgLdQAAAADuyelB5keees4GmCP799HAfr30xpQPS9tatWim02Mj9dPvKUpMm69TYwY5u3sAAACoJQcOHdLMufNtcHnBxs0O7SH+/rpsUH9bazmyQ3t5eXmxLwAAAAAP4NQg8559+zX909kKDPDXOy88pV+T55YLMhsD+va0QebfU+cRZAYAAPBwxcXFSlqzTlOTUvTp/Awdys932CaqQ3uNjY/RpQMi1CAw0CX9BAAAAOAhQeaFS1aooKBQ0QP7qVmTsAq3CW/Tyq43bdnuzK4BAACgBu04eFDTU9M1JTFFq3fucmgPCw7WVVGDbHC5V+vDf/8BAAAA8ExODTKbif2MsEYN7bqiKyALi4qc2SUAAADUEPN33I/LVthyGF8tWqKCCv6uG9yjm621bCbzC/B12RzUAAAAAGqQU/+ybxLWyK5379l3zG3Wbthk161bNHNavwAAAFB1G3bv0dTkVL2XkqYt+/Y7tLdu1EijY6M0OjZaHZo2YagBAACAOsapQeb+fXraeszzFy3T/gMHHSZzOZSTq5mffWNvx0cPdGbXPFZWVpays7Pt7fz8fPn4+Li6SwAAoB7ILSjQlwsX26zlOStW2drLZfl6e+v8vr1t1vJZPbvLx9vbZX0FAAAAUIeCzCHBQRp75SV2sr/b//pPnREfZe83H0oWL1uph554Rjt371GfHl1L23B8EydO1IQJE0p/Dg8PZ8gAAECtWbZ1myYnpeiDtLnak3X4i+6yurZorjFx0bo6OlItGjRgTwAAAAD1gFfx0WkntcxkK4++5V4lps7/oxNeXqXZLy2aNdXMt55Tt84dnNmtOpHJPGzYMJvJnJycrLouMzPTrkNDQ13dFXg4jiVwLMHduON5KTM3V5/MW2An8Utbv8GhPcjPT5cOiLCT+MV26uhwtRpcwx2PJXgujidwLMHdcF4Cx5J7cfpsK0GBAZrx+jOa/MGn+mDWV1q2aq3y8vLVqkUznXfWabrz5nFq2Zx6zJUVEhJiF8PPz68W9xwAAKhPTAJA+voNmpKUqo/nzVdWbp7DNv3btbXlMEYMGqCGQUEu6ScAAAAA13PJlN5+fr66YfQIuwAAAMB97M7MsqUwzER+S7duc2hvFBSkK6MGakxsjPqFt3FJHwEAAADU4yDzoqUrtXXHTp19WiwT1AEAALiJoqIi/bJyta21PDtjkfIKCx22ObVrZ5u1fFFEPwX5c/UUAAAAABcFmVetXa9bEh5V65bNNfKyCzRqxEVq37a1M7sAAACAI7bs26dpyWmalpyqDXv2OoxLi4YNNDomSqNjo9WZcmYAAAAA3CHI3LdXd51z5in68ddk/ffVd/TMa+/q9LhIjR5xsS4Ycob8yYoBAACoVfmFhfpm8VKbtfzD0uUqOmoOaB9vb53Tq4edxO/cXj3l6+PDHgEAAADgPkHmrp3aa8pLT2vbjl2a/slsvffRF/o5Mc0uTRo30hUXn6fRV1yknl07qy6bOnWq9u4tny3k7++vm2++2WV9AgAAddvK7TtsneXpKenamZnp0N6pWVONiY3W1TGRat2okUv6CAAAAMAzeRWbqcNdxLz0bynz9N5Hn2v2d3N0KCfX3h/Zv4/uvPkaDR18quqinj17qmHDhoqJiSm9LyAgQP/+97+r9bzx8fF2nZiYqLou88iH49DQUFd3BR6OYwkcS6jL56XsvDzNmp+hKUmpSlqz1qE9wNdXF/fvpzFx0Tq1S2d5e3tX+zXhPvg/DhxPcEecm8CxBHfDeckDM5mP5uXlpdNiB9ll/4GD+uiLbzVt5udKX7BYMz//ps4GmY0LLrhAjz76qKu7AQAA6hjzJf6CTZs1JTFFM+fO18GcHIdt+rRprXHxMboicqAaBwe7pJ8AAAAA6g6XBpnLOpCZpZ2792rP3n2u7goAAIDH2ZedrZnp8zUlKUULN29xaA8NCNCIyAEaGxejAe3C7Zf9AAAAAODxQea8vHx9+cPPNnvZ1GU2mTe+vj46/+zTdf2oy1WXrVixQq+//rqaNWumQYMGqUOHDq7uEgAA8DC29NiqNTaw/HnGQuXkFzhsE9e5ow0sX9w/QiEB/i7pJwAAAIC6zSVB5mWr1mjah5/rw8++1p59++19ndqHa9TlF2rkZReoRfOmNfI6WVlZ+umnn/Tzzz/b26eccopGjx59wsft3r1bH3/8sQ0EBwYGKioqSsOGDZOfn59qyuLFi+1kfxs2bNCvv/6qO+64QxMnTiSrCAAAnNC2/Qc0PTXdBpfX7trt0N4sNEQjY6LsRH7dWrZgRAEAAADUnSDz0hWrdd+jT9uay0aAv7+GX3COxoy4WKfGDqqxAKsJEl9xxRX6/ffflZeXV3p/Tk7OCYPMs2bN0rXXXqt9+8qX7YiIiLBtR2ccL1y4UHPmzDnuc/r6+uqWW24p/fl///ufTj31j3rTM2fOtP3t3r27br755kq/TwAAUH8UFBbqu6XLbWD52yXLVFhUVK7d/B01pGd3m7U8tE8v+fu6TVU0AAAAAHWcUz99LF+11gaYe3XvotGXX6grLj5fYY0b1vjrHDx40GYwh4SE6JxzzlFBQYG++eabEz5u0aJFuuqqq5Sbm6v4+HhdeumlOnDggN555x1lZGTooosu0rx582zQuMTevXu1bNmy4z7v0RnQZQPMxogRI9S3b1999tlnBJkBAEA5JlN5WnKqXbYfOOgwOu3CwjQ6NkqjY6PVNqwxowcAAACgbgeZTXD5i2mvKLJ/31p9naZNm+qHH36wwVxTkmLSpEmVCjI//PDDNsBssoqnT58ub29ve78pZTFw4EAbhH733Xd1ww03lD7mjDPOsEt1mbIcZbOuAQBA/WVqK3+VPk+TE5NtzeWj+fn46IJ+fTQuPkZndOta+jcLAAAAANT5IHOPrp2c8joNGjTQWWedddLZz7Nnz7a3n3rqqXIf1lq2bKn77rtP9957rw0+lw0yn6wtW7YoNDRUDRv+kcGdlpam+fPn6x//+EeVnxcAAHi+RZu36O1fftfHCzK0/1COQ3uPVi01Ni5aV0VFqmloiEv6CAAAAABHo1jfESbIazKJu3btqi5dujgMlJn4zwSZU1NTVR0myDxmzBgbBDevs3btWluOY+jQobrrrrsq9RymlEdFTKZ1r169lJmZqbouOzvb1V1AHcGxBI4luNrBnFzNylik6enzlLF5i0N7sL+fLu7XV1dHDdTA8LZH5rAorhf/36N6+D8ONYnjCRxLcDecl8CxVDUm+dWjgszJ6Qv08tvvKzYyQrdeN6rcfZVR9nHOYIK9Rrdu3SpsN8Fn86HO1GA2S1hYWJVeJyoqSikpKXayv+XLl6tTp0766quvdPrpp1er/wAAwHMUFxcrbf1GvZ8+T7MXLdGh/HyHbQaEt9XIqIG6qF8fhQYEuKSfAAAAAODSIPPW7Tv11Q+/KCDA3+G+yij7OGcoyQZq1KjRMSfvCw4OVlZWli2tUdUgc8lrVKfkRmJiYult05+Sb+9MtrUJhNfWNxLuqD69V9QujiVwLMEZdh7M1PTUdE1JStGqHTsd2sOCg3VZ/366OnKAoro6XlkFVAX/x6EmcTyBYwnuhvMSOJbqeJD5rNNi9d2Hb6lRowYO91VG2cc5w+FLT6WioqJjblPS5k6T60ycOFETJkwo/Tk8PNyl/QEAAOUVFhXpx2UrbGD5q0VLVFDB3xpndu9may1fENFX+TmOtZgBAAAAoF4GmRs1bGCXE93nLkoymE0pjIrk5OTo0KFD5bZ1BwkJCRo/fnxpJrOPj4+ruwQAACRt2L1H01LSNC05VVv27XcYk9aNGml0bJRGx0arQ9Mmpfc7Fs4AAAAAAPfm1In/Fi5doRmffKl+vbvrqkuHVXmb2mBqLhtLly6tsL3k/pYtW6pBA/cMlAMAANfKLSjQlwsX26zlOStW2drLZf1/e/cBHlWVPn78Ta8QQi+h10AIpCdiQ0SMoqI0aboqtgX7xrK6q+hasWH9Y9+lCYgiWAFREExPaAm9h9AJkEJIm/9zDkx+CZOEZBIy7ft5nnlmmHPvzJmbw70z733ve1ydnWVYUF+dtXxNn97iYkVXRwEAAACATQSZd+7eJ5/OXii3xA6pNoBcm2UuhQEDBug6PllZWZKeni4hISGV2hcvXqzvL7vsMrEmlMsAAMDythw8JLMTkmVBSqqcyD83V0JF3Vu1lIkxkTI2Ikxac7IaAAAAgJ1p1CBzbZSUlur7xs7s8fDwkNGjR8uXX34pDz30kPz666/i4+Oj2zZu3CjvvPOOfnzHHXeINaFcBgAAlpF39qx8n75BZy0n79lr0u7l5iY3DwyWCdEREtOta/n8DwAAAABgb6wuyLxrb5a+929Wv7rHr7zyimRnZ+vH69at0/fx8fEydepU/VjVLp4xY0aldV588UVZsmSJrF27Vnr37i1Dhw6V3Nxc+emnn3Q95iFDhsiIESPEmqhAuDEY7ubmZunuAABg11T5i/R9+2VWQpJ8m7ZO8s8WmSwzoGMHmRgdKSNDB0pTLy+L9BMAAAAA7CrInJS2QWb+b4F+fPDwEX2fnL5R7nn0OZNlc06eksS0DfpxVFhwvd537ty5kpGRUem5zMxMfasuyBwQEKAzmMePHy/btm2Tr776qrxNBZcr/tta5OfnS0HBuctyi4uLmfgPAIBL4ER+vnyTkq6zljMPHjJp9/PyklFhITprOTigA38DAAAAAA7lkgeZsw8dkR+X/2HynLpV2SFXF5k46iYZPvTqer3vs88+K8ePH6+23bmachxhYWF6kj+VzawCzaqMRkREhM5stkbUZAYA4NIoKyuTNTt2yqz4JPlxwyYpOl/Sq6JBPbrprOXhwf3Fy50rigAAAAA4JifDhdOeN7ATJ0/J7r379ePV8Sny+vufyZUx4fLUQ5Mrd8TJSTw9PKRzQHvx8fG+lF2yKxUzmWNjY3Umc2Jioti7vLw8fa8mawQYS7AG7Jfsx8GTp2ReUorMSUyWvcdPmLS3btpExkWEy/jocOneqlWDvz9jCYwlWCP2TWAswdqwXwJjycEymZs389M3xdnZRfZnH5KQoEAJGxB0qd8aAACgVopLS2V5xmZda/m3zVul7IJz8M5OTjK0bx+ZGBMp1wb2ETcXF7YsAAAAAFhi4r+Q/oH6hoZDuQwAAMy38+hRmZOQLF8npciR3HNXyVTUpUVzmRAdKbdHhEm7ek5KDAAAAAD2qlGDzGh4cXFxMmXKlErlMgAAQPUKiorkh/UbddZy/M7dJu0erq4yfECQTIiKlMt7dKt2HgcAAAAAgAWDzEePnZA5i5ZKyvoMOZFzUkqqmEhn8KBIeeaR+y3RPZvi4+Ojb4qbGxMOAQBQnQ1ZB2R2QpJ8k5IupwsLTdr7tmsrk2KiZFRYiPgzPwQAAAAAWG+QeX3GFhl33xN6QsCadO0U0Gh9AgAA9ulUwRlZlJaus5Y3ZmWbtPt6eMhtoQN1reWQjgF6ImIAAAAAgJUHmR997lUdYJ446ibp0bWzvDD9A7n+mivk4XsnyXufzpI/E1JkxsvPypUx4Y3dNZuUn58vBQUF+nFxcTHlMgAADs9gMMhfO3fpWstL1m+QwuISk20S1bWLTIyOlJsHBouPh7vDbzMAAAAAsJkg8/Zde2Xztp3SrGkTeeXZx+WnFav08x4e7hIa3Fe+mPGyXHXLJHly2nRZtWR2Y3bNZjHxHwAA5xw+nSvzk1JkdmKy7Dp6zGSztPT1kTERYTIxKkJ6tW3DZgMAAAAAWwwy79qzX98H9+st7u5uIucvSS0rK9P3amKd224cKq+//5ks/mm53DtpTGN2zyYx8R8AwJGpeR1Wbtmmay3/mrFZSs9/pzBS5S+u6d1Ll8MY1i9Q3F2Z8xgAAAAAGlqj/tJycj4XVPb28tL3nucvT80vOFO+TPvzmUVbd5jO9g5TTPwHAHBEe44dl7mJyTI3KUUOnTpt0h7g30zGR0XI+KhwCfD3t0gfAQAAAMBRNGqQuVNAO32ffeiwvm/XppW+33/gUPkyx07k6HtnF5fG7BoAALByhcXF8tPGDJ21vHrbDpN2NxcXuaF/P5kQFSFX9e4pLs7OFuknAAAAADiaRg0y9+jSSVq28Jftu/dJXn6B9O3VQ/ya+sr2XXtk2e9rJGxgkHz93U962T49ujZm12wWE/8BAOxdZvZBHVhekJImJytc/WTUq01rPYnfmIhQaenra5E+AgAAAIAja9Qgs6urq9x2w1D5ZNYCWfD9z3L3+JEy9e4J8vK7M+WOqU+XL9e2dUsZO+KGxuyazWLiPwCAPcotLJRv09bJnIRkSdt3bk6Hirzd3eTWkIE6uBzepZOuvQwAAAAAsAwng8FgaMw3LC4ukYIzZ8TNzU28vTxFvf1nsxfK/MU/S86p0xLct5c8+9iD0qNrp8bsll1kMsfGxoqLi4skJiaKvcvLy9P3vmSsgbEEK8F+qf7Ud4LkPXtldnySLF63XgqKik2WCevcSSZER8itIQOkiaen2CPGEhhLsEbsm8BYgrVhvwTGknVp9CnW3dxcxc+tSfm/VebRvZPG6Bvqjon/AAC27lhenixITtMlMbYdPmLS3szbS8aGh+ngct/25+Z3AAAAAAA4cJAZAACgtKxMVm3drgPLP2/KlOLSUpONcmWvHrochprMz9PNjY0GAAAAAFaKIDMAAGg0WTk5MjcxReYmJktWzkmT9rZ+TWVCVISMiwyXLi1b8JcBAAAAAEcOMiemrpePv/ra7PWjwoLlwb+Na9A+AQCAxldUUiK/bMrUWcu/b92uay9X5OLsLMP6Beqs5Wv69BJXFxf+TAAAAABgQy5ZkPng4aPyy8o/zV7fw8O9QfsDAAAa19ZDh3VgWdVbPp6fb9LerVVLmRgVIWMjw6VN0/+brwEAAAAAYFsuWZB58OVRsuKbL81e38+PH5u1kZ+fLwUFBfpxcXGxuJD9BQCwoPyzRfL9uvU6uJy0e69Ju6ebq9w0IFgmRkfIZd276QmAAQAAAAC27ZIFmf2aNtE3XFrTp0+XadOmlf87ICCATQ4AaFSq/EX6vv0yOyFZvk1bJ3lnz5os0z+gvUyKjpSRoSHi5+3FXwgAAAAA7AgT/9m4uLg4mTJlin4cGxtLJjMAoNHk5BfIwpQ0mZOYLBnZB03am3p6yqjwED2R34COnAQFAAAAAHtlsSDzH2uT5M+EFDmec1IGBgXK326/VXLz8mXv/mxp0sRHOge0t1TXbIqPj4++KW5ubpbuDgDAzpWVlcmaHbt0OYwfN2ySsyUlJsvEdO+qs5aHD+gv3u7MsQAAAAAA9q7Rg8z5BWdk8qPPyu9rk8qfO1N4VgeZVduwsZOlTasWkrL8G3F2dm7s7gEAgCocPHlK5iWl6KzlvcdPmLS3buIrYyPCZUJ0hPRo3YptCAAAAAAOpNGDzP9+7T0dYA4b0E9C+gfKZ7O/KW9r27qlXBEVJn/8lSTxKetkUGRoY3cPAACcV1xaKsszt+is5RWZW6TMYKi0bZydnGRIYG+dtTy0X6C4MfksAAAAADikRg0ynzh5SuZ//5N4erjLfz94TdYkplUKMisDg/roIPNfyekEmQEAsICdR4/KnIRk+To5VY6czjVp79yiuYyPipBxkWHSvlkz/kYAAAAA4OAaNci8MXOblJSUSkRIf2nZ3L/KZQLat9X3WdmHG7NrAAA4tDNFxbJ0w0aZHZ8kf+3cZdLu7uIiNwYHyaSYSLm8R3dKWgEAAAAALBNkVhP7Kf5+TfW9k5PpMqVlZY3ZJQAAHNqGrAO6HMY3KelyurDQpD2wXVtdDmNUeIg0Pz/RLAAAAAAAFgsyN/f30/fHT5ysdpnd+7L0fbvWLRutXwAAOJJTBWdkUdo6HVxWQeYL+Xi4y22hA3VwOaRTR3Gq6qwwAAAAAACWCDIP6NdH12Net2mLnDqda/Kj9UzhWVm0dJl+HBMR0phds1n5+flSUFCgHxcXF4sLky4BAKpgMBgkftduXQ5jyfoNUlhcYrJMZNfOMjE6Um4eGCy+Hh5sRwAAAACA9QWZfby9ZOLom/Vkfw898x+5Mia8/Idvxpbt8uwr78rR4yekX+8e5W2o2fTp02XatGnl/w4ICGCTAQDKHT6dK/OTU3XW8q6jx0y2TAsfHxkTEaqDy73btmHLAQAAAADqzMmgIryNSGUrj3/gCYlPXvd/nXBy0oFmpXXLFrLoy/ekZ7fOjdktu8hkjo2N1ZnMiYmJYu/y8vL0va+vr6W7AhvHWII9jqWS0lJZuWWbDiz/mrHZZL4Dddwd3LunDixfH9RX3F0b9ZwzbGgswbYxlsB4gjVi3wTGEqwN+6WG0ei/Kr08PWTBp+/KrIXfy8Ilv8iWHbulqKhY2rZuKcMGXy6P3DdJ2rSiHnNt+fj46Jvi5uZ2Cf9yAABrt+fYcZmbmCzzklLl4KlTJu0dmjWT8VHhMj4qQjo297dIHwEAAAAA9sciqUtubq5y9/iR+gYAAMxXWFwsP23M0FnLq7ftMGl3dXaW2P79dNby1b17iouzM5sbAAAAANCgrPL62B2790lS+gYZf9twS3cFAACrlJl9UOYkJMuClDTJOV82qaKerVvLxJgIGRMeJq2aUHYBAAAAAOAgQebDR4/Jmx9+IfO++1FuHHo1QWYAACrILSyU79LXy+z4JEnbt99k23i7u8ktAwforOXIrp117WUAAAAAAOwiyHzoyDFdgzlz6w79g7dv7x5y55gR0qplc92en18gH3w+R/7f/+bLmTOF4unhLjHhAxujawAAWDU1MW7ynr06a3lx+nrJLyoyWSakU0eZGB0ht4UOlCaenhbpJwAAAADAcV3yIPP6jC0y+p5H5XTuuZnSlZ9WrJZZC76XJbM+ktN5+XLXw/+UrOxD4uzsLGNH3CBPTr1HOrRrI/bsyJEj8vrrr8uqVavEw8NDxo4dK1OmTBEXFxdLdw0AYAWO5eXJguQ0XWt52+EjJu3NvL1kdFioTIiOkKAO7S3SRwAAAAAAGiXI/OS0N3WA2a+pr4y++Xrx8faSX1auka07dsu/X39f0jZkytHjJ2RQZKi8/Oyj0qdHN7v/y+zZs0cGDRokV1xxhcyYMUO8vb1l9uzZ8uWXX8rkyZMt3T0AgIWUlpXJqq3bdWD5502ZUlxaarLMFT176KzlG4ODxNPNzSL9BAAAAACg0YLM+w4c1JnMKkN58f8+ksCe5wLIjz94lwwddbf8+vsa/e/H7r9Tnnr4XnEU999/vwQGBsq8efPK62WGhIRIaRXBBACA/cvKyZG5iSkyNzFZsnJOmrS3adpExkdF6FvXli0s0kcAAAAAACwSZN6+a4++Dw3uWx5gVjzc3WX0TcPk5XdnSscO7eTJhxwne1dlMS9btky++eYbkwmZKJUBAI6jqKREfs3YrCfxW7l1m669XJGLs7Nc1zdQJsZEyJA+vcWVckoAAAAAAEcMMuflF+j7tq1bmrS1P19zuW+v7ibB1oZWUlKib66urvpWW2VlZToLuyElJyfr+2bNmsnIkSNl27Zt0qlTJ7nzzjtlzJgxDfpeAADrs/3wEV0OY35yqhzLyzdpV5nKE6MjZWxEmLT1a2qRPgIAAAAAUBcNG0G9gKHMUG2GrsrQUjw9PRr+fQ0GSU1NlVdffVUGDx4sPj4+4uXlJQ888MBF1y0uLtYT8vXp00fc3d11veQrr7xSfvzxxwbp2/Hjx/W9muhP9W3WrFkydOhQmThxorz77rsN8h4AAOuSf7ZI5iWmyI0zPpKYV9+UD39fXSnA7OnmKqPDQ+X7qfdL0rNPyiPXDibADAAAAACwGZd84j9L2Lt3r4SHh9d5PVUTecSIEfLTTz/pf6sM6zNnzsiff/6pb++995489NBDldZRE/a98MILNb6uh4eHZGRklD9WJk2aJFOnTtWPBw4cKFu3bpWXXnpJHn300Tr3GwBgfdQJz3X7s3TW8qLUdZJ39qzJMv07tNdZyyPDBkozb2+L9BMAAAAAAJsIMv+68k/pf+XNlZ47W1RUbZsSO+QKeeP5OLPeT5W4CA0Nleuuu07f4uPj5dlnn73oev/v//0/HWBu2rSpfP7553LLLbdIXl6evPHGG/Laa6/JE088IbGxsdKjR4/ydW666SaJjo6+aH+MOnfurO9V/ypS/1bvf+zYMWnZ0rS8CADANpwsKJBvUtN1reVN2QdN2pt4esqosBCZGB0hAzoGWKSPAAAAAADYXJC58GyRFJ49Uae2U7l5Zr+fqnGsymUYVXxckxkzZuj7d955R0aNGqUf+/v767IbKhN56dKl8vHHH8tbb71Vvo6fn5++1VZUVJQu3ZGdnV3p+QMHDujnmzdvXuvXAgBYB1XD/69du2V+Srr8krlFzpaUmCwT072rTIyKlJsG9hdvd3eL9BMAAAAAAJsLMl971WXy59I5Zq3bxNdHGtPOnTtl+/btugazqo98ofvvv18HmX/++edKQea6UvWhVZmM999/X2677Tbp2bOnbN68WWcx33XXXbWaaDAmJqbK5zdt2iSBgYE6+9reFRScm1QSYCzBkg6fzpVv0tfLgtR02Xsix6S9pY+PjAwdIGNCB0r3VueuUikrKpK881fzAFXhGIeGwlhCQ2I8gbEEa8N+CYwl8/j6+orNBZl9fbylZ7dz5SGsnQrQKsHBwXrCvwtFRkbqexWILioqqnKZ2nrllVf0znDAgAE6C/rUqVNyzz336AkHAQDWraS0TH7ftl3mp6br+9Lzk9waOTs5yVU9u8vYsBAZ0qeXuFUx+S0AAAAAAPbELif+M8eRI0f0ffv27atsb9Wqlbi5uUlxcbHk5ORImzZtzH4vV1dX+eCDD2T69Oly4sQJadeuXa0ymI1UjemaMpwv1RkJa+RInxWXFmMJF7Pr6DGZm5gs85JSdAbzhQKaNZOxYQPlzisuk/bNmrFBwX4JVoNjHBhPsEbsm8BYgrVhv1Q/BJnPKyws1PceHh7VbixPT08dZD5z5ow0BFWDuUOHDvV6jfz8/PJLRFTfXMiYA4AGc6aoWH7YsFFmJyTJ2h27TNrdXVzkhuAgmRQdKSHt2oqzsxNfTAAAAAAADocgc4WAr3L27NmLBqJV3WZrobKhp02bVv7vgIAAi/YHAOzBxqxsHVj+JjVdTlVxYrFP2zYyMTpSRoeHSovzcwg4Qj18AAAAAACqQpD5PGP5i6ysrCo31OHDh3WmsCqZ4e/vL9YiLi5OpkyZoh/HxsaSyQwAZjp95owsSlung8vr9x8wafdxd5cRoQN01nJY507i5OTEtgYAAAAAgCDz/1ET/ikbNmzQ5TCMmc0X1kHu06ePDjQDAGyfwWCQhF17dGB5yboNcqa42GSZ8M6dZGJMpNwyMFiaeHpapJ8AAAAAAFgzMpnP69y5s/Tt21cyMzPliy++KM8ONvroo4/0/Q033CDWhHIZAFB3R3JzZX5yqsyOT5KdR4+ZtDf38ZYx4WEyMTpC+rRryyYGAAAAAMARg8xFRUVSVlamH5eUlOj70tLS8rrK6jLnCyf5e/zxx2Xy5Mny5JNP6kn+RowYIbm5ufL666/L8uXL9XN///vfxZpQLgMAaqe0rExWbtkqsxOS5ddNmVJy/hhhpI4LV/fqKROiIyS2fz/xcLXbQyQAAAAAAA3KyaCuFbZDQUFBkpGRUW27i4tLefDZSAWlx40bJwsWLDBZXgUfVIbz3/72N7Em+fn5UlBQUKkmc2Jiotg74wRbvr6+lu4KbBxjyf7tPX5C5iYmy7ykFMk+ecqkvX0zPxkXGS4ToiKkU4vmZr8PYwkNhbEExhKsEfsmMJZgbdgvgbFkXew2TUtlKV+YqVyRaxUZas7OzjJv3jwZPHiwfPnll7Jt2zb9GhERETq7+YorrhBrQ7kMADB1tqREftqwSWctr9q23aTd1dlZZyurwPLgPr3ExdmZzQgAAAAAgJnsNpPZUZDJTCYz6oez3/Zl88FDehK/BclpknP+Ko+KerRuJROjI2VMRKi0btKkQd+bsQTGEqwN+yUwnmCN2DeBsQRrw36pYdhtJrOj8PHx0TfFzc3N0t0BgEaXW1goi9PX66zl1L37TNq93NxkRMgAXWs5qmsXXf4IAAAAAAA0HILMdpTJXFxcrGsyA4C9UxfhqIDyrIQkWZy2XvKLikyWGdgxQGct3xY6QJp6eVmknwAAAAAAOAKCzDaOmswAHMnxvHxZkJIqcxKSZcuhwybtfl5eMiY8VGctB3Vob5E+AgAAAADgaAgy27i4uDiZMmWKfhwbG0smMwC7U1ZWJqu375BZ8Uny88YMKSotNVnm8p7dddbyjf2DxMud0kEAAAAAADQmgsw2jprMAOzVgZyTMi8pRWct78/JMWlv07SJjI+K0LeuLVtYpI8AAAAAAIAgs82jJjMAe1JcWiq/bsqU2YnJsnLzVikzGCq1uzg7y9C+fXTW8rWBvcWVOvQAAAAAAFgcmcw2jprMAOzB9sNHZE5issxPSpWjeXkm7SpTeUJUhIyNDJN2fn4W6SMAAAAAAKgaQWYbR01mALaqoKhIlqzbILMTkiVh126Tdg9XV7lpQH+dtXxZ967i7OxskX4CAAAAAICaEWS2cdRkBmBLDAaDrM86ILPjk2RR2jrJLSw0WaZf+3YyKSZSRoWFSDNvb4v0EwAAAAAA1B5BZgDAJXeyoEAWpa6T2QlJsvFAtkm7r4eHjAwbqLOWB3YMECcnJ/4qAAAAAADYCILMAIBLlrW8dscuHVj+YcNGKSwuMVkmqmsXHVi+eWCw+Hi485cAAAAAAMAGEWS2cfn5+VJQUKAfFxcXi4uLi6W7BMDBHTp1WuYnp+rg8u5jx03aW/r6yNiIMB1c7tmmtUX6CAAAAAAAGg5BZhs3ffp0mTZtWvm/AwICLNofAI6ppLRUVmzeqgPLyzO3SGlZWaV2Vf5iSJ9eOrB8Xb9AcXfl8AMAAAAAgL3gV76Ni4uLkylTpujHsbGxZDIDaFQqU3luYrK+HT6da9Le0d9fxkeFy7iocAnw9+evAwAAAACAHSLIbON8fHz0TXFzc7N0dwA4gMLiYvlhwyadtbxm+06TdjcXF7mhfz+ZFBMpV/bsIc7OzhbpJwAAAAAAaBwEmQEAtbLpQLbMSUiWhalpcrLgjEl777ZtZGJ0hIwJD5MWvudOfgEAAAAAAPtHkBkAUK3cwkJZlLpOZy2v259l0u7j7i4jQgfIpOhICevcSddeBgAAAAAAjoUgMwCgEoPBIEm79+rA8vfr1ktBUbHJFgrv3EkmxkTKLQODpYmnJ1sQAAAAAAAHRpDZxuXn50tBQYF+XFxczMR/AMx2NDdP5ien6uDyjiNHTdr9vb1lTESoTIyOlMB2bdnSAAAAAABAI8hs46ZPny7Tpk0r/3dAQIBF+wPAtpSWlckfW7frwPLPGzOkpKzMZJmre/eUCVERckNwkHi4ctgAAAAAAACVES2wcXFxcTJlyhT9ODY2lkxmALWy7/gJmZuUIvMSU+TAyZMm7e38/GR8VLiMj4qQzi2as1UBAAAAAEC1CDLbOB8fH31T3NzcLN0dAFbsbEmJ/LIpU2bHJ8kf27br2ssVuTo7y/VBfWVCdIRc06e3uDg7W6yvAAAAAADAdhBkBgA7t+XgIZmdkCwLU9LkeH6+SXv3Vi31JH5jI8KkdZMmFukjAAAAAACwXQSZAcAO5Z09K9+nb9C1lpP37DVp93Jzk1sGBuvgclTXLuLk5GSRfgIAAAAAANtHkBkA7IQqf5G2d7/MSkiS79LXSf7ZIpNlBnTsIBOiImVU2EBp6uVlkX4CAAAAAAD7QpAZAGzcifx8WZiSrrOWNx88ZNLu5+Ulo8NDdHC5f0B7i/QRAAAAAADYL4LMAGCDysrK5M/tO3XW8k8bNklRaanJMoN6dJOJ0ZEyPLi/eLkzMSgAAAAAALg0CDIDgA3JPnlS5iWlypyEJNl3IsekvXXTJjIuIlzGR4dL91atLNJHAAAAAADgWAgy27j8/HwpKCjQj4uLi8XFxcXSXQLQwIpLS2VZxmZdDuO3zVulzGCo1O7s5CRD+/bRk/gNDewjruwHAAAAAABAIyLIbOOmT58u06ZNK/93QECARfsDoOHsOHJU5iQky/zkFDmSm2fS3qVFc5kQHSm3R4RJu2Z+bHoAAAAAAGARBJltXFxcnEyZMkU/jo2NJZMZsHEFRUXyw/qNutZy/M7dJu0erq4yfECQrrU8qHs3cXZ2tkg/AQAAAAAAjAgy2zgfHx99U9zcmNgLsFXr92fJ7IRk+SY1XXILC03a+7ZrK5NiomRUWIj4+3hbpI8AAAAAAABVIcgMABZyquCMLEpL11nLG7OyTdp9PTxkZNhAXRIjpGOAODk5WaSfAAAAAAAANSHIDACNyGAwyF87d+ms5aXrN0hhcYnJMlFdu+hyGDcPDBYfD3f+PgAAAAAAwKoRZAaARnD4dK7MT0qR2YnJsuvoMZP2lr4+MjYiTAeXe7Zpzd8EAAAAAADYDILMAHCJlJSWym9btsrs+GRZlrlZSsvKKrWr8heDe/fUtZaH9QsUd1d2yQAAAAAAwPYQ0WhkmZmZ8uSTT1bZ1rNnT3nnnXcau0sAGtieY8dlbmKyzE1KkUOnTpu0B/g3kwlRETIuKlwC/P3Z/gAAAAAAwKYRZG5k7dq1kwceeKDSc0ePHpW7775bpkyZ0tjdAdBACouL5ccNm2ROYrKs3rbDpN3NxUVu6N9Pl8O4slcPcXF2ZtsDAAAAAAC7QJC5kfn7+8vw4cMrPTdjxgx9rwLNAGxLZvZBmZ2QJAtS0uRkwRmT9l5tWuvA8piIUGnp62uRPgIAAAAAAFxKBJmtwFdffSUDBgyQ0NBQS3cFQC3kFhbKt2nrZE5CsqTt22/S7u3uJreGDNTB5fAunXTtZQAAAAAAAHtFkNnCNmzYIOvWrSvPZgZgnQwGgyTv2Suz45Nk8br1UlBUbLJMaKeOMjEmUm4NGSBNPD0t0k8AAAAAAIDGZrdB5lOnTsnKlStl2bJlsnr1asnPz5fbb79dXnvttYuu+/3338uXX34p27ZtE09PTwkPD5dHH31U+vbte0mymN3d3WXChAkN/toA6u9YXp4sSE7TJTG2HT5i0u7v7S1jwkNlQnSE9G3fjk0OAAAAAAAcjl0GmbOysqRLly5SWlpa6fljx45ddN2HH35Y3n///UrPpaeny//+9z9ZuHCh3HTTTZXafvzxR/n4449rfE0VRP72229Nni8pKZE5c+bILbfcIi1atLho3wA0jtKyMlm1dbsOLP+8KVOKL9iXKGryPlUOQ03m5+nmxp8GAAAAAAA4LLsMMqvgra+vrwwePFiuu+462bp1a63KUaggsgowu7m5yb///W+59dZb5fTp0/Lmm2/qILHKNt6xY4e0bt26fJ1+/frJAw88UOPruri4VPn8zz//LEeOHGHCP8BK7D+RI3MTk2VeUopk5Zw0aW/r11QmREXIuMhw6dKSE0MAAAAAAAB2G2Tu2LGjHD9+vDy4q4LEtWEspTFt2jR55plnKgWfL7/8comPj9dZy88//3x5m8qYVjdzS2UEBAToQDgAyygqKZUVW7bKN+s2yO9bt+vayxW5ODvLdX0DZVJMpFzTp5e4VnPSCAAAAAAAwFHZZZC5uszhmmRnZ0taWprOYp46dWqlNmdnZ3nkkUd0kHnJkiWVgszmUkHwH374QeLi4vTr10VMTEyVz2/atEkCAwMlLy9P7F1BQYGluwAbt/3IUZmfmi6L0tZLzpkzJu1dWzSXMWEhMjJkgLRu4qufK6xiOcCI/RIaCmMJjCVYI/ZNYCzB2rBfAmPJPKr6w6Vgl0Fmc6xfv17f9+/fX5o0aWLSrjKZlYyMDF3r2ZxAdkXz5s2T4uJiueuuu+r1OgBqr6CoSH7YmCnzU9MkdV+WSbuHq6vcGNRXxoaFSGSXTuLk5MTmBQAAAAAAuAiCzBUymZVOnTpVuaHat28vrq6ucvbsWTlx4oS0atVK6uOyyy6T5cuXS/fu3eu8rsqorinD+VKdkbBGjvRZYR5V/iJ9336ZlZAk36atk/yzRSbLBLVvJ3dcFiUjQ0PEz9uLTY16Yb+EhsJYAmMJ1oh9ExhLsDbsl8BYsg4EmS+4zMLLq+oAk8poVG25ubmSn59f7yBzaGhovdY3Un0x9l1lRtc3wxqwFzn5BbIwJU1mJyRJ5sFDJu1NPT1lVHiI3BYcpIPMfDEBAAAAAAAwD0Hm8zw8PMoDtdVRWcyKp6enWIvp06friQqN1ESCgKMqKyuTNTt2yqz4JPlpY4acLSkxWSame1eZFBMlw4ODxNvd3SFqmAMAAAAAAFxKBJnPa9mypb4/dMg041HJycmRoqIiPUmfv7+/WAs1ceCUKVP049jYWDKZ4ZAOnjwl85JSZE5isuw9fsKkXU3cd3tkuIyPipAeret3FQIAAAAAAAAqI8h8Xt++fcsnACwpKdH1lytKTU3V9926dSvPegZgOcWlpbI8Y7Outfzb5q1SZjBUand2cpJr+/aRiVERMrRfoLhRSgYAAAAAAOCSIMh8Xp8+ffSkf/v27ZPvvvtORo8eXWlDffnll/r+uuuuE2tCuQw4mp1Hj8qchGT5OilFjuSalrro3KK5TIiKkHGR4dKumZ9F+ggAAAAAAOBICDJX8OCDD8ozzzwjU6dOlfbt28ugQYN0VvOHH34oc+fO1aUy7r//frEmlMuAIygoKpIf1m/UWcvxO3ebtLu7uMiNwUEyMTpSrujZXf9fBQAAAAAAQOOw2yDzsGHDZOvWrfrx6dOn9f38+fNlxYoV+rEqh7Fjx45K6zz66KOyZMkSiY+Pl8svv1zXaT5z5ozk5+fr9ueee06Cg4Mb/bMAjmpD1gGZnZAk36Sky+nCQpP2wHZtZVJ0pIwKD5HmPj4W6SMAAAAAAICjs9sg84EDB2Tv3r2VnsvLy9M3xaWK+qyenp7y66+/yr/+9S/573//K8eOHdPP9+zZU5566im55557xNpQLgP25lTBGVmUli6zE5J1kPlCPh7uclvoQB1cDunUUZycnCzSTwAAAAAAAJzjZDBcMFuWncjOzpaioqJq21VgqnPnztW2l5WVydGjR/Ukf82aNRNrpbKsCwoK9OPY2FgdPE9MTBR7ZzxZ4Ovra+muoAGo3VD8rt0yOz5JlqzfIIXFJSbLRHbtrMth3DwwWHwbcPJNxhIYS7A27JfAWII1Yt8ExhKsDfslMJasi91mMquayvWharq2adNGrJ2Pj4++KW5ubpbuDlAnh0/nyvzkVF0SY9fRc1cOVNTCx0fGRobJxKgI6dXW+v8/AgAAAAAAOCK7DTI7ioqZzMXFxVWWAQGsSUlpqazcsk0Hln/N2CylZWUmVxkM7t1TZy1fH9RX3F3ZTQEAAAAAAFgzojc2jprMsBV7j5+QuYnJMjcxRQ6eOmXSHuDfTMZHRci4yHDp2NzfIn0EAAAAAABA3RFktnFxcXEyZcqUSjWZAWtRWFwsP23MkDkJybJq23aTdjcXF4kN6quzlq/q3VNcnJ0t0k8AAAAAAACYjyCzjaMmM6xRZvZBHVhekJImOefLuVTUq01rmRAdIWPCw6RVEyZvBAAAAAAAsGUEmQE0iNzCQvkufb3Mjk+StH37Tdq93d1kxMABMjEmUiK6dNa1lwEAAAAAAGD7CDLbOCb+gyUZDAZJ2bNPT+K3OH295BcVmSwT0qmjTIiKkJFhA6WJp6dF+gkAAAAAAIBLhyCzjWPiP1jCsbw8WZCcJnMSk2XrocMm7c28vWRMeKhMiI6Ufu3bWaSPAAAAAAAAaBwEmW0cE/+hsZSVlcmqbTt01rKazK+4tNRkmSt79dBZyzcGB4mnmxt/HAAAAAAAAAdAkNnGMfEfLrUDOSdlbmKyzE1Mkf05OSbtbf2ayvjIcBkfFSFdWrbgDwIAAAAAAOBgCDIDMFFUUiK/ZmzWk/it3LpN116uyMXZWYb1C5QJ0REypE9vcXVxYSsCAAAAAAA4KILMNo6J/9CQth8+osthzE9OlWN5+SbtXVu2kEnRkTI2MlzaNG3CxgcAAAAAAABBZlvHxH+or/yzRbJk3QYdXE7cvcek3dPNVW4eECwTYyIlpltXcXJyYqMDAAAAAACgHJnMNo6J/2AOVf5i3f4sHVhelLpO8s6eNVmmf0B7nbU8MjRE/Ly92NAAAAAAAACoEkFmG8fEf6iLnPwC+SY1XQeXM7IPmrQ39fSUUeEhMiEqQgZ0DGDjAgAAAAAA4KIIMgN2rqysTNbs2CVzEpPkh/Wb5GxJicky0d26yh0xkTJ8QH/xdne3SD8BAAAAAABgmwgyA3bq4KlT8nVSqsxJSJI9x0+YtLdu4itjI8JlQnSE9GjdyhJdBAAAAAAAgB0gyAzYkeLSUlmeuUWXw1iRuUXKDIZK7c5OTjIksLeutTy0X6C4ubhYrK8AAAAAAACwDwSZbVx+fr4UFBTox8XFxeJC0NAh7Tx6VOYmpMi85BQ5cjrXpL1Tc3+ZEB0p4yLDpH2zZhbpIwAAAAAAAOwTQWYbN336dJk2bVr5vwMCmKzNUZwpKpalGzbK7Pgk+WvnLpN2dxcXuTE4SCbFRMrlPbqLs7OzRfoJAAAAAAAA+0aQ2cbFxcXJlClT9OPY2FgymR3AhqwDMichWRampMnpwkKT9sB2bWVCVISMiQiV5j4+FukjAAAAAAAAHAdBZhvn4+Ojb4qbm5ulu4NL5FTBGVmUtk7XWlZB5gv5eLjLbaEDZWJUpIR27ihOTk78LQAAAAAAANAoCDIDVspgMEjCrj06sLxk3QY5U1xsskxEl84yMTpSbgkJFl8PD4v0EwAAAAAAAI6NIDNgZY7k5srXSakyJyFJdh49ZtLe3MdbxoSHycToCOnTrq1F+ggAAAAAAAAYEWQGrEBpWZms3LJVZicky6+bMqWkrKxSuyp/cVWvHjIpJkquD+orHq781wUAAAAAAIB1IFIFWNDe4ydkbmKyzE1MkYOnTpm0t2/mJ+OjImR8ZLh0atHcIn0EAAAAAAAAakKQGWhkZ0tK5KcNm3TW8qpt203/Uzo7S2z/frrW8tW9e4qLszN/IwAAAAAAAFgtgsxAI9l88JDMjk+SBSlpklNQYNLes3VrmRAdIWMjwqRVE1/+LgAAAAAAALAJBJltXH5+vhScD1gWFxeLi4uLpbuECnILC2Vx+nqdtZy6d5/JtvFyc5MRIQN01nJk18669jIAAAAAAABgSwgy27jp06fLtGnTyv8dEBBg0f5AxGAwSMqefTI7IUkHmPOLikw2y8COATpreWToQGnq5cVmAwAAAAAAgM0iyGzj4uLiZMqUKfpxbGwsmcwWdDwvXxakpOqs5a2HDpu0+3l5yZjwUB1cDurQ3iJ9BAAAAAAAABoaQWYb5+Pjo2+Km5ubpbvjcMrKymTVth06a/mnjRlSXFpqsszlPbvrchg39g8SL3f+RgAAAAAAALAvBJkBMxzIOSlzE5NlbmKK7M/JMWlv07SJjI+K0LeuLVuwjQEAAAAAAGC3CDIDtVRUUiLLMjbrrOXftmzTtZcrcnF2lqF9++is5WsDe4srkzACAAAAAADAARBkBi5i++EjOrA8PzlVjuXlm7SrTGUVWB4TESrt/PzYngAAAAAAAHAoBJmBKuSfLZKl6zfo4HLCrj0m7R6urnLTgP46uHxZ967i7OzMdgQAAAAAAIBDIshsQWfOnJGTJ09K27ZtxcnJyZJdgYguf7Fuf5bMSUiWRWnrJLew0GS7BLVvJxNjImVUWIg08/ZmuwEAAAAAAMDhEWS2gM2bN8sDDzwgSUlJ0qxZMzl9+rRMmTJFXnvtNTJiLeBkQYF8k5ous+OTZFP2QZN2Xw8PHVRWweUBAR04IQAAAAAAAABUQJDZAtmyt9xyi7Rr104OHTokfn5+snr1ahk6dKi0atVK4uLiGrtLDqmsrEzW7tyls5aXrt8oZ0tKTJaJ6tpFJsVEyk0DgsXHw90i/QQAAAAAAACsHUHmRrZ3717Zvn27vPTSSzrArFx55ZX69uuvvxJkvsQOnTotXyelyJzEZNl97LhJe0tfH7k9MlwmREVIzzatL3V3AAAAAAAAAJtHkLmRNWnSRFxcXHQt5opycnKkW7dujd0dh1BSWiorNm/Vk/gtz9wipWVlldqdnZzkmj699CR+1/ULFHdX/lsAAAAAAAAAtWX30bS8vDyJj4+X/Px86dKliwwcOLBW6+3evVtnHHt6ekpwcLCundwQWrRoIc8884zOZFYT/qk+LViwQL/fF1980SDvgXN2HT0mcxOTZV5Sihw+nWuyWTr6+8uE6AgZFxkuHfwb5u8LAAAAAAAAOBq7DDIXFBTIO++8I8uWLdMB5uLiYv38PffcI5999lmN6+7atUsv98cff5Q/5+7uLvfff79Mnz5dPDw8Ki1/6tQpOXr0aI2v6ezsXClLWb3+mjVr5Pbbbxd/f385fvy4vPDCC9KvXz8zPzGMzhQVyw8bNupyGGu27zTZMO4uLnJDcJBMjI6QK3v2YKJFAAAAAAAAoJ7sMsh85MgRee655/RjX19fCQgI0JnCF6OCvddcc42um+zj4yMxMTFy+vRpSU5Olvfff18Hk+fNm1dpnaVLl+oAcU1UYDojI0M/Pnz4sISHh8ttt90mv/zyi27bsmWLXHvttTrA/emnn9brszuqTQeydTmMhSnpcurMGZP2Pm3b6KzlMeFh0sLXxyJ9BAAAAAAAAOyRXQaZVYD4n//8p1x33XVy2WWXyYwZM2o1oZ4qYaECzEFBQbJixQpp06aNfv7333+X2NhY+frrr2Xy5MkyZMiQ8nUmTpyob7WlgtIqmD1t2rTyrOg+ffro7ObXX39dZs6cSXZtLZ0uLJSF6zfq4PL6/QdM2n3c3eXW0IEyKTpSQjt3FCcnp1r/nQAAAAAAAAA4cJC5VatW8vLLL9dpnZKSEpk1a5Z+/NFHH5UHmJXBgwfLlClT5O2339Z1kysGmevKz89P3584cULatWtX/vyxY8d01rUqrYGaJe3eI5+vXis/bsqQwuISk/bwzp1kYkyk3DIwWJp4erI5AQAAAAAAgEvILoPM5ti4caMO/LZu3VquuOIKk/bRo0frIPPq1avr9T7Dhg3T9ZnvvPNOeeWVV/Tkf6r+s6oV/eSTT9bqNVQZj6ps2rRJAgMD9WSH9uyTP/6Uxes3VnrO39tLbhsYLGPDQqRXm9bnniwpsfttgYap4Q40BMYSGgpjCYwlWCP2TWAswdqwXwJjyTwqyfVSIMh83tatW/W9KpVRlf79++v7rKwsyc/P1yU5zNG0aVM96d9bb72ly3OcPHlSOnbsqGsx16XshiNTgWRjkPmK7t1kbHiIDA3sLR6uDGcAAAAAAACgsRGVO08Fe5UWLVpUuaFUUNnT01MKCwvl1KlTZgeZFVUm48033zR7/fj4+PLHKuBtPHun6karusOX6oyEtbi2fz95Zti1ckO/QAns1NHS3YGdsPf/N2g8jCUwlmBt2C+B8QRrxL4JjCVYG/ZL9UMB4Ao1mRXXGrJhjW3FxcViLaZPn65LfKhbamqqZGdni71TgfT7r7hMOjb3t3RXAAAAAAAAAIdHkPmCsxW5ublVDorS0tLyjOEmTZpYzcCJi4uTI0eO6FtYWJi0b9/e0l0CAAAAAAAA4EAIMp/XqVMnfb9z584qN9SePXukrKxMB5j9/cmgBQAAAAAAAACCzBWEhISIi4uLbNmyRQ4ePGgyOlasWFG+nCrXYC0csVwGAAAAAAAAAOtBJvN5Kjt58ODBYjAYZNq0aZU2Ul5eXvlEfSNHjhRrQrkMAAAAAAAAAJZU/Sx3Nm7lypVy+vRp/TgjI0Pf7927VxYvXqwfOzs7y80331xpHRVcVuvNnDlTjh8/LiNGjNA1mj/88EPZsWOHLqlx7733ijXx8fHRN8XNzc3S3QEAAAAAAADgYJwMKnXXDgUFBZUHl6uiSmOUlJSYPP/JJ5/I1KlTpbi4uNLzHTp0kJ9++kmCg4PFmuTn55dPSBgbG6s/V2Jiotg7lV1eccJGgLEES2O/BMYSrA37JTCeYI3YN4GxBGvDfqlh2G0m85AhQ6RHjx7VtqtgbFXuu+8+ufrqq2XOnDmybds28fDwkIiICJk4caL4+fmJtVE1mSuW9wgICLBofwAAAAAAAAA4FrvNZHYUZDKTyYz64YwlGgpjCYwlWBv2S2A8wRqxbwJjCdaG/VLDYOI/AAAAAAAAAIDZCDLbOFUuo3Xr1vqWmpoq2dnZlu4SAAAAAAAAAAdCkNnGxcXFyZEjR/QtLCxM2rdvb+kuAQAAAAAAAHAgdjvxn6Pw8fHRN8XNzc3S3QEAAAAAAADgYMhkBgAAAAAAAACYjUxmG5efny8FBQX6cXFxsbi4uFi6SwAAAAAAAAAcCJnMNo6J/wAAAAAAAABYEkFmG8fEfwAAAAAAAAAsiXIZNo6J/wAAAAAAAABYEpnMAAAAAAAAAACzEWQGAAAAAAAAAJjNyWAwGMxfHZaWn58vBQUF+nHfvn3lzJkz0r9/f7F3paWl+t7FxcXSXYGNYyyBsQRrw34JjCVYI/ZNYCzB2rBfAmPJPEFBQfLpp59KQyOT2cZNnz5dWrdurW/Hjh2ToqIiKSsrq/PrqHWysrJqtW5tl63NcjUtU1Pb5s2b9c1W1GX7Wsv7mPtajKVLi7FUv23TEMtU125r+6XGGk+2tl+qy/LmjpWLtTOW6v+3uRjGkvWyteOco4wlW9w3MZbqt10YS4ylhvo/RlzA8cZSXddlLFnvWKozlckM25WXl2c4cuSIvmVmZqqsdP24rtQ6tV23tsvWZrmalqmpLTo6Wt9sRV22r7W8j7mvxVi6tBhL9ds2DbFMde22tl9qrPFka/uluixv7li5WDtjqf5/m4thLFkvWzvOOcpYssV9E2OpftuFscRYaqj/Y8QFHG8s1XVdxpL1jqW6crV0kBv14+Pjo28AAAAAAAAAYAmUywAAAAAAAAAAmI0gsx3x9vaW559/Xt9fynVru2xtlqtpmfp8HmvTWJ+lId/H3NdiLF1ajKX6bZuGWIZ9k33vl+qyfH3HCmOp7hpqmzGWrJetHecYS9aLsVS/7cIxjrHUUP/HiAs43liq67qMpbqz1t8RTqpmhqU7AdRVTEyMvo+Pj2fjoV4YS2gojCUwlmBt2C+B8QRrxL4JjCVYG/ZLDYNMZgAAAAAAAACA2chkBgAAAAAAAACYjUxmAAAAAAAAAIDZCDIDAAAAAAAAAMxGkBkAAAAAAAAAYDaCzAAAAAAAAAAAsxFkBgAAAAAAAACYzdX8VQHbsXHjRvnmm28kNzdXIiIiZOzYseLszDkW1E1paan88ssv8tVXX8nu3bvl3Xfflcsvv5zNiDorKSmRH3/8UZKTk8XJyUnCw8Pl5ptv1o+BunjzzTdlx44d+rGPj4/07NlTxo0bJ35+fmxImC0rK0tGjx4txcXFkpiYKC4uLmxN1Nr3338vL730ksnz//znP+W2225jS6LOjh49Kl9//bXs2rVLAgMDZdKkSeLl5cWWRK29/fbbMnfu3CrbHn74YbnjjjvYmqg1g8EgP/zwgyQlJUlRUZH0799fx5jc3Nwcfis6GdTWAezYwoULZeLEiXLvvfdKp06d5OOPP5a+ffvKkiVL+NGEOrnmmmv0F9orrrhCnnnmGVm6dKkMHz6crYg6OXDggAwaNEg/vvvuu6WsrEw++eQT6dGjhz6J4e3tzRZFnYI5Bw8e1I9Pnz4t3377rQ46r1mzRvr06cOWRJ2pnwbDhg2TDRs2yOHDh3Wg2dWVvBTU3meffaaDNqtXr670fOfOnaVVq1ZsStTJH3/8IbfeeqsMGTJEfwffs2ePfi49PZ0tiVrbv3+/PqZV9L///U/ef/99SUhIkKioKLYmav09acSIEfLXX3/Jgw8+qOMD6rjXpEkTWbt2rU76cGQEmWHXCgoKdGB58uTJ8tprr+nn1I9v9cP7yy+/1GfBgdpSmfDq4LFp0yZ9tpIgM8yhxo86STFv3jzx9fXVz+3cuVN69+4t06dPl8cee4wNC7OpgGBQUJC+LVq0iC2JOvvggw/kww8/1Cfon3vuOYLMqDP1Y/vRRx+VvLw8th7qncGsfrc9/vjj8uyzz5Y/rwLNXbp0YeuiXtSVhGfOnJGMjAy2JGpt1apVcvXVV8vPP/8s119/vX5u79690rVrV/0d6u9//7tDb03qBcCurVixQo4fPy533XVX+XMqW1CVOFABHqAuVIAZqC914ksF/4wBZqV79+7SoUMH2bx5MxsY9aIu0wsODtYnLoC62r59uz4JpoKEHh4ebEAAFvXpp5/qEmP/+Mc/Kj1PgBn1pQLLqamp+qpCoC727dun79X37YpX6qhSdfvOtzkygsywa+vXrxd3d3fp1atXpedVhpe6DBQAGlvTpk31fqkidfZbldG4cF8F1JUqmaEu+1QZFkBd5x1QNSnViXljSR/AXGfPntUZXmpfpK4oVHUrgbr6/fffdRkDdeL0X//6lzz99NOyYMECXWoMqA81x446Mc+Vzagr9R1JlRH79ddfy59T81ecPHlSBg8e7PAblCAzLEbVRJo9e7b+QaMyi9WtNpfVqZIF77zzjq7Nde2118o999xT6T94RSdOnNABnQsn02rWrJlug31cGq5q/qlLeiMjI3W2scoQrU1GqArqqctZ1ERZLVq00CUw1BdYLu90XOpvryZxULUkr7zySr1fUl8aLkb92JkzZ46MHz9e1wy8/fbb9ZdXFbSpzbr333+/3lfxRdd+FBYWyvLlyyUuLk4HWdRYUmOrtnWW77zzTn2MGzVqlHz00Uf69aqjsiYeeOABXd5AzTmgJpE0loiC7du6dauuGXnTTTfpY5U6xr3yyisXXU9l/6nvS2rC45YtW+rMPzVGqrssWI2ZQ4cO1eq1YZvUCU2VGaomdWzTpo0eS1OnTq1V/cnPP/9c78dat26tr8hRE/jFx8dXubyaXFuNNVWrUmXGqx/jMTEx8t57712CTwVLUQk7avLZG2+8UY+NC7ONq5OZmSlPPPGEPgmh1lUTQqoJ/aqSnZ2t24YOHarHoZq3QpViUcdVtY+D7VO/ydWJA3UySh2n1H5J/aarDfU9S40hdTVg27Zt9fw5aoLIi1Hfz1UcQq2r9mmwH+o7sboaS03Cp/ZLsbGxtVrvyJEj8vLLL+vv0Nddd52OEaikjap069ZNFi9eXL68ei91XFVz7AwbNqyBP5ENUhP/AY1t6tSpBicnJzXpZKVbTk5Ojevt2rXL0KVLF5P11G3y5MmGsrKySss//vjjhhYtWpi8zj//+U+Dj49Pg38uNL7HHnusyvGwcePGGtfLyMjQY6OqdQMDAw3Hjh2rdl312mq5pUuXXoJPBEv56quvDG5ubibj4eeff65xvfz8fMPVV19d5ViKiYkxnD59+qL7Q1dXV8OPP/7YwJ8IlvLLL78YvLy8TMbDp59+WuN6JSUlhjFjxlQ5lvr06WM4ePBglesdOXLE8PHHHxveeOMNww033GBo27atYfny5Zfo06ExrV27tsrx8Pzzz9e43tmzZw1Dhgypcl0PDw/DsmXLKi2/YcMGg7u7e6Xnp0+frpcvLi6+ZJ8PjWfPnj1Vjod77rmnxvXUd+vx48dXua6zs7Nh1qxZJusUFhaaPHfvvffq/WJeXl6Dfi40PnWsUseZC8fDsGHDzP6u5e3tbfj+++9Nlu/bt69uX7VqVflzmZmZeuyp4x5sX7t27UzGQ79+/S663rvvvlvlfkndHn744RrX/eGHH/RyS5YsacBPAku76aabTMaCn5/fRddLSkqqMi6g4lUvvviiyfIFBQWGsWPHGnr06KHbX3vtNUNoaKjhqquuMhw6dMjg6MhkhkUcPHhQzy6tsv5Utl9tqGy/kSNH6okeAgMD5b///a8+e6kmgVCXuqgzVirbqyKVpaEuW7jwTLeaREK1wfap7Bg10/SLL76ozza2b9/+ouuoTAiVYaPqdavMGpWpeuzYMfnll1/0GXSVBa2yJOBY1H5B1SBVWQ0zZszQ+5naUJPRqFnOmzdvLu+++66uBa+yDtU+TmV51TT5w7///W+931KzW99www0N+GlgSTk5OfqYpbLaX3/9dZ1JURuvvvqqzuZRmVr/+c9/9DFOHdvUfmnLli0ybty4KtdTY01lMqus6R9//FFnYKjjK5cT2z51vFJldFS2qcpwV1dv1cYbb7whv/32m/j7++s5KFSGjpp0VF0FpsoYqGOgujLMyHjFhso6VRMhqZvaDyrR0dF6UlLY/lhSNSNVtqDaz6js0dpQ37fnzp0rXl5e8vHHH+ts923btunXUfuY++67T7KysiqtU1U9b5VNpibYUnW/YftjSY0DVX5QfQeq7YTFah+kxo26ClFl/qnjlcoGVN9/1GTt6hi3f//+Suuo7FR1laK6usxIfT9TmYSUYLEP6jhlzAJV+5raUFfkqGx4RX332b17t75CVR37XFxc9FUTanzVtF9TY6u2Wa6wDerKB3WljfqupH6T1UZ+fr7+bqTiAur7zvz58/VV8sbfb+q32oVjSX0/Ut/J1qxZo6+Cfuqpp2Tt2rU6TvX0009fks9mUywd5YZjUtlYFbOOa5PJrM5uq2VatWplOHr0aKW2mTNn6jZ1JrS0tLT8+d9++00/n5ycXGl5daZJZYvB9l2Yvd6hQ4eLZjKvWLFCL6POWJ44caJS27p16/RZS5UhkZ2dXeX6ZDLbJ7VfKSoqKv93VFTURTOZ1RhxcXHRYyY+Pr5SW1pamh5Hqm3nzp0m66osQdX2xRdfNPAngaWpY5nKcjAaOXLkRTOZz5w5Y2jatKlebtGiRZXa9u7da/D19dVtq1evvuj7f/jhh3rZmq7IgG0e4x555JGLZjKrLMOWLVvq5b799ttKbWofpzLEVJsaJxX3f+q7UsWb8b0SEhL0GIR9jSVjpvrFMpmDgoL0cu+9955JmzFb/plnnrno+6v11bKMJftQ8cqaefPm1SqTedy4cXq522+/3WRsXnPNNVVmoD799NMGT09Pk/HbqVMnw5QpUxrks8CyKv5t//zzz1plMqsrmNVy6iqLqq5YVm2DBw+ucl31209d0fPkk082QO9hTSr+dt+9e3etMplnzJhRfiWz+i5ekTq2qbbIyMhKz9955506i/lCN954oyE6Otrg6MhkhkWoM4cX1km+mO+++07f33vvvbq2YEXqbJXKTFYZ0hVr56iz3t27d5e33367/LlVq1ZJWloaM8naibqOI8V4NlJl+qmz5xUNGDBAZ0ar7Jyff/65wfoJ66f2K+qqiLpYsmSJruumJnlQZ78rCgkJ0RkS6jyaytSpaObMmfLkk0/qLGY1yRbsi6r7r7L+6kJlnapJ+1TWqqp1WpHKypgwYUKlY6GiMlFXrlxZaVmVparqEarXUfV74XjHOOPVOerKnhEjRlRqU/s4VQNeqVgjXO3/jBnMxltAQIBuCwsL02MQjjeWVG1LlX2qMpOryqKfMmWKvr+w3ryq662+kxup792qdqWql8pYsp/fcnWhvistXbpUP74wi16NTXUVxYXHOEV9R1JXpM6aNav8uWXLlumxqWo6w7F/yxn3QRUZ68yrOXsqXrFjpL4jqe9Kd999t1n9hfVq165dndcx7nPUFRmenp6V2lSWvLpqWl01oTLljUJDQ3XWsqpLb6Su7lBxqJCQEHF0BJlhM9QXVOWqq64yaVOXxRgvR05PTy9/Xu0U1GU36vJ1FThUQUV1KbwK7lCU3XEZDwgXBgWNVAkNZePGjSaXsqsf3mpSN+PBSP27tpcJwrH2S4qamObC/ZIaf+oSLDVJybp163SZA+PtwpI/cBzmjCV17FMnUdUXWhWEHjNmjL4cXpWJUpf7wbGPcVFRUVX+eK/uGAdUN5aCg4N1GZ/qxpIq51OxNF3Hjh3193JV6qdr1656OTU50sKFC9nIDkqVWFGTK6vSYmqi7Qup32nqmKbKZajL1o3UCVNVpkV9R1KTn6qTsOrkmbokffjw4Y38KWAN1ElUdRJLjRc1sW1VgUb1XUid2FCTTF5IleocNGiQ9O7du5F6DGtm/F5d1fdvlYymEtAU9ZvNSE1qq2JKKpagyrmqUj/9+vXTZXxUuTtH52rpDgC1Zaz3pr6sVsX4/IV14dTstDt27NCBZnU287nnnpO+ffuy4R2YOtOoGLO0LqR+HCmHDx+u9LwK4qjZravKWoRjMme/pDIGP/zwwyqXV1+K4ZjMGUsq6KMyCNWPdxWkdnZ21nXhVOYpHJe5x7gLTZo0SZ/cUCfs4ZguNpZUNqsaH6rG7okTJ6R169blY0fdVMBQZQyqY1tdrxSCfTEeu9SJh6qobHkVHFTLqVvFK3FUHWd1ZZi6GlWNozfffFMHc+DY+yW1v6luv6KOc3v37q3yOKcSOuqaiQ/7pGJDp06duuj379TU1Erfv9W4U1epqit91IkMdQxU8zmpk/sgyAwbooqyKz4+PlW2+/r66nt1lvxCTZs2Nbn8GI5LTTyjXHhJjJHxMnc1CUlF6hJPLvNEffdL6hJ2lZED1HcsVcz0UjegLsc49aNIZZ9WF0RWZciYJNmxXWwsGceT+qF+4Xemiic0gIsd4y52nFNXf6krUoHa7peUqvZLnIjHhfslFTSu7oRFTfslNfmpuqEyymXAZhj/41e8HK8i9WNJcXd3b9R+wfYYv5So7JqqFBYW6vu61lSF42G/BMYSbPUYp4LLZCmjPmOp4njiOxPq831J4bccaoP9EhoK+6VLgyAzbIZxgrYjR45U2W58/sKJ3IALGS/nrDgpTUXZ2dn6vlWrVmw8sF9Co+AYh4bCMQ6NNZZUbVQVGFS1Ufn+jfoc45SjR49WWhaoab+kxouqu1wVfsuhNtTV7ur4pSZpV8ezqhBjqjuCzLAZgYGB+n79+vVVthuf79OnT6P2C7bHeFlLcnJyle1qBllFFfAHasJ+CQ2FsYSGwjEODT2W1HfsoqKiar8v9ezZkysJUatj3J49e+T06dMm7bt379bPq9rM1dVGBRRVxknNb6JOcFWcjM1ITRy5a9cuPfEt8zDhYpnM3bt3rzHGZJwAlxhT7RFkhs0YPHiwvv/6669N2rZv3y4pKSn6TNSVV15pgd7BlgwbNkzfz50716RW186dO+X333/Xj6+//nqL9A+2t19asmRJeY04I/WDfNGiRfrxNddcY5H+wfbG0h9//FHlRDXGYx9jCRcTExOjs3NUMOe3336r1KaydT7//HP9WE2kBdRE/fju0aOH/q40b948k/ZPP/2UsYRaUdnJAwYM0JmnCxcuNGk3ji/1O079ngNq81vus88+M2lTz6ljXXR0NJOzo14xppUrV+rv5M2bN9f7L9QOQWbYDDVLtar3tmLFCnnrrbf0wUNRlzbccccdUlZWJrfcckv5JTRAdVTwuHfv3vpSqjFjxsi+ffvKz1Teeuutul6cGktqNnSgJurHkBpL6lKqe++9t7w2pQowP/jgg3LgwAE9k/rQoUPZkKiRCuSoL7pqDKljmnG2a3Vse/bZZyUtLU3/WBo9ejRbEjVSc1MYJxe988479YkL9Z1JZXep51X2qZ+fnx5nwMU8/PDD+v7RRx+V77//XgcJ1UR///rXv2Tx4sU6E4zJbFEb9913n75/+umnJT09vfz5VatWySuvvKIfq+9SQG32SypTeebMmfL222/rRA+V2Tx79mx54YUXKu27gJpMnjxZj6UvvvhC5s+fX+nqCuOx7W9/+1u1EwPClJPBGKkDGtHPP/8sL7/8cvm/165dq+/VGUfj2etHHnnE5Mf0O++8I48//nj5LMNt27aVzMxMfWBR9XMTExO5xMrBqB/Pw4cPL/+3yrZRuzV1QsLZ2bl8LFUcb4oaKyoj0JjJrA4cxglH1NhKSEiQgICARv0ssCx1sqHizOXqpIP6Ia3KpqjgnnLttdeWf3mt+OPouuuu04FltZwKFqrL9E6cOKH3Zz/88ANZ8Q5GHZMqnljYsmWLDvCpsaEu81SCg4Plo48+qrReRkaGXHbZZfqSYTWbtbo0b//+/eWZzeoL8F133dXInwaWpo5FJ0+e1I/VfkYdq9QxyzjRsTohqsZORWoW9KuuukqfnFDUBH/GCbfUjymVNTh27NhG/yywrMjISP29WVHjSI0nNTZUiQJFPTaONSM1bm688UZZtmxZ+TIq0Gz8CakCPI899lijfxZY1j/+8Q/9XdmY8LN161b9HahiqTl1lZfKAKw4lq6++mr9u0/th1Q5FvXc5s2bdbv6Pr906VILfBpY0tSpU+Wrr74qP7GuvkOp33AVJxP9888/JSQkpNJ66gS88eSEGk9qHWONZnV8U8c59Twch/qerG7GCWuNV7qrGJPRq6++KldccUWl9VSs4L333tOPu3Xrpk/Eb9y4Ue+f1Hd3dXKeWvF1oILMQGP78ssv1TfTGm/vvPNOlevOnDnT0LZt20rLXn311YbMzMxG/xywvOXLl190LD3xxBNVrrtp0ybDiBEjDD4+Pnq5Fi1aGO655x7DwYMHG/1zwPI2b9580bE0duzYKtdduXKloV+/fpWW7d27t+GXX35p9M8By8vNzb3oWBo0aFCV66alpRmioqIqLdupUyfD3LlzG/1zwDr4+fnVOJY6d+5c7TiMi4szdOjQQS/n4eFhGDx4sOGPP/5o9M8A63DhcerCm4uLS5XrnT171vDSSy8ZunXrZnBycjK4ubkZoqOjDYsXL270zwDrMGzYsIse56r6Pn3y5EnD3XffrfdHxuW8vb0NjzzyiKGgoMAinwWWpX57XWwsJScnV7nurFmzDCEhIQZXV1eDs7Oz/u6tYgglJSWN/jlgec8///xFx9J3331nsl5paanhP//5j8Hf37/S8VDFCbKysizyWWwZmcywCHVp+bZt22pcRp1Fat++fZVt6iynWl9l6nTs2LE8MwyOR52xvrAW7oVUtpcx46s6xswwOC41jlJTU2tcRl0xocpjVEfVQFX7N7UcE9c4LnWM+uuvv2pcRmVJ9O/fv9p2Vc5HlVsxZseTjeO48vPzy7NGq6Kyt7y9vWt8DY5xMB7njJl+VVH7GR8fnxo3lsrsUplh7JMcm7p6Iicnp8ZloqKiqv1ura4U27Fjh95/qYkjL7YPg/1SGafGq0mro8aH8QrV6r53qeMk9bwdm7oq1VgGszpqMsiKV1hUpK7uUXN9qdJ16ndcdcuhZgSZAQAAAAAAAABmY+I/AAAAAAAAAIDZCDIDAAAAAAAAAMxGkBkAAAAAAAAAYDaCzAAAAAAAAAAAsxFkBgAAAAAAAACYjSAzAAAAAAAAAMBsBJkBAAAAAAAAAGYjyAwAAAAAAAAAMBtBZgAAAAAAAACA2QgyAwAAAAAAAADMRpAZAAAAAAAAAGA2gswAAACAiPyxNkn+8/bHsj5jS/n2KDx7Vj/32eyFddpG5q6H6p04eUpv01kLvmczAQAAWBlXS3cAAAAA9ic/v0AS0zbI9l175eTpXGnWtIm0btlc+vTsJoG9uos1SkhZJx98Pkd6dO0sA/r10c+dPVukn+vXu4dMnji61q9l7nqo3qlTuXqbxkQMlEljbmFTAQAAWBGCzAAAAGgwZ4uK5M0Pv5Av5i6S/IIzVS7TrXOATHvqYRl61WVWv+U9PT3k2Ufvl5Ytm5sE0d+Z+V9p16a13DNhZK3XAwAAAOwRQWYAAAA0iLz8Ahkz+VFJ25Cp/60ylqPDBkjL5v6Sm58vR44el20798imLdtl0+ZtNhFk9nB3l4funWTyvAqgq6za4H69qwwyV7ceAAAAYI8IMgMAAKBBPP7v13SA2d+vqcx45Vm57upBVS63e29WtVnOAAAAAGwPQWYAAADUm5osb8kvK/Xjz2e8LJdFhFS7bNfOAVU+bzAYJCF1vaRvzJTcvAKdAX15VKj07tG1ykngPvpirnQOaK/r8x46ckx+/X2NHD56XFq18Jdhgy+X9m1bVzsp37I/1uqsam8vT4kOGyihwX2rXVaV/2jbumV5beU1iWny04pV+vGhw8f0ZHRGqq+jb76+yvUs8VmrYs7rqRMDcxYt1ZnbNw+7xuQ1V/6ZIH8lp8uI2GslKLBnle+zP/uQLP9jrX5ePXfj0Kv19ldKSkrkt9UJsnn7TnFxdpbBl0eXv0519mZly4pV8XI856QEtGsj1w0epLdjdXbs3idrk9L05/TycJegwF5yZUy4uLi41Lh9Dh4+KstXrZWDh47KwKBAGXbN5TX2y1hKpbm/n/z9rvGV2tQ2UttKjYt7JowSJyenGl8LAADAVhBkBgAAQL0t/vk3fX/VZRE1Bpirs3f/Abn38X/JhsxtJm233nCtvDntKfHx9qpyEjh3d3d56sXpUni2qLz9hTc+kI/eeF5uHHpVpdfavH2X3Dn1KdmXdbDS86NuHibt27Su1QR+yekbdM1p5cix47rd6PprrtBB5pom/musz1odc15vf/ZBvc6YW2KrDDKr4KlqVxM7GoPDFd+ntKxM/vXqDCkuKSlf540PPpdvv3pfykpL5Y6pT8vWHbvL216Z8Yk8/48p8sDfbq/yM3w25xt54Y33paSktPw5Xx9veeelZ+SmYYMrLXs6N0+eeP51Wfrr7yav071LR/n07Zekb+8eVW6fktJS+fdr75X3+86xIy4eZD5fSqVLxw6VgswrVsfL5Eef1XW853/2DgFmAABgVwgyAwAAoN7SN24uDzKbVcv53sdk7/5sadrEV2649kpp26qlbN25W379fa1899MKKSoukc/f/Y/Jult37NFlOoL69JTo8AHi6uIiy1f9pbOUH/vXq7o/KvhoDDZOeOAfkn3oiLRs4S/XD75cWjRvJus3bZVvlvyqH9fG5VFhOoj87if/k3ZtWsnd424rb+vWpZNVfNbaaOjXq/Z9tu+Wf6a+I+ED+klkaLAUFRXrz7n/wEF5+qW35MDBw3L02AmZOOomadWiuaSs3yR/JqTKa+99IiNuuFZn/V74egkp66Vvr+5yeXSYlJWWyR9/Jcn2XXvlwSdfkE4B7WRAvz7lGdITH4yTpPSN+nWuvTJG2rRuqf8OfyWly8bN22TsvY/L6iWzxb9ZU5P3eTb1XX2iICZ8oM7yVtnP5vhx+Sp5MO4Fnak+d+Zb+rUAAADsCUFmAAAA1NvxEzn6vn3bNnVed9bC73XQNaB9W1ky66NKpRr+WJsk4x/4h/y4/A9d7/nCshYnck7KYw/8TZ56aHL5c08/fJ9cP3ayZGzdIav+Si7PyJ21cIkOMPfs1kW+++/7lUorzPlmqc52rY2IkP66lIIKMrdq2bxOE/w11metjYZ+vWrf5+Qp/R7qvYzuvWOMXDF8vPy2Ol5nE6/5ca40b+ZX3n7fE//W5Vd+WP6HTJ4wyuT1xo8cLtOfjysvdaEC1yqI++OKVfLWR1/K/z4897f8ZukyHWAeft3V8vEbL4ibW+WfP8+/8b7M/O98mf3NEnlo8kST97l34miZ9tRD4uzsbPbn//aHZfLwsy9LZEiw/PeD16SJr4/ZrwUAAGCtzP+2BAAAAJQ7V1vWUFZW522iavEqcVPuMakFfPWgSLlt+FD9eOWac8tV1Ny/mcRNubvScyqQeMO154Kj+w5klz//+5pEff/k1HtMavdOGHWThPQPvOR/z8b6rLXR0K9XHZUh/sh9d1R6rmP7tuUlKlTwuWKAWblhyJX6fv8FZU0UL08PeSFuaqVayu7ubvLys4/px38mpEhx8bnyFipIfW4dT3nroy/k1Rkz9e2Vd8/dTp3O1e1pGzJM3keVLPnnYw/UK8A899sfZOoz/9EnNuZ98hYBZgAAYLfIZAYAAEC9qcv/t+/aI1kHD9d5XVUuQakuyBsW3E+Xs8jKPmTS1qNLxyqDgKochqLKWhgZ1x8QdK6UwoVUiQVj2Y9LpbE+a2009OtVp3vnqt9HBbl1P7p2rqLtXND55PkgcEVdOwXoUiMXUuUw1E1NZHjsRI4uZbJ7737dtnDJLzX28dTpPNN+d+moA9rmUlnzz7z0tn4dVW9alecYfHmU2a8HAABgzQgyAwAAoN7CBvTTk7+pbOELyw7UlpocrqbnnZzOZUtX5OL6f9msVTEYDOWPjeurGr5VKTMjC9tcl/qz1oY52646xsxhc95H1YKuTR+Mymr4nKXn/7blf+uyc8uqCQRbXJAtXVGHdqZlXnzqWY9a9eHL916RXt27yJCRf5MpT78kK775wiSDHQAAwB4QZAYAAEC93XbjUPng8znlgea6ZGyqidp278uS1HWbJLBnN5P2lPSN55br0K5efTS+T/rGTOnSqYNJe12ymMuDrnUM7DbWZ21oHu7u+l5lCFdl8/adjdaX3XuzJOfkaZOJ+vZnH5Kjx0+It5eXtDw/iWPXzgF6e/fp0U1uv/UGaUwqk/qaK6L149f/HScP/ON5uf+J53U9cFdXfoYBAAD7Qk1mAAAA1Ftgr+4y+ubryydtW/zTimoza9dnbKlUA3foVZfp++kffi67zpc3MPppxSr5/peV55cbVK8+XntljL5//f3PdCmDij753wLZuHlbrV/L29tL3x86crxOGdCN9VkbmipRocSnrJO9WZVrNS/6YZmsjk9ptL6cLSqSZ195R0/2Z1RwplCefukt/XjwoMjyIO4t1w/R9y+++aGs27SlytdLTt9o8rdoaCNih8jYETdI8rqN8tLbH1/S9wIAALAETqEDAACgQbz2ryd0LWGVzfxA3Avy8rszJSo0WE/8lpdXIIePHZdtO3fLvqyD8tRDkyU0uJ9eb/zIm+Srr7+THbv3yZCRd+kgYdvWrXQd27VJaXqZUTcNk6DAnvXqn3qfz+cskj37D8jVI+7QE+2pCec2ZG6VtA2ZOvP04OGjtXotNSmcCryqLNnR9zyq++bm6iq9e3QtD7ZX14fG+KwNrVXL5jIoMlT3ceiou2XY4Mv1NsjYskMHTlW5CWO96UvelxbNdTBeZZ7HRAzUJTLWJKbq91cZ1/+Yek/5sqNuuk6+/XGZrPorWa4fO1kiQ/rrSfg8PT0k+9Bhydi6Q49HVdaiW+eOl7Tfr/zzUUlK2yAz/ztfosMGSOz5yQ0BAADsAUFmAAAANAhvL09Z8Nk78uEXc3Ugbf+Bg/p2oYFBgbqGc+X13pW/P/WiJKSsk59WrC5vUxPGTRg5XP7zz0fr3T8VFJ038y3528PP6KDukvNZw8rfbr9V/Jr6yoxPZtX69Z56+F6Z+vSLOvBqDBBff80VNQaZG+uzXgpvTXtKxt73mOzdn10+kZ7q8+MP3iVFRUW6XEpj6NGtk4y5JVaefvEtmbvoh0oTCX7w6nOVypC4uLjIV++/Jv95+2OZvXCJJKVv1LeKZU/UiZBLHWA21nj+8PV/y82THpRHnn1F+vbqLp07mpZtAQAAsEVOhrrOEAIAAABcRElJic403b5rr5zOzZOmTX2lTasWEtize40Tn23avF3WbdosefkFOgM6JnygBLRva7LcqdO58r/5i3UG7W3Dr6vydX5fkyDR4QMlIqS/Sd/WJKbJ9l17xMvTUyJDg/XkbAmp6yU5bYNce9VluvyHsTTDJ/+dLy1bNpdxt95o8j4qe1YFmFWt4tKSUunWpZPcOPSqi67XWJ+1KvV5PfW5/liTpLPBm/j6yOXRYbp+tMpeV3Wmhw4epOsf1+Z9lv76u+zZlyW33zZcWrXwN6mvvPjH5dKnV/fyEiMXvt7RYyfkj7+S5ETOKT2mVB1w3xom6ztx8pQkpq7XfzMVHO/Qto3069PDZJtfrN8Xk19wRr6Y8434+TWRO8aMMGn/+bfVsmPX3kqfDQAAwNYRZAYAAAAAAAAAmI2J/wAAAAAAAAAAZiPIDAAAAAAAAAAwG0FmAAAAAAAAAIDZCDIDAAAAAAAAAMxGkBkAAAAAAAAAYDaCzAAAAAAAAAAAsxFkBgAAAAAAAACYjSAzAAAAAAAAAMBsBJkBAAAAAAAAAGYjyAwAAAAAAAAAMBtBZgAAAAAAAACA2QgyAwAAAAAAAADMRpAZAAAAAAAAAGA2gswAAAAAAAAAALMRZAYAAAAAAAAAmI0gMwAAAAAAAADAbASZAQAAAAAAAABmI8gMAAAAAAAAADAbQWYAAAAAAAAAgNkIMgMAAAAAAAAAzEaQGQAAAAAAAABgNoLMAAAAAAAAAACzEWQGAAAAAAAAAJiNIDMAAAAAAAAAwGwEmQEAAAAAAAAAZiPIDAAAAAAAAAAQc/1/axWT1bwborEAAAAASUVORK5CYII=", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "Solve a sensitive system and inspect both errors" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Condition number:** 10000.0\n", "- **Relative input perturbation:** 1e-08\n", "- **Relative solution change:** 0.0001\n", "- **Perturbed solve residual:** 0.0" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "A=diag(1,1/κ), b=(1,0), δb=(0,10⁻⁸). The actual solve amplifies this chosen perturbation by κ=10000; its small residual does not undo sensitivity to input changes." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(7,1,10000)\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='Solve a sensitive system and inspect both errors'))\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": "ch07-cell04", "metadata": {}, "source": [ "**Use the idea:** Use rule 7.1.1 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 solve of a constructed diagonal matrix. Worst-case amplification depends on perturbation direction.\n", "\n", "
Does a small residual guarantee accuracy relative to unperturbed inputs?\n", "\n", "No. It checks the equation actually solved. Conditioning determines how much altered inputs can change its solution.\n", "\n", "
\n", "\n", "**Book source:** [Rule 7.1.1: Estimate digits lost from the condition number](source.html)." ] }, { "cell_type": "markdown", "id": "ch07-cell05", "metadata": {}, "source": [ "## C07-D02: Fit data and read the residual pattern\n", "\n", "Can a better solver fix a model that omitted the intercept?\n", "\n", "Compare the same constructed data with and without an intercept. The residual panel reveals model structure left unexplained.\n", "\n", "$$\n", "\\min_\\beta\\|A\\beta-b\\|_2,\\quad b_i=2+3x_i+0.1\\sin(9x_i)\n", "$$\n", "\n", "**Symbols and inputs:** Intercept in model. 101 points on [0,1], stable NumPy least squares. Data are deterministic teaching values, not a sample for statistical inference.\n", "\n", "**Predict:** Can a better solver fix a model that omitted the intercept?" ] }, { "cell_type": "code", "execution_count": 3, "id": "ch07-cell06", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:57:36.748688Z", "iopub.status.busy": "2026-10-03T00:57:36.748597Z", "iopub.status.idle": "2026-10-03T00:57:36.884453Z", "shell.execute_reply": "2026-10-03T00:57:36.884381Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "Fit data and read the residual pattern" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Fitted intercept:** 2.0205226079378424\n", "- **Fitted slope:** 3.001383505941882\n", "- **Residual RMS:** 0.06866349413901184" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "The data are 2+3x+.1 sin(9x), not measurements. With an intercept the line recovers 2+3x, and the leftover wiggle of RMS size about .07 is the sin term no straight line can capture." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(7,2,'include')\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='Fit data and read the residual pattern'))\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": "ch07-cell07", "metadata": {}, "source": [ "**Use the idea:** Use rule 7.2.6 when its stated conditions fit. Compare the calculation with your own decision threshold; retain the relevant error or uncertainty.\n", "\n", "**Assumptions and limits:** 101 points on [0,1], stable NumPy least squares. Data are deterministic teaching values, not a sample for statistical inference.\n", "\n", "
Can a better solver fix a model that omitted the intercept?\n", "\n", "No. Solver stability and model adequacy are different issues; the omitted intercept changes the fitting problem.\n", "\n", "
\n", "\n", "**Book source:** [Rule 7.2.6: Prefer orthogonal transformations for numerical stability](source.html)." ] }, { "cell_type": "markdown", "id": "ch07-cell08", "metadata": {}, "source": [ "## C07-D03: Reconstruct a matrix at different ranks\n", "\n", "What spectral error remains at rank two?\n", "\n", "Compute an SVD and reconstruct the truncated matrix. Compare its actual spectral error with the next singular value.\n", "\n", "$$\n", "\\|A-A_k\\|_2=\\sigma_{k+1}\n", "$$\n", "\n", "**Symbols and inputs:** Retained rank k. Constructed diagonal matrix with singular values 10,3,1,.1; best approximation in the spectral norm.\n", "\n", "**Predict:** What spectral error remains at rank two?" ] }, { "cell_type": "code", "execution_count": 4, "id": "ch07-cell09", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:57:36.885735Z", "iopub.status.busy": "2026-10-03T00:57:36.885663Z", "iopub.status.idle": "2026-10-03T00:57:36.982596Z", "shell.execute_reply": "2026-10-03T00:57:36.982511Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "Reconstruct a matrix at different ranks" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Retained rank:** 2\n", "- **Actual spectral error:** 1.0\n", "- **Next singular value:** 1.0" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "Keeping rank 2 gives spectral error 1, equal to the next singular value in this actual SVD reconstruction. Compression is justified by an error budget, not rank alone." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(7,3,2)\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='Reconstruct a matrix at different ranks'))\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": "ch07-cell10", "metadata": {}, "source": [ "**Use the idea:** Use rule 7.3.5 when its stated conditions fit. Compare the calculation with your own decision threshold; retain the relevant error or uncertainty.\n", "\n", "**Assumptions and limits:** Constructed diagonal matrix with singular values 10,3,1,.1; best approximation in the spectral norm.\n", "\n", "
What spectral error remains at rank two?\n", "\n", "The next singular value is 1, which equals the spectral norm of the omitted part.\n", "\n", "
\n", "\n", "**Book source:** [Rule 7.3.5: Use the next singular value to price a low-rank approximation](source.html)." ] }, { "cell_type": "markdown", "id": "ch07-cell11", "metadata": {}, "source": [ "## C07-D04: Watch the eigenvalue ratio set the speed of power iteration\n", "\n", "How many steps does ratio 0.9 need to reach 10⁻⁶?\n", "\n", "Power iteration multiplies a vector by the matrix again and again. The top eigenvector wins, but only as fast as the runner-up eigenvalue fades. A ratio near one means a near tie and a long wait.\n", "\n", "$$\n", "\\text{error}_k\\approx C\\,|\\lambda_2/\\lambda_1|^k\n", "$$\n", "\n", "**Symbols and inputs:** Ratio |λ₂/λ₁|. Constructed matrix diag(1,ratio,0.3), start (1,1,1)/√3, 60 normalized steps, target error 10⁻⁶.\n", "\n", "**Predict:** How many steps does ratio 0.9 need to reach 10⁻⁶?" ] }, { "cell_type": "code", "execution_count": 5, "id": "ch07-cell12", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:57:36.983778Z", "iopub.status.busy": "2026-10-03T00:57:36.983702Z", "iopub.status.idle": "2026-10-03T00:57:37.102663Z", "shell.execute_reply": "2026-10-03T00:57:37.102597Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "Watch the eigenvalue ratio set the speed of power iteration" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Eigenvalue ratio |λ₂/λ₁|:** 0.9\n", "- **Error after 60 steps:** 0.0017970081237983393\n", "- **Steps to reach 10⁻⁶:** More than 60" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "Matrix diag(1,0.9,0.3), start (1,1,1)/√3. Each step multiplies the error by about 0.9. After 60 steps the error is still 0.0018. A ratio this close to one needs about 132 steps, so use a shift or a different method." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(7,4,0.9)\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='Watch the eigenvalue ratio set the speed of power iteration'))\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": "ch07-cell13", "metadata": {}, "source": [ "**Use the idea:** Use rule 7.3.2 when its stated conditions fit. Compare the calculation with your own decision threshold; retain the relevant error or uncertainty.\n", "\n", "**Assumptions and limits:** Constructed matrix diag(1,ratio,0.3), start (1,1,1)/√3, 60 normalized steps, target error 10⁻⁶.\n", "\n", "
How many steps does ratio 0.9 need to reach 10⁻⁶?\n", "\n", "About 132. Each step only removes 10% of the error, so 60 steps leave it near 0.0018.\n", "\n", "
\n", "\n", "**Book source:** [Rule 7.3.2: Power iteration speed is set by the eigenvalue ratio](source.html)." ] }, { "cell_type": "markdown", "id": "ch07-cell14", "metadata": {}, "source": [ "## C07-D05: See the normal equations square the condition number\n", "\n", "With κ=10⁶, about how many correct digits can the normal equations keep?\n", "\n", "Solve the same exact least-squares problem two ways. QR works with A itself; the normal equations form AᵀA first, which squares the condition number and doubles the digits lost.\n", "\n", "$$\n", "\\kappa(A^{\\mathsf T}A)=\\kappa(A)^2\n", "$$\n", "\n", "**Symbols and inputs:** Condition number κ of A. Constructed 50×2 matrix with chosen κ, seed 705, exact fit with true answer (1,1); binary64 arithmetic.\n", "\n", "**Predict:** With κ=10⁶, about how many correct digits can the normal equations keep?" ] }, { "cell_type": "code", "execution_count": 6, "id": "ch07-cell15", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:57:37.103883Z", "iopub.status.busy": "2026-10-03T00:57:37.103809Z", "iopub.status.idle": "2026-10-03T00:57:37.318053Z", "shell.execute_reply": "2026-10-03T00:57:37.317980Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "See the normal equations square the condition number" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Condition number of A:** 10000.0\n", "- **Condition number of AᵀA:** 100000000.0\n", "- **QR relative error:** 1.0150195407824842e-13\n", "- **Normal-equations relative error:** 1.940666539514091e-09" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "A is a constructed 50×2 matrix with κ=10000 and an exact fit, so the true answer is (1,1). QR works with A directly and loses about log10 κ=4 digits; its error is 1e-13. The normal equations solve with AᵀA, whose condition number is κ²=1e+08. Their error is 1.9e-09, about 1.9e+04 times worse. Squaring κ doubles the digits lost." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(7,5,10000)\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='See the normal equations square the condition number'))\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": "ch07-cell16", "metadata": {}, "source": [ "**Use the idea:** Use rule 7.2.4 when its stated conditions fit. Compare the calculation with your own decision threshold; retain the relevant error or uncertainty.\n", "\n", "**Assumptions and limits:** Constructed 50×2 matrix with chosen κ, seed 705, exact fit with true answer (1,1); binary64 arithmetic.\n", "\n", "
With κ=10⁶, about how many correct digits can the normal equations keep?\n", "\n", "About 4. κ²=10¹² eats 12 of the roughly 16 digits, while QR still keeps about 10.\n", "\n", "
\n", "\n", "**Book source:** [Rule 7.2.4: Prefer QR to normal equations for accurate least squares](source.html)." ] }, { "cell_type": "markdown", "id": "ch07-cell17", "metadata": {}, "source": [ "## Continue with the chapter workbook\n", "\n", "The original decision worksheet, additional calculation, exercises and solutions follow." ] }, { "cell_type": "markdown", "id": "ch07-cell18", "metadata": {}, "source": [ "# Chapter 7 notebook: Linear Algebra: Choose Stable Matrix Methods Before Computing\n", "\n", "**Goal:** Choose a matrix method from verified structure and report what its residual actually certifies.\n", "\n", "**Start with:** Rules 7.1.1, 7.2.4, 7.3.4. 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 7](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: Matrix dimensions and structure; right-hand side; scale and conditioning; precision; memory limit; requested residual and forward accuracy.\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", "- **Start with sensitivity.** Estimate conditioning and the digit budget before setting solver tolerances.\n", "- **Verify claimed structure.** Check relative symmetry, positive definiteness, sparsity pattern, block meaning, and scale before choosing a specialized factorization.\n", "- **Choose the direct method by matrix type.** Use Cholesky for verified SPD systems, pivoted LU for general dense systems, and QR or SVD for least squares according to conditioning and rank.\n", "- **Avoid unnecessary objects.** Solve for inverse actions, apply Schur complements through block solves, and keep orthogonal factors implicit when possible.\n", "- **Budget memory as well as flops.** Consider matrix-free actions, cache blocking, and fill-reducing ordering before the matrix outgrows the machine.\n", "- **Verify outputs.** Scale residuals, inspect orthogonality where relevant, and refine a solve only while backward error continues to improve.\n", "- **For spectra and compression, inspect cheap evidence first.** Use Gershgorin, eigenvalue ratios, storage counts, and singular-value tails before escalating to shift-invert or large decompositions.\n", "- **For Krylov methods, separate problem difficulty from solver design.** Check SPD requirements, conditioning, clustering, preconditioner cost, restart behavior, and true residuals.\n", "\n", "**Chapter-specific stop check:** Residual and forward error are different quantities. A low-rank storage win, symmetry claim, or converged iteration must pass its own accuracy or structural check.\n", "\n", "## 3. Work the lab\n", "\n", "A calculation starts with 12 reliable decimal digits and has a condition estimate of 10^5. A first-pass budget is 12-log10(10^5)=7 digits. Separately, storing a 1,000 by 800 matrix uses 800,000 scalar entries; rank-20 factors use 20 × (1000+800)=36,000, or 4.5% of that storage, excluding overhead. Storage savings do not certify approximation accuracy; inspect the singular-value tail.\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": "ch07-cell19", "metadata": { "execution": { "iopub.execute_input": "2026-10-03T00:57:37.319289Z", "iopub.status.busy": "2026-10-03T00:57:37.319223Z", "iopub.status.idle": "2026-10-03T00:57:37.321558Z", "shell.execute_reply": "2026-10-03T00:57:37.321495Z" }, "jupyter": { "source_hidden": true }, "tags": [ "practice-lab", "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Rough remaining digits: 7.0\n", "Dense entries: 800,000; factors: 36,000\n", "Storage fraction: 4.500%\n" ] } ], "source": [ "import math\n", "digits, condition = 12, 1e5\n", "rows, columns, rank = 1000, 800, 20\n", "assert condition >= 1 and 0 < rank <= min(rows, columns)\n", "dense_entries = rows*columns\n", "factor_entries = rank*(rows+columns)\n", "print(f\"Rough remaining digits: {digits-math.log10(condition):.1f}\")\n", "print(f\"Dense entries: {dense_entries:,}; factors: {factor_entries:,}\")\n", "print(f\"Storage fraction: {factor_entries/dense_entries:.3%}\")" ] }, { "cell_type": "markdown", "id": "ch07-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", "A full-rank least-squares matrix has condition number 10^4. What happens to conditioning in its normal equations?\n", "\n", "**My approach, assumptions, calculation, and check:**\n", "\n", "_Write your attempt here._\n", "\n", "### Exercise 2\n", "\n", "A symmetric matrix is claimed suitable for Cholesky. Is symmetry alone enough?\n", "\n", "**My approach, assumptions, calculation, and check:**\n", "\n", "_Write your attempt here._\n", "\n", "### Exercise 3\n", "\n", "A solver has a tiny residual. Can it promise a tiny forward error for an ill-conditioned system?\n", "\n", "**My approach, assumptions, calculation, and check:**\n", "\n", "_Write your attempt here._\n", "\n", "**Coaching prompt:** “Use the Chapter 7 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", "In the 2-norm, kappa(A^T A)=kappa(A)^2=10^8. QR avoids forming that squared-conditioning system; rank uncertainty may motivate SVD.\n", "\n", "### Answer 2\n", "\n", "No. Positive definiteness is also required. For example diag(1,-1) is symmetric and indefinite.\n", "\n", "### Answer 3\n", "\n", "No. Residual measures an equation defect; forward error also depends on conditioning and scaling. Report a scaled residual and a sensitivity estimate, or bound the quantity of interest.\n", "\n", "## 6. Build the complete chapter toolkit\n", "\n", "The new lab samples the chapter; the following checklist covers all 23 rules. Study one thematic group at a time. A large group can take several sessions.\n", "\n", "- **Diagnose Accuracy and Structure Up Front:** work with rules 7.1.1, 7.1.2, 7.1.3, 7.1.4, 7.1.5.\n", "- **Match the Algorithm to Matrix Structure:** work with rules 7.2.1, 7.2.2, 7.2.3, 7.2.4, 7.2.5, 7.2.6, 7.2.7, 7.2.8, 7.2.9.\n", "- **Estimate Spectra, Compression, and Iterative Difficulty:** work with rules 7.3.1, 7.3.2, 7.3.3, 7.3.4, 7.3.5, 7.3.6, 7.3.7, 7.3.8, 7.3.9.\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", "| 7.1.1: Estimate digits lost from the condition number | Independent | compatible matrix structure; scale aware tolerance | new |\n", "| 7.1.2: Check matrix symmetry relative to scale | Workflow | compatible matrix structure; scale aware tolerance | new |\n", "| 7.1.3: Certify an eigenpair with its residual | Workflow | compatible matrix structure; scale aware tolerance | new |\n", "| 7.1.4: Equilibrate rows and columns with wildly different scales | Workflow | large row or column scale disparity; recoverable scaling factors | new |\n", "| 7.1.5: Use iterative refinement to recover linear-solve accuracy | Workflow | compatible matrix structure; scale aware tolerance | new |\n", "| 7.2.1: Solve systems instead of forming an explicit inverse | Workflow | compatible matrix structure; scale aware tolerance | new |\n", "| 7.2.2: Use partial pivoting for general dense LU | Workflow | compatible matrix structure; scale aware tolerance | new |\n", "| 7.2.3: Treat Schur complements as first-class operators | Workflow | compatible matrix structure; scale aware tolerance | new |\n", "| 7.2.4: Prefer QR to normal equations for accurate least squares | Workflow | compatible matrix structure; scale aware tolerance | new |\n", "| 7.2.5: Use Cholesky for symmetric positive-definite systems | Workflow | compatible matrix structure; scale aware tolerance | new |\n", "| 7.2.6: Prefer orthogonal transformations for numerical stability | Workflow | compatible matrix structure; scale aware tolerance | new |\n", "| 7.2.7: Go matrix-free when storage dominates arithmetic | Workflow | compatible matrix structure; scale aware tolerance | new |\n", "| 7.2.8: Use blocked matrix algorithms to exploit fast BLAS-3 kernels | Workflow | large dense matrices; level three blas available | new |\n", "| 7.2.9: Reorder sparse factorizations to control fill | Workflow | compatible matrix structure; scale aware tolerance | new |\n", "| 7.3.1: Use Gershgorin disks as a cheap eigenvalue screen | Independent | square matrix; matrix entries known | new |\n", "| 7.3.2: Power iteration speed is set by the eigenvalue ratio | Independent | compatible matrix structure; scale aware tolerance | new |\n", "| 7.3.3: Use shift-invert for interior or smallest eigenvalues | Specialized | compatible matrix structure; scale aware tolerance | new |\n", "| 7.3.4: Check low-rank storage before compressing a matrix | Independent | compatible matrix structure; scale aware tolerance | new |\n", "| 7.3.5: Use the next singular value to price a low-rank approximation | Independent | compatible matrix structure; scale aware tolerance | new |\n", "| 7.3.6: Define numerical rank relative to the largest singular value | Workflow | compatible matrix structure; scale aware tolerance | new |\n", "| 7.3.7: Expect conjugate-gradient work to scale with square-root conditioning | Independent | compatible matrix structure; scale aware tolerance | new |\n", "| 7.3.8: Judge a preconditioner by clustered eigenvalues and total time | Workflow | compatible iterative solver; affordable preconditioner application | new |\n", "| 7.3.9: Increase GMRES restart when convergence stalls | Specialized | compatible matrix structure; scale aware tolerance | 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 19: optimization; Chapter 20: numerical methods; Chapter 21: scientific computing. 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": 7, "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": "34a79479314a9e68ea8df753851d4f5ec42f18fefb26d88a86fd53fe5fdd1473", "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 }