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<h1>Chapter 6: Exercise 9</h1>
<p>Load the Boston dataset</p>
<pre><code class="r">set.seed(1)
library(MASS)
attach(Boston)
</code></pre>
<h3>a</h3>
<pre><code class="r">lm.fit = lm(nox ~ poly(dis, 3), data = Boston)
summary(lm.fit)
</code></pre>
<pre><code>##
## Call:
## lm(formula = nox ~ poly(dis, 3), data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.12113 -0.04062 -0.00974 0.02338 0.19490
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.55470 0.00276 201.02 < 2e-16 ***
## poly(dis, 3)1 -2.00310 0.06207 -32.27 < 2e-16 ***
## poly(dis, 3)2 0.85633 0.06207 13.80 < 2e-16 ***
## poly(dis, 3)3 -0.31805 0.06207 -5.12 4.3e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0621 on 502 degrees of freedom
## Multiple R-squared: 0.715, Adjusted R-squared: 0.713
## F-statistic: 419 on 3 and 502 DF, p-value: <2e-16
</code></pre>
<pre><code class="r">dislim = range(dis)
dis.grid = seq(from = dislim[1], to = dislim[2], by = 0.1)
lm.pred = predict(lm.fit, list(dis = dis.grid))
plot(nox ~ dis, data = Boston, col = "darkgrey")
lines(dis.grid, lm.pred, col = "red", lwd = 2)
</code></pre>
<p><img 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" alt="plot of chunk 9a"/> </p>
<p>Summary shows that all polynomial terms are significant while predicting nox using dis. Plot shows a smooth curve fitting the data fairly well.</p>
<h3>b</h3>
<p>We plot polynomials of degrees 1 to 10 and save train RSS.</p>
<pre><code class="r">all.rss = rep(NA, 10)
for (i in 1:10) {
lm.fit = lm(nox ~ poly(dis, i), data = Boston)
all.rss[i] = sum(lm.fit$residuals^2)
}
all.rss
</code></pre>
<pre><code>## [1] 2.769 2.035 1.934 1.933 1.915 1.878 1.849 1.836 1.833 1.832
</code></pre>
<p>As expected, train RSS monotonically decreases with degree of polynomial. </p>
<h3>c</h3>
<p>We use a 10-fold cross validation to pick the best polynomial degree.</p>
<pre><code class="r">library(boot)
all.deltas = rep(NA, 10)
for (i in 1:10) {
glm.fit = glm(nox ~ poly(dis, i), data = Boston)
all.deltas[i] = cv.glm(Boston, glm.fit, K = 10)$delta[2]
}
plot(1:10, all.deltas, xlab = "Degree", ylab = "CV error", type = "l", pch = 20,
lwd = 2)
</code></pre>
<p><img 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" alt="plot of chunk 9c"/> </p>
<p>A 10-fold CV shows that the CV error reduces as we increase degree from 1 to 3, stay almost constant till degree 5, and the starts increasing for higher degrees. We pick 4 as the best polynomial degree.</p>
<h3>d</h3>
<p>We see that dis has limits of about 1 and 13 respectively. We split this range in roughly equal 4 intervals and establish knots at \( [4, 7, 11] \). Note: bs function in R expects either df or knots argument. If both are specified, knots are ignored.</p>
<pre><code class="r">library(splines)
sp.fit = lm(nox ~ bs(dis, df = 4, knots = c(4, 7, 11)), data = Boston)
summary(sp.fit)
</code></pre>
<pre><code>##
## Call:
## lm(formula = nox ~ bs(dis, df = 4, knots = c(4, 7, 11)), data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.1246 -0.0403 -0.0087 0.0247 0.1929
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.7393 0.0133 55.54 < 2e-16
## bs(dis, df = 4, knots = c(4, 7, 11))1 -0.0886 0.0250 -3.54 0.00044
## bs(dis, df = 4, knots = c(4, 7, 11))2 -0.3134 0.0168 -18.66 < 2e-16
## bs(dis, df = 4, knots = c(4, 7, 11))3 -0.2662 0.0315 -8.46 3.0e-16
## bs(dis, df = 4, knots = c(4, 7, 11))4 -0.3980 0.0465 -8.56 < 2e-16
## bs(dis, df = 4, knots = c(4, 7, 11))5 -0.2568 0.0900 -2.85 0.00451
## bs(dis, df = 4, knots = c(4, 7, 11))6 -0.3293 0.0633 -5.20 2.9e-07
##
## (Intercept) ***
## bs(dis, df = 4, knots = c(4, 7, 11))1 ***
## bs(dis, df = 4, knots = c(4, 7, 11))2 ***
## bs(dis, df = 4, knots = c(4, 7, 11))3 ***
## bs(dis, df = 4, knots = c(4, 7, 11))4 ***
## bs(dis, df = 4, knots = c(4, 7, 11))5 **
## bs(dis, df = 4, knots = c(4, 7, 11))6 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0619 on 499 degrees of freedom
## Multiple R-squared: 0.718, Adjusted R-squared: 0.715
## F-statistic: 212 on 6 and 499 DF, p-value: <2e-16
</code></pre>
<pre><code class="r">sp.pred = predict(sp.fit, list(dis = dis.grid))
plot(nox ~ dis, data = Boston, col = "darkgrey")
lines(dis.grid, sp.pred, col = "red", lwd = 2)
</code></pre>
<p><img 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3u+uz8vEZFNyEWkE7If39gVa4i+G1ja+55GmiRb132uubn5v4CdisXiLcVi8VJ3v87djwcOAJqXLFnyvLsPM7NGYGczm2Vml5hZJcY4c93kDhBCmApcbWY3mVnn4MGDd3P3Ye7+nJn9E/izuz/j7hWgEmOcnSTJ0WY2AHgEeNbM3gVMc/etSX+YbGdmD5bL5Xe6+yshhGNrPzi0BFBEpI/SEH33+R1wNzDVoWBQARg/fnwF+FKpVBqYJMkWEydOfK72+isuu+yyoUmSDE6SJLNs2bIXhg4dOtLMNnf35UmSPJvP56uvrsTM9nT3583sr+6+zcqVK7c3szVmNrCW4AcCFTNrd/eOEMKeMcZH3b0KrAAWkA7b/93Mqu4+JISQcferpkyZ8mCpVOqIMe4ALAXesRE+NxER6QG9KcE7cCbwn9SSY19i4J7OqP8dMBmYse7ztfvZz617bcqUKStIk+5az9Yeb2RRkiQdMcatgB0HDhz4fGdn5wBgubs3kd4eyJAOvePuT8cYn0+SJLg7ZrZrY2Pjws7Ozv1ijAF4pTa0P27mzJnDgYbaD4jNgAfe6uchIiL11duG6LuAa4Ex9Q7kLZoP/AU43dP78d3OzH7m7pPM7HPA8o6Ojt8BZXcfaWb7m1kW2Io0wTe6+95mdoq7G7BvjHFge3v78THG80MIXcD+Mcb7gY9ns9knapP8fkh62+EnPdEGERHpeb0twZ8FfIN06dl/kU4E6zNqG918G9gF+EJP1JHL5e6OMX4euM3MRgLDgSdI76+/DIyrbZTzNzN7JITQDGwOXGFmd5rZTsDpwJ+6urr2An5oZkOBFe7eAAx195fd/YO5XO6OnmiDiIhsWpx06Rikvc/TgGeAO0gT0tt1LlDohnLWy+Emh4X+GkvcRERkk3IRaadvo+ttPfi1ukjvZ+9MOjt99/qG86Z9l3RJ3hfrHYiIiGyaetMku9dSBa6vPXq9K664YkhHR8eHCzGOPOL44+9uWLPme1efe+4rHdts81K5XB6SzWZvXTuLvlQq7VytVrcDMLOFLS0t/1ojWSqVRler1SHlcvnRo48+evWr67n88ss36+joGA0sam1tXd+kPBER2QRpo5tuUiqVjnL335DeXrDhTzwx8KOnnWYPtrTEh484wkiXnQ0ALgU2c/fRZrZjuokdTwPPxhi/lCTJb9y9amaLgH3dfWpLS8t1a+spFApHhxCOd/d7zGxXd39uwYIFX5w2bVrsiXaJiMjboo1u+rLLL798M+A8M/uLmU0GHl02atS9L+69d9ztqqts2OOPf9DMOs3sM2Z2DPByCAEzGxVC2NHMKsBtmUzmCncvtbS0TMrn81/p7Oz8iJn9oFQqDQaYM2fOqBDC0cAH8vn813K53CHAU2PGjOmRCX0iItJ39YUEfzCvcwzr67z2gtd5fBgY1v3hQblc3sfdO929saOj40ZgSIzxm39vafGGlSvt3eefP8ndl5L2yNcA27j7dblcrr12CM3lwPPuPiaE8K+97GvD8zcC7wSoVqvvBUq5XO5fG+DEGC8GxvdEu0REpO/q7ffgAW5hw28l/J30jPbXMoR0iLwnLDczc3ffaqutWL58uQHbvDxqlC8eN+7l5r///bMNq1Yt6hw0aFntMJdXSJe3rbU56TK3yoABA5qAles+F2N8ZW097r7tuhW7+3AzW95D7RIRkT6qL/Tg34ylwF9f57GI9Pz2brds2bIHYoxd7r7lsmXLCu7+dAjht+5evf/oo4cYDNn1mmt2BPK1rWE/GEI4tK2t7bRisfhNYIqZfdHdCx0dHb8olUoDAUql0geBPUIIDwM0NjbeAkycNWvWWICZM2cOz2QyZ4cQLu2JdomISN/VmybZDQdOASaQToZLSLd2nQ/8gP+9petb0aOT7IrF4hfN7KwYY5OZJbXLDth7zzmHrR58kKt/+Uu6Bg2itmXsv97r7h1mFoH57v57M/sS6Xa9j2Wz2W9NmDBh8drXzpkzZ1S1Wj3bzEbULv0ol8td2xNtEhGRt61uk+x60xD9DOAp4HDSWeUGbAccW3vuiLpFth7z5s1rLpfLrcuWLdtis802W2BmlwJPxhh/bmarHsrlttv27rvDnnPnvnD/0UdvGUJY6u7NtcR+v5kNGzx48EdXr179txhjW0tLy4GvV9dRRx31BOm58yIiIq+rNw3Rvx84GfgH0A6sAR4l3fp13zrGtV7lcnk/M/v9yJEjG4FBlUrlgmq1envthLeXlm+3HQv32WfNqBtuGNGwcmWsTbgjhLACWAIsXrVq1S7ufkcI4fC6NkZERPqF3pTg7wR+Rrpr3UCgEdiVdGjj/jrGtV4xxpdijCM6OzvXmBkhhBExxuDuEciYGQsmTlyedHZmRl97bVI7EAbA1r4mSZKXzKwZWFi/loiISH/RmxL8Z0h77fNJe7UvAdeQnso2pY5xrdfIkSP/amb7uvt4d7/dzH6XyWTOJ/1hspu7+yujRw9eeMAB1d1+//tMsmrVjmZWcfdmM3s36da8h8QYx8YYf13f1oiISH/QmxL8MuBU0h78YGAQaQ/+ZKBXLwMbP358xcxagInu3kw6+vAeMxsbY1wBdLr7oAdbWpLsmjWMueqqgaSTCDvMbHNgv2q1eryZHdra2qoevIiIyJuw0U6TeyMOsxxWOoxY/6tFRKSP02lym5CppHMMvl7vQEREpP9Sgt/IDB4DisCJ6sWLiEhP6U3r4Pu9QqGwfwhh1P1z55beWSzmgJNmzZr18yRJjgsh7FepVJaZ2UNm1uTuW5jZCzHGP7W0tNxqZhu6H7+IiIgS/Mbg7lYsFn9b26/+3kcnTDhguwceeGqLRx89sWn16uM7hgxpjDESQmggHVWpmFm7mVVDCEuKxeKT8+fPn3DYYYetqXdbRESkb9AQ/UZQLBaPMrMX8vn8v+fz+fPy+fyUByZO/DMxNu3xu99lQggPAIe5+99qp811kS6x+w7wpJk92d7efnJdGyEiIn2KEvzGsb+7z1/3wtJx46557r3v7Rh9/fWDBi5Z0mFmO5rZkyGE1e7ebmblcrn8B3dfu2n9u+sQt4iI9FFK8BtBCOHFEMKO616LMQ77+1FHrQmVio2dN283M1tkZgPcPQtk3X1QCGGkmXWaWSfa4U5ERN4E3YPfOGa5+1XFYvGFNWvW3N3U1PR+M/vcqm23vf6Z971vwo633Tby4UMP/eKqrbc+GBhYS+qrkyS5KMbYYGZbxxiPq3cjRESk71CCfxtKpdJk4KQY4xgzawDczJa5+3Qzu8/dDwXc3UtmNsHdv9nU1PRt4OFqtXp4kiSLnvrwh8/a/s47Txp93XWfuP+zny0DL7s7wP7AKuD2GOOPW1tb/1a3hoqISJ/Tm86D72ndeh58sVj8kZl9wt13BAaZWdXdV5pZg7s3Acvc/QPu3mVm/xlCeDCXy/3itcpy+C3QCow2eL474hMRkV5B58H3VqVSaXPg58A+AO7+e3dvM7ODYoxrz3a/g/RLPAXYzt0HAPea2biWlpa5U6dOPW7PPfe8A3jNBE/65X8G+AbwzR5vlIiI9HuaZPcGZs6cOdzd/wnsFWPscvfFwJfc/QJ3z4QQqu4+BOiKMf4D8BhjV+0e+gBgB4Bp06ZFYFWpVBr4WvXUdrebBXzRoXnjtE5ERPozJfg3EEI4E7gL6Fq+fPm78/n8h4ArM5nMM8BeQMbdXzGzZjPLm5mHEAYDTTHGbIzxPoBZs2ZtaWaDcrlc+xtUdzrp0bjf7uFmiYjIJkAJ/g0kSTIWuMvdXzj++OPLACGE69x9V+AZYKWZ7RhjfJ+ZTXP39wKbA+0hhN3NbM9CoXBCkiRXVqvV77xRXQZPA5eR9uK36eGmiYhIP6cE/waq1epDZvZ+M9uuVCo1AMQYP1Ubtl8GfCSEcGoI4Up3vyfG+NcY42/N7MPZbHZcCOGlEMJLZnZYa2vrLRtQ5Rmk58TrPryIiLwtmkX/Bkql0jB3f8zdXzCzAKwys7Hu/oC7f7+lpeW67g7S4X+AycAups1tRET6urrNolcP/g3kcrnlZjbKzG5390rtlLcZ1Wr1+BDCLYVCYa9SqbRDN1d7BunqBvXiRUTkLVMPfgOUSqURQCnG+KyZrQEOSg+G81uBLc1sCJDL5XKruiNQh0uBI4GdDZZ0R5kiIlIX6sH3ZjHGn7v7f7a0tBzd3Nz8FdLT3lbn8/kv5/P5PHC+u/+kG6v8AdAI/Ec3likiIpsQbXSzAUII2+dyuTsBlixZMgb4Y4yxua2tbZvW1taFuVxufqlUOrW76jN41OES4KsOv9jYu9vdfPPNmUWLFn3IzIZkMpl7qtXqNqRr+hd0dXU93dDQcLC7BzO7LZfLvbwxYxMRkQ2jHvyblCTJCmBoCGFQtVpdBWlCdPdyN1f1fdLv55RuLvcNlUqlEYsXL77BzA4Cti2Xy3e5+xnuPtzdz8pmsw+7+x7ALu4+v1gsvm9jxiciIhtGCX4DuPv1xWJxaqlUSiZMmPCMu+8NDJwyZcqKUqnUsHjx4p8Bhe6ss7YufgZwnMN23Vn2G3H3HwCn5/P57wKrkiQ5B0gqlUqRdGOfm2OMf8rn8z+rVqtHAN15a0JERLqJEvwGaG5u/rGZVdz9ptmzZ9+UJMndMcZni8XiTe5+PfB4Lpe7oAeq/gHpd9Rtw/8bYEwul7u99u/9y+Xy1cBtjY2N7zSzTAihFEJ4N8DkyZOXmtkrpVJp2EaMT0RENoDuwW+A8ePHV0iXr53xeq9J59p1L4NnHC4GvuBwpsFz3V7Jq+s0W3H55ZePABYDL2YymZ3cfedyufy8mTW6+2jgBQB3t9mzZ4946KGHVvZ0XCIi8uaoB9/7nUn6PW2sdfHnlsvlGXPmzNm1Wq0WY4znufu27e3tz5jZA8ApIYQ/zps3b4tSqfQz4JraYToiItKLaB18HV1wwQXZ4cOHf97dPwC0Aw8CH3D3sUCXmQUzazrgF78Ytt1ddw295rzznunYcsutPPWkmR3f3Nx815IlS4519/Hu3mFmM/L5/M1vJ662traDzOwLIYThZvZQjHEzYEd3fzCTyTxWqVT+zcyCu1+Rz+cvNTPvho9DRKQ/qts6eCX4OioWi78BnjGzi9y9FTjN3VeY2TnUZtGb2ZNNixc3f+Ib39j2iYMP9vu+8IX57j7W3RtDCJu7+3zgkUwmc4G7D4sxng1cmMvl5tezbSIiAtQxwesefJ3Mmzdvi3K5vG0+nz8OoFgsHh5jvDyE8A5gHPAoUAFWrh4x4pGnPvCBI0bdfHNjdtWqaXd/4xu7AO9x90PM7KO5XK61VuwLM2bMaBkwYMB8QAleRGQTpnvwddLV1bWduz+x9m8zCyGELdzdge3MLNZOrUvMbOCCSZNWuZmPePTR06rV6uNm1kR68lyybrlHH330aqBhozZGRER6HSX4Omlvb3/EzA644IILsrVLy0lPqzPg3tpOcQe4e5O7V9cMHz7wyfHjY9NLLx2+9WOPtdQ21mlw9+o111wzYG25c+bM2cPMXqpHm0REpPfQPfg6KpVKk4FjgTZgd+AEd19iZo/GGD9QO6L2n8BWZja4cdmycMhXv5p99v3v77zruOMqZrbS3U81s39391lmNgzIu3trS0vLRr/fIyIi/4cOm9kU5XK5WdVq9fNAl7v/ccCAAbu5+ynAvWY21cxOcfebgLOr1Wpr+2ab/eD5ffZ5eodbb81u8cgjP21ubt6+paVlRiaTOcbMOszsicbGxg8ruYuIyPqMe41r79/oUXSPc+nm7WTrwWGkw2qHC+sdi4iIrNdFwC71qHh9PfjLgRNJh/IbgbNId1aTOjF4EfgN8FmHUfWOR0REeqf1Jfj9gH2Ba4G/AEOAd/Z0ULJeZwJl4Dv1DkRERHqn9SX4lcBDpMMLg4GbgFU9HZS8sVov/nzSXvxu9Y5HRER6n/VtdHMb8ARpL34w6fD8BKD1Dd7TL7W1te1kZuOBnWKM92UymRtyudyqQqHwHjM7hHSJ2xW5XO4RgDlz5uxaqVTeGUJ46aGHHrqlB/Zr/5ac+fwAACAASURBVDFwHPBt4JhuLltERPq49S2TywGldf4OwNeBc3osop7zlpfJFYvFL5Im0S1qS9j2rK01fxkYY2YPuvsQd98uSZLpMcYuYD93v9HMtgXeVy6XD5syZcqK7myQw9nAN4CxBo90Z9kiItIteu1WtaVX/R3pm8n9LattKftpd7cBAwbsd+SRR77S1tZ2MOnRsfua2ZdzuVwbQLFY/GmM8UgzWz5p0qSD1x7CUiqVjspms6fS/ffMfwZ8GTgF+Fw3ly0iIn3Y+u7Bb046LL8YWApcAgzv4Zh6lUqlshdwl5k9c+SRR74C0NLSciuwg5klgwYNunadl1/t7lXg6XVPWGtsbLyG9DZHt6rdiz+P9F78mO4uX0RE+q71JfhfAF2k6+H3JJ25fW5PB9WbhBAWAiOBrdZemz179lYhhFeAuGbNmh3XXjezUWbWFWMcuG4Zq1at2hl4vodCPBtYDUztofJFRKQPWt89+BeBnYCO2t8DSSfdbd2DMfWUt3MPfi7Q5O4L3L0tSZKfuns0s12Bl7u6uj6fJElzkiQ/r+0R72Z2cWNj4686Ojp2iTH+ysyudvdO0qWH1Wq1Ou/RRx+9cvfddz8ySZKPxRgHhxAeB+7I5XLXFYvFj5pZC7DK3X/R0tLy+Ny5cw+rVCoTzWxZJpP50YQJExZPnz698ZNnn33piAULJt5x6qkXL9xnnxBjfLharf566NChlfb29sPdfRBwZ0tLy8Pd93GKiMgG6LXnwSvBA9OnT28cPHjwF2OMnwU2N7PH3P0cM/ubu58BfKg2JB+AX1Wr1SUhhJNJE/39pMPnt7n78cAyd38yhDDK3RPSz7ZiZll3b3D3h0IIuwLZGONVZrYF8AHS/zm2A64ws+3c/SAzO9rdTxm0bNmf/u3kk09aOmZMvO2b37wnhNDk7sPNbGmMcQawJITQ4u5X5/P589/+RykiIhuo1yb4S0kT0NrJYWcAA4CjezKoHtKjh80UCoXp7v6r1tbWewCmTp0axo4de2OM8Rl3vyBJkotjjD/M5/OXlkql6yqVyp2ZTOY7pJMWPZ/Pf2v27NnnxxgPArYHpuXz+Z8BzJ49e2qM8XQzG5bL5VbV6jvezM6KMX7KzI7du1A4ZMzvftd863e+8+fnxoyZ1NDQcK+7P5rP59+/Np4999zz5oaGhsPXziUQEZEe12sPm/kaaUJfUHs0ki6Tk1cxs1FrkzvAtGnTorvfYWZ7t7S0/Mndm1taWmaYmZvZ7ZlM5r1AO7BX7UAZqtXqjUAVWOPuO61TfAQqpJMeAWhoaJgDDPzHP/5xZwhhr0cPO+xqYPE+l1wyvKGhYS93bzezIa+K548dHR179uTnICIivcP6EvzLpL31LWuPz9Suyf/1Sltb2zbrXnD3PczshUKhsCPQXigU9gGIMe7u7v80swbgSdKjYjGzPWpvHWBmL6xTTgeQjBgxYvHaa+VyeW+gMm7cuJ2AF7sGD94DOG/wc8/tvt+vfz3UzBpq8wH+xcz2aGhoeKbbWy4iIr3O+obov0E6LD/wVdf74jnyPTpE39bWdlCSJGfEGE929xdDCJ9x97EhhF+6+9kxxj8lSXJ8jPHaEMLmQMbd3+vuj4cQzN3vAsYDz7v7O0MIj1Wr1RNDCNuRDuM3AveY2XdijHuEEM4xs0vdfV93v9Tdv9fQ3v7CJ7/ylbHtw4e/+Ief/WwQsDDGeEySJIvd/Wh3362lpaUv3l4REemreu0Q/XeBT5Em9HUf8iqtra23Ayea2RQzO8PMFoUQjs7lcn8ysy+ZWTbGeD9woLuPijE+nSTJHmZ2B+n38FFgsbvfmM1m9wDuCCFcCJzi7lPNbCvgmRjjZSGEE2OMX5o0adKJlUrlOGD3EMI9XQMHNjz2yU+uGPbcc9vv/z//8z13/2wI4egY4w+BhSEEbWkrIrKJWF+y/hvp6XG+ntf1BT3ag+9OM2bMaM5ms0eHEAab2Z/dfVCM8YkkSRpjjFtns9mF1Wp1a2AJ8KdcLlctlUrvdPddhj333D8/dvLJVwFPG7x/bZmlUmlfd98pSZIHjjrqqMfq1jgRkU1Lr51F30q6NOt80pPl+rI+keBLpdIn3b1IOhy/E7Ctu18H7OPuK2vL7j4C3Ao8ZWb7uvsS0lP+/gp88B0zZmy++9VXHwx8/DcXXHDT8OHDZ8cYl5rZA2b2UXd/IJ/P66hZEZGe12v3op9V++9Zr7quYfoe4u6/NbOjqtVqOYRwVCaT+UmlUnkshHCMu78jxnhoCGGEu1+dJMl/VavVr5rZAblc7n21Is6bc9llvxl9ww27J52dZ2w2dOh0d7+1paVl7Q6E5xUKhZmlUumAXC53d73aKSIiPWt99+Bffe9d9+B7mJkNyOVy1yZJsr+7z584ceLTQCXG+GyM8UkzeyWXy1Xd/epKpbKvmWXcPbtuGZVM5vInPvjBPwP7jrrllsPdff6r6rgCOGAjNktERDay9fXgpYeUSqWPk54Et21tzXtj7amGYrF4ZozxiRDC9rVrSaVSGZwkyRRgbLFYnAO0m9kF7r7GzDrXLTuEsP1DU6Zcvet11+2159y54546+ODt+d/DQ9u7+1M92kAREakrJfg6KBaLH3P3E2KMP0yS5Hrgj8A7YownhxAuBj5vZn83syGlUum4GONzmUymCCwC7jOzle5+ZAhhbrVafU+McXhbW9u7Ozo6/jZo0KD3AseWGxs/BqxsWrq0uPNNN11QKBRa29vbFwwaNOhgd584cODAj9TvExARkZ62viH6jWlb0skI+wJ7A38mnTh2MzC6jnF1OzP7Ujab/XwI4fO14fPEzK5OkmSBu08jPR3ugBjjTjHGoWa2GnjGzB42s7K7jwYejTGeFWM8JZPJHBZCOK6pqenKGOORlUrl8FwutxyYDdz3rosvHpCUyyc1NTXNd/ePZbPZQw877LA1dfwIRESkh/WmHvxs4E7gUdIZ4tcARwLHkSb+g+sWWTdz96GVSmUikAOypAfLrDSzT4QQlsUYtzSzZWa2kPSwn2FAdPddazvcDQaedfdhIYSfVqvVsUAwszXu/kImk7mnVCptOxsY+Ze/cNDZZ9tRn/nMGQYX1qnJIiKykfWmHvyuwOmky/F2Bn4FvACcSboWvz95xd3zpOvYlwI3hBCGuvvt7p4JIawAhrj73939ZXe/G1gBfBPYxsw+DQw1s8XAPjHGw/P5/GbuXgwhTIwxblOtVg8Fdnphv/3ue2n06FhuajrX/++OhCIi0k/1pgQ/B/gN6fD8BaSH2mxNul1uv1rO5e5VMxtE+mOmQrqLnZvZYcAod6+GEH4KHBFCmGJmS4FXgBOBJe7+Y9Jh/AFmdmWSJHvVym2qlf1Ka2vr1blc7hngkicOOeTG7Jo1g4Av1qG5IiJSB70pwX+VdOe8i4EvACeRbtyyG33zeNrXZWaJmf3Q3f8KfA5oc/d73L1Y25t+jrvfbmYhhLDazLJm9ryZ3ejuy9z97hDC5bXi2t29sVZuo7uH2tn0a+vqePJ973t66W67VYFTHAZt/BaLiMjG1psSfAX4KbAPsAXpveltgGOAF+sYV7czs2tjjAeEEPYys78BvwV2DSE8aWaXxhjf4+5fA+6uVqv/FWNcDXQCt7r7ru7+2xjjR4BF7n6kmd1ZK/rpEEJ0983mzp279fz585uAycCER4844i5gJOkRwCIi0s9tSpvW9PhWtYVCYZ8Qwq4xxtHu/lII4RF3H2tmoVKpvBBC+Etra+tT7m6lUuknZvZR0nXwRno2fNbMbnD3d9Z64/cAnzSzAe7eaWZNMcYXzWyomf0J2DLGONzMhrl7O9AYQngcGO3um5OeI4+7P9XS0jLa4QrgQ8AuBotfuxUiItKNeu1e9L3BwaRL5TYk1sNIh/pfy26kM/Q/2j1h/X+lUmmgu88jnd2+H9Dh7o21895XmlmIMXaGEB5391vy+fy3AKZPn97Y2Ng4YuDAgYQQXhoyZEjXkiVLthkxYsTC8ePHV0ql0rYdHR2vNDY2Dogx7tLV1bVg0KBBw5cuXbpo+PDhWwPP53K56rx585q7urqa29vb/3nMMcd0XHPNNQNijNuuXr1672HDht328Y9//GUAh72A+4FfGJzc3Z+DiIj8H0rwG0GP9eBLpdLpZrYwxnhGNpv9t3K5fCTwFTP7M/ABYDjw+9qytr9XKpWLa8fLbnQOM4BJwO4Gz9QjBhGRTUivPQ9eNoC7Hwi8aGbtEyZM+BvwHmBFjNFqPfdRwLXAs9Vq9R9JkrzvDQvsWaeT/rA7vY4xiIhID+tNCX446a+cR0jXfK+u/ftsYGgd49oQS6vVKjHG7AUXXJAlXdueCSGsDCFkkiRZEmPc1syazCzr7nW7/23wFOmGN//uMKZecYiISM/qTQl+Buk97MOBrYARwKFAtfZcr2VmF4QQvmpmq4YOHXot8Biwubt/yt2tUqlMDiF8jPSHyqey2ewV9Y2YH5POyv9uneMQEZEe0psS/PtJJ379g3RG+RrSSXHfJt2fvtfK5XJ3AD8AHgkhjHP3U82sTLqRjbv7maQ70z1iZi0TJkx4qZ7xGiwkXZLY4untBBERkR5zFfBfwO6kW6o2km5f+xPgym4o/1yg0A3l9AsOgx1edLil3rGIiPRjFwG71KPi3tSD/wxpr30+6R7tL5EeOJMFptQxrn7J0pP6zgA+6D2wdFBEROpLy+R6uZkzZw7fZpttVq5atWqr9vZ2Bg8evPSQQw7pBJg7d+7WIYT2I4888hUAdw9z5879n2q1OsXMEqDq7ncBFTMLZnZfJpOZ+q/Xpz+eFgCr515yydGVAQMKpMf2dpnZHWa2hbtHMys+9NBDF0ybNi3W51MQEemztA5+I+hTCb5YLI4HfuDuA4F3mBmkO9OVSffs38Pdu0IIGXdfbWbvdfdzgcPN7J5yuRwymczuZrYZ8LK7PwYk7j7azH6Zz+dPB3BoBWb9+atfbX/ywANPa21tPa9QKLQlSfKpEMI3GxoaLlmzZs13QwjtuVzu++vGOG/evOZKpTLe3UMmk7ll4sSJL2xI20ql0u4xxveGEF4Crs/lcu216yPdfby7e4zx5smTJy969XtvvvnmzJIlSz4SY9wO+EtLS8vf3uJHLCKyMWgd/KZq6tSp/+c7mDlz5nAzm5YkyefNbFvg78DPazP1rwQOAG5++OGHt8nlcluaWdHdfw98wt2XxRgxsyOAv8YYV7j7ZjHGm/P5/AFmdi0wolAorP2hU+zYbLOF4woFWidP/uUtt9wSQgjbuHtLtVr9+mGHHbYmn8+fBnxs3RhLpdIB5XL5Snff0sw2q1Qqc0ul0gfX195CoXCCu58TQnBgnLvfNG/evOa2traD3P3y2g+SzTOZzBWlUunAdd87Y8aMQUuWLLk+xvh+0lGG7xSLxe+/ZkUiIpu4TL0D2FQVi8UvAp81s0ypVHqxUql8Z/LkyQ/MnTt3u3K5PNPdx1Sr1QdrQ+1bmNnWMcYBpPMTAjB+7Nix9xeLxW2AVWa2bW04fSVwz+TJkxcVi8UGM2sHGpIk+SCAu79AuvVvK1AwiPdMmnT3vhdeeARw7JIlS24FMjHGlWY2olAofPWyyy67bsCAAV2XXXbZ0Gw2Oy7GuAb4abVaPWxtL3vmzJmFTCZzDXAgr2PevHnN5XI5t2DBgg+tHe5va2u7rVwunxFCGGtmn8zlci8DlEql2bXtfw9a+/4BAwZ8M8Z4QUtLy9rJkjMKhcLsUqk0LpfLPdhtX46ISD+gHnwdFAqFScA+zc3NB+Vyuf2BLydJcsFll102tFqtXmpmN5GuIrgoxvgK0OXur5Ducf8DdzczWw2s7Orq+rC73xJj7DSzTmBLd98GwN0Xku4nUHb3jvnz5zeZ2UEhhCdqy/gAePwjHzl30d57lysDBpzbsGLF+e6+QwjhhtqhNrnGxsa/uPve2Wz2BuCTIYTPA3tnMpl//UD89Kc/vQx4qVQqDXu9dpfL5bHufuu69/JbWlruMLMxwIq1yR0gl8stMbPOa665ZsDaa2b2rhDCda8q9g8xxne96S9BRKSfU4KvAzM7ysymjR8/vgKQy+WeMbOrstnske7+PNABJJlM5kIzczNrcPdFZpYxs2+Zmbv7EHe/f8qUKQ8AW4UQOiqVyiHunoQQJhaLxdVmNqn2YyALZNrb2/8A/CjG+C13n7M2nnw+f9vfjzrqnqRcbtqrWBxlZlsC5u73AcvdfYGZDXX3c/L5/Gn5fP7L7v4M8LO1ZdROxNt80qRJK96g3c+a2f9aLlIoFLau7ew3dN3bFaVSKXH3prUTCgFijM/GGP/X+81sdC0WERFZh4bo66OhUql0vupal7s3mVlX7e/nK5XK94Al7j4ceB/ppMiBZnavu48DPlcqlaaY2WPAH7feeus/L1q06E4zu9rdT6gNz79crVafSpJkZ9IJeie5+/SWlpar1q38pd13v+KVHXbwUTfdtP8jRxyxfPWIEZPdvdndD21sbDy5vb39JtLh8gKAmf3a3ae2tbXtlCRJLJVK3wZ+Z2b+eo3O5XL/LBaL2VKp9LVKpVIIIYw0s3NijN8NIRw4ZsyYX8+dO/dHXV1d5u7fdfe2dd8fQvilu08vFAon1Y7F/bi775skyXfe2tcgItJ/KcHXx5WZTOYE4PsAV1xxxZCOjo5PhRCOAlrdfRZwYrlcPjObze5gZmcBj8YYMzHGiZlM5nbSTYHek81mJ3R1dX3ZzJ5YsmTJsWZ2rbtfRrrcbXd3fxQ4K5fLPftGAZnZ0vuOPfbyD51++jvHzZrV9KcTT5waQhjg7q9UKpUVZjYEeG6dt/wPcIKZfb/We5+bz+d/t76GNzc3f3rJkiVfTJLkXGC1mX29tbX1QeCPhULh8Eql8sPaqEUxn89fve57c7ncI3PmzJlSrVZPjjFuEUK4f82aNYcec8wx1Q383EVENhlaJlcH7m6lUuknZnaguy8FmmOMU1tbW28sFAp7mdl5wJakh8GUgQoQzOxOd88ACbC1u68ws13d/aUQwuoY41OdnZ1fGjhw4HXuPrurq+uyAQMGHBhj/JGZ/drM2nK53JOvFdOsWbO2TJLkmoO/973lIx555CPXn3nmimXbb/+suxdDCEcD24cQvvPyyy+fN2jQoIGZTOZsM7svn8+fv5E+NhGRvkjr4DeCXpPg15o+fXpjY2PjiJaWludePbRdKpVGlsvlziRJdhg4cOCLhx9++KK5c+duXa1WvwDsb2Y3xhj3A3Z19+juV5rZsBDCCTHGB0IIJeDr7j7MzF6KMTYCXUBbS0vLf75WPHPmzBmVLFt2+6dOPLH55Z137rj1e9/rcvcE8CRJjq9Wq3sBHzAzjzFelM/nZ73RkLyIiCjBbwy9LsG/WbXe/bR8Pj8R0h8IAwcO/EcI4Ve5XO7sUqn0NXfPm9lyd/9v4ARgO+BMYBzpKMC7qtXq6a2trX98rTqKxeItudbWucR4HvApg6uLxeLUGOMdra2tN26stoqI9BPa6EbWz8wOAP51X7qxsXGMmd3o7vsDuPt73P3C2gS89wDlGGMb6X39u2KM8919eQjhddequ/uDcy688BHgIeBnTx58cKOZHezu2jFORKQPUYLvQ8xsEbDNOpcWmdnOwIsA7r6oXC4/WdvW9iPA9kmS/DvQkM/nLzezbWtL7F58vToaGhq+50OGfPv+KVMeAnZfvcUW97r7pZMnT17aU+0SEZHupyH6PuSaa64ZsHLlyhvM7AzgetJZ8rcA5w8ZMuSMlStXvhuYB3y/Wq0+nMlkZsQYNwPG13bEuxBY09jYOP7www9f+Xr13HzzzZlFixZ96LATTjizcdmyncx9F4OXX+/1IiLyunQPfiPo8wkeYNasWVslSXIqsBewOJPJ/LparR4MvM/dO0jPdz8AaCZd1rYlsB8Q3f2mbDZ72sSJE5977dL/N4e9gXuBcw3+o/tbIyLS79UtwW9KzqW2SYtsOIeLHdoddqp3LCIifdBFwC7rfVUP0D14WZ/vAFXSH0giItJHKMHLGzJ4HjgLOMLh3+odj4iIbBgleNkQZwNPA+e6tjcWEekTlOBlvQzagW8BewLH1TkcERHZAErwskEsnaB4G/ADhy3qHY+IiLwxJXh5M04BhgPfrncgIiLyxpTgZYMZ3AVcAnzVYY96xyMiIq9PCV7erP/H3p2HV1GdfwD/fs/crAQIyCIqCIgL4L7vCqgoVlAkMxPABbFFrHVXrNoitWqtW1tX3FAKycwJQUFBXLGi1r0oEsBdUcGwJSRkvXPe3x9zwy8gq0RZPJ/nyWMyzDln5t6Yc+cs73sVgJUA7t/aF2JZlmWtn+3grfUaPXr0j34/UiFr/wygtzhO3qbWsa66LMuyrJ+PDVVr/YjWupuI/ANAFoB0AP8rKyu7asSIEfUA8FRhYZ9eV1/9VGZFRdq0f/7zw2R29r89z7t/rTpGisg5ItJKKdVBRL4EUA7gNs/znv/Fb8qyLGvrsOlirW2DiFBEHiZ5led5fTzPOw5ASW5u7vUAUFxc3KHecW6E45ydsXJlxsDhw18QkYO01qc21BGG4UnGmMONMX8C8G4ikdgDwAqSI0heo7XutJVuz7Is61fDBi3ZjmmtO4nILYj3p1eT/E5EOpFMGGNmA2iLOJNcAkAdgEUkV4rIsyLyDslrAOyFeGTDIWmKioq+AjDHdd0FDe24rjtWa/0qgDH19fW9AQS533zzogCFMOaqfadNO2Pub37jA5iRKnKmUupuY8xwEbln4MCBy7TWE1P56scjjoj36C/zKlmWZf062Sf47ZTWOl1ECowxd3ued4hSaoaI7AXgX67rHgZgP6VU7/T09K4AponIdAAt0tLSfKVUa5IPici/AWQDeF9E3iJ5uoi0BHDK1KlTsxu3x1SSeaWUImlShy8FUL3XpEljRGT175KIKGOMkFSO4wgAGGOMiCiSRillf+8sy7J+ZnYOfjultT5cRHzP864EgDAMZ5EcgHgb29kiMh/A9yTPBzAdwDfGmCOVUlNEJIvkSSJSCyCT5EGpp+tcpdQgAMeLyMcico/v++PCMLxIRHbzff/G4uLi3aIomiYi3wPIOmD8eLP3tGm9Pj/ppDs++N3vKkWkN4C9Ec/fLyBZlbqeyWlpaSPr6uomklwGIEtEsklWkVxhjLnX9/0X1ne/kydP3qm+vv7PJI8Rkb1FJEMpZURkPslrXNd98ed8vS3Lsn4iOwdvbbYcEalo9DNXrVpVBSArIyMjAwBIrjTG/C3Vkfcj+bWIHCEiR4vI1yRLAEQicruIVCilhopIJYBlIpIkeVMQBJ8B6F5eXj4GAJLJZFdjTC2AliJS8dE55+y8vHPnmo5vv31x5rJlFSQrEWegKwHQTkQOArAQQEZ9fX2hUsqQHC4i1QCeAZBMT0+/mOSlhYWFfdZ1o2PHjk2rr68vchznLRHZk2SpUupjpdS1ADobY27XWvf+WV5ly7Ks7ZTt4LdTdXV175HsPX78+GapQx9nZWXdAuClAQMGVIjIShE5jGRrAKUkTwHQHECZUqoGQBqAKSTrAPQk+bvUMHsnEYmUUn1J9lRK/eB53mUNK+hFZIRSyvM87+isrKzBru/3KHHdqemrVmWffMMNextjlnue93hZWdkJAL4l2RPA65mZmacA+FAplR9F0U4kF/i+P1pE3qmtre1ijPmdUur367rXVq1aHQrgA2PMPgBKjDHTjTF5yWTyCGPM5YhHAy7+GV9uy7Ks7Y7t4LdTQ4cOXSkiN2dkZDwfhuHjAHYH4InIoWEYPqmUqgeQBHAUgD2NMU+RXEqyk4i0ADAFwBnGmCqSewE4heTBItIFwBWu6y5xXbcScS741ZRSbQAsBoABAwZUAMD3hxzy+beHH74oY8WKC9qXlNQBwIgRI+pJSl5e3vcikjlgwIAKkm2NMYuUUu1ILkrV9x2AtitXrlwCoOW67tUY0w7AImNMJ5IrSS7Kzs5eRHKntLS0j0k2I5nb1K+xZVnW9syuot+O+b7/wtixY2e2atVqHwBLPM9brLXupJTKNsZ8WlJSIj179vwgiqK/R1H0bHp6egdjzP0k0zzPG6W1bikiPUXkgUQi8Y/6+vpRSqlerusuBoCCgoKeIrK0cZsi8l8AZwIoBACttSMiR3xwwQXLdn377YwDn3zSnTp69KU1PXvuJSKLioqKTgIwJ1X2TZJnkZwB4Dqt9R0icroxZnhubm5/AG8XFBS0V0pdmxrGzwDwjVLKE5FL0tPT70smk08AOLKmpuYKksuiKCoEkGuM2UNrfZ0xpqVSal8R6Z7aTfBMVlbW9bW1tVXGmCEicrjjOHnGmBbxekHOMcb80/O8Can7yRKR34vI6SSrROTfnueFJOWXeVcty7Kahl1kt4PTWh8rIneLyHOIF76dBAAkXwVQTvI0Y8wY3/efC8PweAB3iMgMAFlKqeMB5Luu+2VDfVOnTs2uqal5yhjzFcmFqfomAviy68svP3joww93+2jIkPL5/fuvFJGXlVJ71NfXDxgyZMiKcePGZWZnZz8F4FsArUn2BvCaiCwi2U0pdY0x5t8i0gPAUgArAHREvBDwehG5BEAHkpSYSi3uL03VsY8xZrHjODuLSI2IvJqamvgBwGdKqXeMMX8kWW+MSZCsJNmc5PLUCMcVIvIKgLYiMjF1jacAeMfzvME/+5tlWdaOaKstsrMd/K/AlClTmtfU1BwEICL5LuJh98MBpKelpX141llnlTWcO2HChBZpaWkHGmOSK1eufLdh7n1tQRAcTLIlyXkNT/xa65ZnjBgxLaO8/JC3L7rowoUnnvjp3Llz3xszZoxpXLawsPAgx3FaAVgiIm1IrszLy/tAaz3eGHMayUrf9zsDQBiGU0n2AvA14jS1lQDuANDDGDMyNWS/XEQ+dhzn38aYySLyoDFmnFJqpIg8opR6WUT+h/gDTjcAUErdKCKZhpxOjQAAIABJREFUxpiLSOYAaCYiN5I8VUTubljRH4bhTSJyrFLqetd132m6d8WyrF+JrdbB2yH6X4HUXPlrax3+77rOHTp06Mp1nPsjvu9/sPYx13XLBRgMYO6RDzww5KgHHui3rrL5+fn/W9fxMAw7KaWakSxudPidKIp2V0p1BbCc5CLXdR/WWp+VerrONMZEJEuMMQaAkHxr/vz5H/To0WMP3/ffCsNQpZ76OwOYDWB/kjOMMdc5jjPFGPN7AMsAHEoyIz09fXVHLiJvk9wf8dY/28FblrXdsB28tdm01o4x5jClVDaA2a7rLm/4NwLfSJyM5u6vjjnmLx+NGvVoXV3dkVEUdXIc54VBgwZ9tIGqvzHG9CTZt9Gxwx3H6QrgaxFpBaC51rolgPcB7AZgFcmEiJyglJqbCrV75D777DMPwOdBEBxJ0oiIAPgKwIEAICKnkpwfRdFFJMsAtADwnoi0qa2tPRzACwBA8ggRaUFyASzLsrYjdoje2ixa67YAnjbGvKuUWi4ip5G8zXXdqal/z2IyOaXfZZcdnFZdnT7tgQcy6jIyygDMRdy5vup53sD11L03gGIAPVKL+xrm4DNIdhGRq0ieZ4xZDuB1pVQ+AMcYsyC1ir69iPyglGq1oTl4APUiYufgLcv6JdhAN9b2wRhzWxRF1/m+f7nrun/JysrqIyJ/HDduXCYAiMi1kkg8kb1kSd9EVVXOYffe+zXJOSTPIdlDRA7TWvdfV92u6y5IJpN9RORuxFnsOorIwszMzF1c1/3G87zLoii6EPG+/uNEZJkx5kkAS0jOJXkryXoAL6aOHSAij2VmZu5P8tQoihaIyH1KqTIAdSQzRORdY8zlnuf91nXdSpInIM51f7RSqqOI3Oi67pBf5MW1LMuyfpJ7AARb+yK2d1rrH83PB0HwjyAIDgaAMAxnpLaacX7//mUCmI+GDh0bhuGZqXNfC4LgX01xLWEY/mcdx4pTowyWZVnbgkcB7LE1GrZP8NZmEZHatRPRANhVRJakvl+qlOpAUj72vGV1OTnf7f30037uV1+tAgCSbYwxi5roctTo0aPX/h1ugzjvvGVZ1q+aXWRnba5HqqurH9Na/75t27YrS0tLhwBQvu8vBABjzFgA9xcWFg43jlM4a9SoP/QZPbp5nxtvHFhUVPQbEcklOaGJrmVK9+7d7x4/fvwNmZmZ9SJyuYh85HleXRPVb1mWtd2yHby1WTzP02EYRgCeLC0tzRSRN7Ozs89p+Pf8/PxZYRj+XSl1P4CWy/baa84Xffoc2OXlly9qM2fO/BUHHniK67oLm+JaXNe9KwzD4RkZGZMQj0a9WF5efmVT1P1L0Fp3Mcb8DvFivvfq6+vnpKWluSKSCeAlz/Oe2lgEvZkzZyaWLFlynogcBqCM5KMA6lL1tlVKzc7JyXm8vLx8J5IjSHYQkTlKqQDAOamIfwsBPOi67pLGdadiHQwVkUyl1Ct5eXnFNqKfZW0/7Cp662cnQDMAHwKoB3AwgeqtfElbXWrHwJMARgFYLCJXADiT5OkAqkXktwAqPc/704bqCcOwEMB7JJ+NoqgdyX+STDPGXE5yoVKqD4CzUiMnf1ZKfV5fX99LKfU3Y8xljuP8V0S6A/hTWlraaQMHDlwGAIWFhX2UUtelIv+tInkBgMjzvOt+ztfFsnZANtCNteMisEoAD3FwnbsBjNzKl7TVicjVJC9yXXc2AIRhuKdSaoaIRK7rlgC4Qmv9mtY6y3XddX4gCoKgO4A6z/PuSh1aEATBxyLSLj8//+XUsU+CIBgmIoX5+fkzUm3tD+B/SqlS13U/A/BZGIbpyWTytwD+BgBKqevS09PzGkU5vEZrPVNrnZNKQmRZ1jbOdvDbCa313iLyBIC9SNaJyPuI3780AG/U1tbefu65564CgCAIDiD5JMndjTFVSqmxqcQtRyF+en7c87zi8ePHd8nIyCgiuYcxJptkhPjpcWkq29sKAPd4nrfRyHYbQ+B9Af4O4HoBniUwbUvr3M51zsnJmdfwA8m0KIpmA+iKONoeRGQByU4A1hlkRynVVURKGh9LxQPIWeuYpN7bBl0AfECya8MBx3HmRlHUt1GZjMYhjAHAGDMPQGcAH2/WnVqWtVXYVfTbAa31zsaYlwB8VVtb28kY8zCAXgBWtmvXri+ArzIyMiYAQHFx8W4kXyL5wooVK9qlMrHdAKB7u3btTiF5jojkhWF4XmZm5gci8qIx5nul1LskqwBUqzjNWr0x5lIAowsLC49uolsZA+ADAI9IHFf+1+zjioqK4xr9XEmybyKRmAMAY8eOTQNwwIoVK75YXwWO43wMoHEdEJEyY0xF42Mk06MoagYAQRDsBWBnAIPQ6INDMpk8gWTjKIPlhYWFnRt+mDlzZoLkIS1atPh0c2/Usqytw87BbweCILiY5GUlJSXdx4wZY8IwfEVEHgTwN6VUd9d168IwLE4kEpckk8nzSfqu6x4AAIWFhR1JFpFs43leNyDOCFddXf02AJSVlR2Rm5v7ved5uVrr4caYf8ybN69Vjx49lnme13LSpEn7JJPJUb7vD2uKexHgEMRD9SGBczZ2/o6qISIgAA3gSxEZDuAQkjeKSAWAC0Qk9H1//IbqSSXD6aqUmmSM2R3AuSRNqt5PAJxBshbAviKyHMDuiLMIHgCgLoqiUUqpzgCOq6qq6j9s2LAaIE4VnEgkHhORh1Pnny8iT3me9/jP84pY1g7LRrKz1k8p1QZAbaOsbI6IfEMyCaBl6tii2tratiR3EZHSRsXbkPyWZFrDgf79+1eRbAagNCsrqz1Si96MMTUk1ZgxY5IARESUMWZRqv0mwTiG/C0AhgqQ31T1/pymTJmyS0FBwV/DMLypoKCg/eaULSgoaK+17h0EwRqBLlzXXZKTk9PbGPMDgG4iMiaZTO4HwElF0HtMRBZorbM2VL/neTcppe4Wke6O47QWkctI9kn9fuxJ8lHXdf8AwAXQ3RgTkBztum4bY8ytSqk/AJhdUlJyaosWLQ4sKiq6Smt9yODBg+empaWdCgAisotS6krbuVvW9sU+wW8HUiuaHyV5quu6C8IwfJJkMxHp7nleT611DoCXABxvjDmF5MMk93Vdd3kqB/tCkp+4rnsMAKTyvl8C4OSysrJdW7Vq9b0x5lgAl5D0oijKdxznCc/zdg7D8AIAbT3Pu72p7kfiD5bPI14TcCiB+U1Vd1MrKiq62BhzL+Kc80Qcp/63+fn5G+3swjC8FMBAADMB7AegsqSk5IK10+c2NmnSpD2jKJogIq+nnsRPiKJo2ODBg+eur4zW+sDUk/ZMAOkkjwKQ77rulw3nFBYWHqeUOtXzvBsajokItdazPM87NgzD9xEHLJqnlNrPGDPX9/0TNvoCWZa1MXYVvbV++fn5LwdB8DyAN8Mw/ARAewC7kHwmDMNbROR4AKNTAV6eDcNwFoBPwzAsAbAr4qfxtCAI/kpyJ5J7JpNJXyk1Ojc393sRWUzyQ8R54ksTicQzAAqDIBgPILt58+ZNGoudgBFgKOKtcxMFOJpAbVO20VSMMf9USuXl5eVNBoAgCIYopcYB2GAHr7XeD0DvvLy8Xg17x8Mw/GOPHj2GA3hkfeWiKLqf5BDP8z5L1dPJcZzxAE5cXxkRuc8Yc2Z+fv73qWvsTvI+AKc3Om2hiKwxilBUVNQewPLCwsJbSdJ13Z0b/i0MwwVhGF7hed49G7pPy7K2XXaIfjvh+/5FJI8mGQC4AUB7Y8xdJF9IJpP9Pc97vuFcz/M8AH0ATBaRUWVlZbuSPFVEXjLGPDF37txTBg8evNT3/T9kZGQcDWAsgEuNMVcopW7NycnZB8ATSqm7Pc8b1K9fvybvfBlneBsG4CAAtzZ1/U1hypQpuwCQhs4dAHzfnwiAWuvWGyl+FIA1AsOQDETkuPUVmDlzZgJAIrV1DQDguu43AKpTozQ/MnHixFYAljV07qlrnAcgp3EY3/z8/K9IGq31lQUFBe0LCgr2F5GJxpg7lFJ9jDEPNK43iqInAPxmI/doWdY2zD7Bb0dc112ANbdMvbWBc2cjtd0qZfnkyZPn1NXVjerZs+fdQRC0JllbW1urSJaKyOuO49yZl5dXCQBTp05dVFNTc0UYhreJyBKl1IOu6/63obLUVrzLAOwC4J36+vo7hw4dujI1JXAZgONFpEwp9bDrumskhdFanyUivgYy+9x446ydPv30cgGmE3gZ25D+/fv/EIbhuj4E03Xd5Rsqa4xZmlq81lhbkkvXV6ZXr17JMAzTf9QY2Wzu3LlV6ypTWVlZ2apVqxaNj6WG3tXaUwHNmzcfVllZeZHjOPcAWEXyj/n5+e9orZchXny3mlKqI4DGazksy9rO2Dn4X4mpU6dm19TUzCAZGGOGAngOwNUk7wVwfBRFjyulfJKn5+XlGa310wCm1NbWhtnZ2R2NMfeJyGjP895IDT/fb4z5g1LqEwD9ReTCsrKyfrm5uRNE5D9KqfEAdhaRe0ne7bruiwAQBMEwkn2MMdcaY6qb1dVde/LVVw/PXrYsAnAQgcVb6zValzAMF4vIyvbt2x/8ySefOC1btpwNIOH7fscNlZsyZUrzmpqaF0TkUt/33y0sLOyYGmq/1HXdOesrl5pGqS8rK7t1r732ktLS0qsAtPc8b70heMMwvF9EPlVK3Yt4AeZNAKo8z/vrptxjUVHR0SIyA8DZruu+OHHixAGJRGKCiBzl+77d825ZW8auord+XlVVVacCmG6M2VtErgSwh4hcboxxjDEzSf4gIvOjKDpCa31xar62W2ZmZtdBgwbNR7xt6zqt9XUiEojIf8rLy0tc1612XTcE8EHr1q1vQrw/fwTJm/Ly8r6IougcAFc0XAfJ4SQvyM/P/37IkCErqjIynnz15pub1eXktF+x++6fz3rggdXBV7TWJ4RheGcQBH/f0F58EVGFhYV3B0HwYRiGs4qKivo01evWrl27bkqputLS0hW5ublLHcdZoZTaa2PlBgwYUJFIJPIAXByG4ctKqfuNMdduqHMHAKXUaJLLcnNzZ5SWlj5Psr5du3bXbqhMWVnZ5anc9i+IyHMi8nVJSckmT3vk5eW9WV9ff46IjAuCYLnjOP9USp1pO3fL2r5tS0/wDwG4HPG2r38COAXxwqunAFwHYOUW1v+rfoIPguBiAMtJDiR5qYg8ISJXkLyO5EwRUSSbG2OOUUrlGGO+VEppERkD4DaSH4vIPAAXAriI5MsicgLJ01zXjcIwfIJkvoj81xhzn+M4o0QkO7XK/zXXdY8H4nzyDd8XFBTsk0gkPgawrPuUKc/vW1BwzoLf/EYWXHjhbtXV1WeQPIXk7cYYpZS6QUQmeZ735Nr3FobhXJJVURTdLiJ7Oo5zPYBL1nWuZVnWL8w+wQMYgXhNwCMAagD0BLAv4gQl/9yK17WjeJfkaSTfNcacJiLvkbxSRN4WkdMcx3lPRE5TSnXJyMgYRvJIEbk8lWjkbyJyB8lXPM/TAF4B8CWA9wCcXFhY2FFEhorIAhHZbeedd37add3DRGQ3rfVHxphdG+0DL2/4Pi0trUBE3gWwuKR//8yvjzvui72ffZYdnnvueZIXlJWV+a7rvuP7/lurVq3KA3DR2jeltT4EwE6u6x6Wn58/afDgwbcppfoiFVPdsizr12pb6uAb9AZwJYBFAJYBuAZrbvexfgLf998FsMQYcwTJa5RS/QEMVkpdDqBFFEW3ishHIjK7pqZmOMl9SB5ijMkWkf0BDDDG3AgAWVlZd4vIhQD2F5FrHMf5QikFY8yzJFuUlpYuST1VNwPQieT7JGdrrU81xlxLMgzD8I9RFO2JOMjLngAqPxg+/OnlnTubA//9756tvvyyZsSIEfUN1z9s2LAakqu01mssQiN5hIis8ck4Ly/vTZIbDBBjWZa1o9vWOviWiIOeNF7A1A1A+da5nB2L53lXA7hJKTVaRMYqpc5HvEXtUcdxrlBK3Yh41OQ6x3F6KKVONMZMVEp9SDKhlOoJxJHwSkpKTgJQlwp5+idjzEJjzNue57UjSQBdU7Htj/M8z00mk0MBPOL7/rza2toTUjnJv00lRznd87wLBp533lVvXnnlt1EiwWPuueewL/v1W70ve8KECS1EJMN13brG9xRF0Usk9xGR1b/LWuvTRcT+zliW9au2Lc3BvwFgHwDpAN5F/CR/NOJ43TcBeGC9JTfNr3oOflNNmjRpZDKZ/CfJs0k2F5GRJC8XkecAfC4iIcl5ItIHwM4k+7uu23rSpEm9jDFPkwyNMQNI5orIK77vr85QprUuc103t9HPrUVkGYDPoiiapZTqTXLn1vPnf9v7L3/ZvaxLl/KZo0ePiNLTAeBiAH9vvN+/QRiGMwDsDeAJkh1FxCV5dsPKfcuyrK3IzsEDOAZAGwB7Ih6iB+K5+LMBPLi1LurXZtCgQQ8qpeqVUvsBaB1F0aAVK1bME5FskicAWA7gAJKv+r5/LoDyMAxPysvLe7m2tnZ/EWlGsgUAIXmI1nplGIZlYRhqEalp3JbrustJLlNKLUokEkcrpT5wXbfZiu7dd6rs0OHq1p99ttP+hYWPA7gDcQa0O8MwfD0Mw+e01j0a6vE871QRuQXAISLSLJFI7Gc7d8uyfu22tUA3gngfdMNe6A+24rX8ahljJqRW2t+olOqXm5t7M4CpqeHxNbKbicjVACaHYfg3pVSJMWZ3kstEpI0xppzkdUqpY0TkUhF5Ye22ksnkX5VSY0jeRPJ7rfVskgtm3HXXt8fefvtne06fvkeiuvq+90aOPNQY07qurq5vdnZ2xyiKxk+YMOGkoUOHrgQA3/cfRfxJ2bIsy8K29QS/Pici7vg3xW8AvLier4EANhZe1ALg+/6IVOd+IcmRSqlbPc8bvJ5zi0j2E5E+xpg/G2PechznXZIzE4lEEYAbjDEHKaUKSO6ydvnBgwf/g+RQxO/PKBGZ7LrukSLifzZkSG8Ar+0+a9a1R91550Mkp6WlpR2Z2pdfnEgkjv9ZXwjLsqzt2Lb2BL8ur2LT1wo8m/pal4Y5eGsTbM4Tsed5ryEOcAMACMPwRQAVrutehziGAbTW15E8cD3lnwHwTONjSqnMhe3blwM4o6pVq4W7vvvu4zvPnv3oogMOyAIAEakCYFfKW5Zlrcf20MFb2xmSz4rI5VrrLq7rfjl+/PhmInIu4uxxm+qltLS0kQRuf+Wyy2499pZbbjzsoYf+8O3RRz8+bty4TJKeMcbdkutMpWYdD6CjiCxMJBLnDho06FOtdZaI/AdxLIZ6xIv7mjQhThAEjyilvFSAoddc1+3XlPVblmVtS0P0rRCvNFyAOGrdqtT3dwBosYFy1rbnPgBvicj/giD4KjMz81uSK9LS0i7ZzDo6hWH4amm3bvu/fu21dekVFentP/zw1eaO8zqA2xtnUNtcxcXFuxtjPjDGTHccpxfJGVEUfVBcXLy7iPwgIs2jKOoH4M8iclNRUVGTLfTUWv+H5GBjzMhEIuEBOCQIgq+aqn7Lsixg29om9wyArwDcD+BrxNe2G4ALEG+fO3ML67fb5H5hWuu2juPs4TjOd2eeeebCn1LHxIkTW2VmZraIomhRv5Ej85stW/YYHGcGougsxk/XP0kQBAGAct/3RzQcC8PwEZLdjDFH+r6/evi/uLj4sGQy+brneRk/tb212k6Wl5fvNGLEiNV79cMwTLZr1y63V69elU3RhmVZ24yttk1uWxqiPxbxlrjGgUw+AfBHAN9slSvaAU2fPj2jqqpqV8dxlp911lllkydP3imZTLZJJBJCsrS0tHTVTjvt1L22tjatVatWHzfkgk/lP2/pOE5NMpl8GsDeqVznb9TU1HjZ2dntHcdZXlFRUZ+ZmdkBwHeu6y7RWl+ZTCZ/F4ahIyLLAQz2ff+tMAyHkhwuIrkAGhLM1IvIhHnz5l3ZkOpUKXVNMpm8CED6tAceyOr8xhs47N57T1+6zz5fy/z5nQgkG9+f1jpdRG4EcALixZmvAjgecd55isiHSqnTU6v914hVr5T6XxRFp5Esa3z87LPPfjcIAqep3gOllDTu3AGAZO0PP/xwNIAf7TSwLMv6KbalIfo3ANyFOGBJFoBMxHvib8Oaec2tnygMwzMqKyv/E0XRDfX19U8FQTAnmUy+CGBWMpmcVVdX925ubu5yY8zziURiSmVl5TdBEPhhGD6YyiD3p2Qy+QXJMs/zctu2bdtBRLpmZGR8H0XRDXV1de9mZGR8QnKUiLxcWFg4RUTOq62tPdTzvFyl1B1KqecmTZr0OwB9jTEXA9hFRIpIvpuVlXUsgLN79OjxdwAIguA6x3HOdxynD8kMki99dcwxlUu7dbu97fz5HRbvt98CWWsUSkTuBrDUdd0TS0pKeovIcACdS0pK2rqu21optcwY84ZS6m0RyW9c1hiTjzgnfVut9eon+CAI/kxyjT38W0iKi4tXh1+eNGlSVxHJ9Dzv5SZsw7KsX7ltqYM/B0AVgKkAliCOQz8dQBqAoVvxunYIhYWFu5C8ctWqVSd6njccwPMkF4lIdk5OTse6urpDAOwmInMB3Oh53m6p4DH3kiz1PO+UtLS0a0SkWkSytdatFy9e3JpkqVKKACaIyOtKqYdF5K2SkpJjlVInicht55577pcA4LrugyIyP5lMXlVfX/97kmeSXOz7/oXGmM+rqqoSjuNciXgkByRHOo6TF0XRYBFZ4rpuXwBzX7n55sXLunWbuPOcOV0B3N/QyWutHQAHeJ73L5IyZswYo5RqSXLRTTfdFJE0rusOBNB5xYoV1wPYPQzDOWEYPhQEwccispvnecNE5E0RKddaz9JaL1BK/VlE8prqvRCR6+vr66eGYThba/1WFEWfiMh4klFTtWFZlrUtdfArAIxC/ASfA6AZ4if4q2Bj0W8xx3GONsZMHjZsWA0AiEhvEXkKQHW/fv1q09PT9xKRcpJPiEhfACD5CMlMAN8BgDGmbSq+/PRU0ppjAEwSEQPgZJKPishYEek7ZswYQ7IawBq500VkKcms9PT0VSLSBkBZqq1lSqlcY8xS/P/vZWZWVtbXADqQrEgdWwqg/Rt33XXtvDPPNABGAnhUAJWZmZmBeHEmAGDmzJmZIpIUkZqHH3549XQUyboOHTpk+77fGfGaj3SS9/m+34Wk8X3/eBEZZoxJisiH6enpXXzff66p3gvP8+6MougQkt8YY8pFpJ/v+8PWd77WOktr3TsIgt8UFBS0aarrWEc7nYIgGBiG4TGjR4/elv42WJb1E9j/iX89qklmN/q5TkTSGj01VpNUSqlMxCMpQDxVYowxBgAGDRo0n2QO4gxw1QCqReRoABWN6s9pKG+M+YbkcQ0NTpgwoYVS6igReRXAWSIyXUT2nDhx4p6IAxrNBnApyS9SRd6rrKy8XSn1AICuxcXFuwE4LpFIFNbW1oZz8vO/QJxt8AIA4Rn9+9cDUJMmTeoKAL169aoRESGZ05CZLgzDXiTZv3//pQDged5Dnudd4HneQ41fLN/3J/q+38vzPPenLhDckCFDhsx2Xbe/7/t9fd9f77x7YWFhZxF5VUROJNnDcZxnwjA8qamvJwzDiwA8DqATALdnz54vjB8/vllTt2NZ1i9nW1pkZ/28XgcwWmv9tOu6C0TkaZJ/AlCrtd7bGCMkc4wxN5D83fTp0zMqKyvHikg1yZPHjRs3YdiwYTUi8lcAfyN5uFIqHUBXpZSfTCYXkHwAQDnJ+4uLizskk8laALsEQfBdajpgT2PMk3V1dX/MyMj4d+oJvzSRSMxDnF9+PuL8AycAQG1trZuRkTFHRE4gWZlMJheKSFUURW+JiFFKdSKwXAAHcf73qNny5Veuat36yTAMP0L8AXYhgO5hGM4FYEh2xHa0k0IpdXcURRcMHjx4LgBMmTLlwZqampmjR48+vGEh4pbSWu8KYFBeXt7JqYWT0FoPysjIuAHA9U3RhmVZvzzbwf9KuK5bXlBQMCyRSNyutW4pIhSRVwDsJyKvkzQkF4hIDoDHKyoqSPJrY8wpSqnDs7Ozn9daG2PM0vT09EOiKNrDGFMfRdHXiUTiL0qplsaYliRbkRwVRVEdyWtc1329oKDgWMdxOqalpc06++yzv01d0kCtdTdjTLP09PTqZDJ5UCKR+O7DDz98s6HjOvfcc1cB6FpUVHRcFEW7pqWlfZ9MJo8i+ZXneWHDvRG4XeLV9HeePnJk7jf77df/vzfcsKsxRhKJxCVt27ZN+/777/smEgmuWLHihREjRlT96AXaRpFs09C5A8CAAQMqgiAo6d69exc03babQ0RkRkPnDgCrVq16Njs7e2QT1W9ZlvWzugdAsLUvwvr5CDBUgDoBPpY4hsJ2LwzD/4wdOzZtrWMvTpkypXlTtaG1PjwIgn80PjZp0qSuYRgWNFUblvUr9iiAPbZGw/YJ3tphEJgg8YLMAMBMAU7lVggu0ZRE5Inc3NxHtdZXA6gUkT8A+HzAgAEVGyu7Gd4neYvWetCKFSumtGzZspMxZmwqnoBlWdspu8jO2qEwjoh4EoCWAN4R4OStfElbxPf9cQCmicijIjKJZLJ58+aXNWUbrutGyWTSFZGDc3NznyF5K4CbfN9/qynbsSzL+rnYIfpfEQF2EeAtAYwAfxP7YdayrK1jqw3R2z961g6JwPcA+gAoRhxfYYLEsRUsy7J+FewcvLXZgiDII/k7pVTCGFMFoBlJEZGXmzdvfke/fv1qtda7isjNJLsAqIyi6K/5+flvN0X7hYWFhyql/kyyuYh8nUgkbmy0On81AqsEcAHcAOAmAAcK4BGY0xTXYVmWtS2zT/DWZtFanwOgH8mzjDHTUodXzp07tw/JZRUVFQ9qrXNS8eUfcl23l+M4I5VSt2mtD9zS9oMg2NdxnDuMMb93XbeXMea+ZDJZNGHChHWmFCYgBP6K+Gm+JYDuoLq9AAAgAElEQVS3Bfjtll6HZVnWts528NZmEZHzW7RocZHrupUk+5eUlJwhIlX777//Lq7rPog4nn0/kk+5rvsOAJx99tnfkrxGRNYbjnVTkTwPwPX5+fkLASA/P/89kkEikei7wXLAfwAciPi/DwvwgsRR236SMAx7BUEwOwiChWEYvhoEwVaZY7Msy1of28Fbm4VkWkMKWQBIxZwvraura5s6tEwp1RFxwqDGlqRiz2+pndZVN4C26zh3DYzP6wfgUgBHA5gjwG/Xzki3MYWFhUeQnALgPgB9SL6ulHpv+vTp6xxFsCzL2hpsB29tFhGZr7Xunfq+VGt9FMmjWrZsWaK1bkuyC8lpIjJQRNionE9yVhO0PwuA1+hnisggxOmGNyo1ZH8vgAMQx75/GMBzAnTZ1GtQSt0pIn/1ff9R3/c/cV33RhF5u7y8/LrNuxvLsqyfj11kZ22WZDI5KpFIPBWGoQvgexF5AcCLK1euvIlkH5KXDBo0aH4Yhs9rrV8Nw/AVAD1FpGbevHnnr12f1rqtMaaFiLQHUJ2fn/+/dbU7duzY7Nzc3ENJvmmMuS4Mw0kA5hQVFZ1I8mnP8z7c0HVPmTKleW1tbftkMlnhOE6PIvKTPNftBeBixHP0cwW4FcAdBGo3VJeIdEhPT197weA8kntuqJxlWdYvabOGJrdz9wDogO0o0ci2avTo0apnz549RaRFfX39HMdx9iCZoZT60HXd6obzCgoK2pDc13Gcr13X/bJxHVOnTs2urq6eSLKDiBxM0gAoF5E0Y0yfxh19QUHBHxOJxA2IP1C0AlBRW1t7elpaWnvHcea6rrv2kP0awjC8GUAvAG1EZE8AS5RSmSKywPO8IwTYGcCdAIYAWABgDICQwDqTuYRhWAyg1vO8wY2OLXAc585BgwY9snmvpmVZO7hHAdyGrRBV03bw1lYRBMHfSb4H4H7Hcc4zxrwrIlOMMeMcx/mz67odgdWZzuYB6O667ncAEIZhIYBWnuedurF2wjA8A0BfklOMMQWtWrXqXF5eHiSTyesSicQTURTNys/PvxIAJP4Q8E8A+yEevv8jgRlr1zl9+vQWFRUVnwL4GsAHInIyyTLP8w5pkhfHsqwdyVbr4O0cvLVVkDwiJyfnNZIyaNCg6a7rLhGR90m+IyI5o0ePTgBAMpnMM8b8r6FzB4CqqqqRAA7dxKZOFpFHjDFDSRb37dt3lTFmvFKqdyo17umrrwmYiXil/TkAchHPzc9Mdfyr9evXb6Xruh0cx5kAIN1xnGvW1bnPmDGjQ1FR0ajCwsI/jR8/fpPn+DeF1jpHa31yGIb9Jk6c2Kop67Ysa8dgO3hra0mWlZXVGmMarwPJUUqtEhE1ZsyYJAAopcpJrhGBznGcVojTw26KKpI5juNUIN4HDwA5JFcppdoAqG58MgFDYAKAvQFcifhp/hUB/ivAGQ0r7kmaQYMG/cvzvAvy8vImr92o1tpbuXLlp8aYU0gem5GRMaewsPD3m3jNG1RQULB/KtXvUST3TyQSM7TWJzRF3ZZl7TjsIjtrqxCRYsdxbiRZFgTBvSKiSXZSSt0qIp81nKeUKhKRfxQUFOQPHjy4MDU8PkNE9Ca2o0neKiJ/JvlSEAQDSQ53HOcPURTNSCQS68yYRqAOwD0CPAJgBICrAEwFMF+A+wGMJ7ByA+0+oJQ6xXXdNwFg0qRJ+wB4B3HZLZJIJO4A4DWsaygoKHg0kUg8C+DIMAwvBXAHSZW6jume5w3Y0jYty9r+2Cd4a6vwPO9BpdSXJEuVUueRfInkoVEUtSO5+mnUdd3KRCLR13GcW7TWKyoqKr4mOcv3/Us3pR3f9z8QkbtF5K8AvgEwEcD+URS9COCBjS2KI1BJ4C7E2+iGA1iFeJvdtwLcL8DBa5dJTS+ovLy8NxuODRo0aD6Aqi0dqk9tC8xsvGhx8ODBS0VkUeop/m4RucB13bSsrKweAPqunevdsixrR2OzyVlNQoAjBRgvQJUAIsD/BLhUgHYN54RhWN6wjqBBEATlWuv0LW0/DMPXR48evcaHc631a2EYTgnDcM5a514ahuHyLW3TsqyfbKtlk7ND9Ja1mQi8hTgV7R8Q78q4APHq+7sFeB1A8XOLFr3dvXv394uLi/snEoma6urqYpJzXdet29L2RWRS9+7d75s4ceINaWlp9SJyrYj8F/HCw8rG5yqlvo2iaIs/VKzLhAkTWqSlpZ1KMpFIJJ4nGdXW1p5KkslkcsaQIUNWrKvczJkzM0tLS0cB2D0tLe3JgQMH/mdLr6W4uHi3ZDLZR0TKWrRoMaMh2mJBQUFPpdRRJD93XfdVkrKlbVnW9sJuk7OsJiDAXgDOTn0dAgBVbdosXXjEEVmLDzqobuk++zx79pAh56f2+28xrbUHYGgqWuCUkpKSx/bdd98zjTGFZWVl7UaMGFEOAEEQfEXyc8/z+jRFuw2CIDiY5P0AJolIRPJ8kgkReQwASA4CMMp13dfXKrcXgHdJ/g/ADwCOB/CG53mDtuBahpA8T0SeIdkcwBmJRMKvr6+/CEAnpdTrItIVwH4kz2ocq8HasQjQEfEumDYAWqS+vgFwH4GvttJl2X3wvwDbwVu/CAF2B3A6gNMQb7Frhnju/k3EyW5mAXif8bEmFQTB8yRPAlCR2n2wPC8vbxeSUVO2E4bhy8aYc/Lz879P/fwmyXTXdQ8FgMmTJ+9UX18/xfO8Y9cqNxtAoed5twOAiCit9VIR6eX7/gajEa7LuHHjMrOzs/9TVlZ27IgRI+qBeJcByTtJLvF9f0jDuVrr80Wkned5f9+CW7e2QQLsD+Bq/P/f90rE/3/V4f+TShUhjlS5zmiZPyO7D96yACAIglPCMLxVa31DKshNk5k5c2aisLDw1iAI/qu1fiYIgn03VkZr3TsMw1vCMLxRa71J2ecIfE3gAQJnIH6S6A9gHOIPmDcj7uTLBfhQgEcFGJma18/egtsDAPi+37d58+Y7kxwB4ADXdds3deeeGjVIb+jcp0+fngGgWkS+KygoaAMAAwcOXEZyldY6Z63inZs3b7560V9qRON9AD9ppX9mZmZ3EXmnoXMHgMGDB3+klOqilHqx8blRFL2ATY+fYG0HBMgU4DHEgakGIk4A1YVAawIdGc9974H4Ae80AO9L/EHgV8HOwVvbjDAMbxaRdsaYJx3HaQNAa61/77ru7PWVGTduXGaLFi3at27d+rvFixfvtvPOO3/bq1evJABMnjy5XTKZTLquu3zs2LFppaWlH5KsIfmgiOynlJoVBME5vu8/u666tdY3iMgeAEKS7URkYhAEt9fV1c0899xzV611bjqAQEROEhFF8u2qqqqzOWxYGYBnUl+QuMM/AsBhAA5H3PkPT1UTSfwpfz6ABeUdO66Y4/t+WefO+1XvtBOhlBhjZimlThWRUQD6kawXkYKSkpIHx4wZYwBg5cqV7QEMInltGIbfiMjNvu9/8BPflh8hKVprNXPmzESvXr2S/fr1qw3DMItkZiKRWAHEHwK01i1c113jdRKRlRUVFYeiUXIgEelkjPnop1yL4zjfAujc+NiECRNaiEiFiHRZ69yuxpiFP6Uda9sj8ftejPjp/TYA9xBYuvZ5jIforxXgLwCeBPB3AcoZb4HdodkhemubkBrSLfQ875SGY6kn5n+5rnvm2ueLCMMwvFMpdaQxxiG5H8m3EM+5PS8ixyFOD5tGMtMY87RS6joAXV3XjQAgDMPfk7zMdd291q5/ypQpzWtqap4DsAxAgmQm4o55lYjMA/AFyYsaFs0FQfASAEcp1TcvLy+ptZ4AYD/P8/bb2L0LsBviCHoHAugJYG8B9majJ3oB6qvbto1W7rprRnXr1pXpq1ZN3/Xttycls7IWvfKXv7grd931u7zBg/9eUFDQ3nGcSSJyvu/7n2utO4nIv0me47ruN5v4dmxUGIa/BXAkyTEAIhEZDyAnkUicDQDJZPJaAF97nnfXWuXOI3l3fX39Bc2aNfu0pqbmaqXUKXl5eR1/6gK4MAwfRpzsp1Ap1TyKojtF5BGl1OXGmAeMMa8ppbqQvMdxnHMHDRr0xRbevrWVCdAX8ZbXJACfwKubWC4dwNMATgEwmMAmxdPYQlttiN4+wVu/CBFJKyoqmgega+rnz13X7UGyHgBqa2u7kVzjSd113W+01q3XVV8YhsNJ1hhjLldK3QCgr4hMM8YMVEq9Y4y5MT8//7HUuccj/rT+aUPnDgBRFM1yHOf6ddVfXV3dlWQrALdnZma+WlNT81IymTwhkUi84nneiVrrywBcA+CWVJHDfN9v2aiKwVrrFVrrHNd1K3/UQCMEvkX8tXokIQiCgc1/+GF0s9LSvU645ZarCOzt1NYelLN48YGtP/+8eXpFhQfAS1RX45RrroEoJQJcVnPxxVGUnr6sWWnp9R7wHVy39Ks+fd5Y2q3bHwW4A8BiAlUbup5N4XneI1rrH0TkTgAOycdEpDaZTP4DAEgGeXl5xZ7nrV3uySAIkolE4s66uroWSqm3AOy/Javby8rKft+qVasLReThKIpWkrzD87zXtdazSF7uOM5vReRLEbnAdu7bPwEuAfAvxLtZ8gh8t5EiqxGok3gh7HMA/i1ABePvd0i2g7d+EVrrFSKS6TjOVQBgjLkjDMMVAHIAICMj47P6+vo15kcnTZrU1Rizzj3cJE8meZlSalgymZzuOE4XEZlMshfJr0h2azjX87zXgiAwIrJPw7AyAKSlpfUWkR8tdBs3blwmyRySnfLy8qZprY8F8EJmZuYP9fX1lVrrTjk5OQ9VVlZOA3BLaqHYjzooY0ytiPQuLCwEgIUtW7Ysadi+tTEkd1rVoUPaqg4dKgg8AAD60Ue7iMiDItLX8/1miBcPdQSw2yennXbT3tOmTa1p2bJ31rJl6QBOQpwlL73zyy+j88svA8BFACDxqMTC1Ne3iFezL0p9fQngi035EOC67lTE0f0aK95YOd/3JyJ++moSqfn3B1Nfja+vHHFmQGsHIcBIxJ37FABeKuLkZiFQLfH6mFcQx7PYk0BZE1/qNsF28NYvpdm8efOajRkzpgoARo8ePbZHjx6rO9eBAwcuC8PwjSAIxonIkyTbRlF0Dcnfrae+asdxdomi6AKSC40xPZRSZwN4SETSlVJrbIVSSi0VEZaWln4YhuFYAPsZY1wRGdL4PK31UQD+JSJvAkBRUdEikncijn43ieQCANWVlZVpSP1xIWnCMKzRWp/uuu40ACgsLPRItiH5EMlyEcmtrKwsLSwsHJ6fn//exl6sKIredBznQpL7zJw5M7dXr15lADwAByilkoUFBc0HDx48H8D8goKC/R3HeX+fadP+oO+44wRjzDm+71+Yipvf/vVRo+7qMHv253s8//x3AHZBPFW1c+rr0NR/15iuE2AxUp094qHFLwDMBTBvU1b/jx49WnXv3n0ogCOVUosBPNY4YdAvJfXh6y4AfUSkLD09/U9Nse/e+uUJ8DvEoZ6fxU/s3BsQqBDgQsQLPP+EOBT1DsfOwVs/O611DxGZ63neGr9vYRgKyZ6u65Y0OvcEETlRRMqVUkXr6xSCIDgNwL3GmJsdxxkmIleSfEhEEgA6kLzN87x/peocbow5sH379leUlpZeB+Akkj/U1dWNGTp06Oq2UwvD3khLSztz4MCBpUEQjAGwr1KqG4DmIvIAgBPLysrOys3NvQvA+57nPQkABQUFx6biwX+B+A/PISLyoYiM9H3/3SAIDiB5K4AWnucdt4mv2yUichvJZiKSFBGHpKSnp59RX19/o4jMApAF4IDUlrWFqdd1NMkjRORtAAeLyALf969dXzupecndUl+7Ix4V6AigG+L9/R3x/38rDOKOfw7i7UazAfyP8WjAamEYTgCwQESeUkp1FZEbHMfJ/6WHyMMwnENyVRRFdyql9gEwSil13roSBFnbLgF+C2AsgOkABm5J575WvY8AOBfAvgQ+bYo618Hug/8F2A5+KwrDUJLJ5LAhQ4Y8AQATJ048P5FIjFu70/+/9u48vorq7AP47zlzLwk7YcddWy2LxaWu1beKWBdUKIHMTCJgUStuVau2fdW2KRW3qq2tiqYuKGLuzIQExIpvVYyIdd/aQkClrqhARDZJQu6d87x/nAmGkECAS+4lPN/P535IJnNnnjskc+Zsz9nOYy4holVa61yl1P5a66XRgjVTtNZDAQwEYDHzK0qp4m0lOCkvL98/lUpNcRxnPACUlJTEe/TocT2Aq4moipn3YuZPooQuM1zXndr4/cXFxbHBgwe7zNwDwJlKqa62bf+oUbzziejLMAyvbphiti0VFRW96urqxlqWNTIMw5eKiopuAczUtHXr1h0BoH7x4sXvNoygbxAEQf8wDAcCeL+152pJNH3ve41eAwF8n4kGk5kyhzAeX2slkwsAvP7ZccdVv3nhhSfkX3jh+EbxHMPMFzqO01KLTNqVl5cfl0qlZjmOM6BhW1lZ2XCt9aOO4+zTVnGIncPAaJg57P+AKdxb1c3VymP3B/A+gErawamarSCD7ET7xsxPx2Kxab7v3x1t6sLMLQ5uCYLAysnJ6TRq1Kj1Wzns8lgsNiaVSm0EUOu6buj7fnkymSwvKiqaGgRB96gftlmVlZW569at6z5q1KgViURiX6XUWgCb1lafNGlSsri4+MYhQ4YMb1xQNxNrBwBW9AAxIwiCDsycH31uIiKOWgcUM/ewLGuLVehKSko6DRgwoNPIkSM3m+aTn5+/CqbmUtJ4e9SX/2pL77dtezlMM3uLgiDoXlBQsK7xALcgCDoqpQY01LSLi4tj/qBB9xPRSUS0UWt9i+u6k33fr7Lq69F76dLFef/9b89uy5b16/uf//xPp1WrRuz76qtqn9deC9kMqJwP4JlFL7zwZtXJJx+0tXjSbePGjccppTarlRUUFMxrZm6+yFIMnAAzXuM1AGPTWbgDAAHLGbgNwBQGhhMwL53HzzSpwYs289hjj53VoUOH24lIx+Pxq0ePHv1M032Ki4vV4MGDbwNwIoBVRNQNwBVN58IHQXABM9/IzHlEtBGmMPsvESW11s8opSYy85cA+jNzseu6mx4mSkpKOvXo0eMNAPsQUQ6ADsy8Jvr3Y6XUzbZtl5aUlMS7d+9+KxEtcxznz01jDYKgOzM/REQ9YKaKJcMwvKCoqGiF53kPElEvIlrSpUuX369fv/46Ijqcmdc3tBAAwJw5c3rX1ta+QUQ9tNYppRRZlnX2mDFjXm16vuZMnz69b4cOHV4nom5RylgQ0Rm2bb/V0nuCIDgFwM0w0wj7M7NXVVV196BBg5YRUU8AIUwSrGuY+RIiWhaG4TWWZe1PRA+lUqn7LMv6Xe/evfcZPnz45wAwc+ZMW2vtFdh2jxWHH+7Udut29QEvvrgGpo8/ppWqWX3QQV/0Wrr0FgBPkBnot0tFYxPmOY7Tp2FbIpEYS0S3ua6bkcU/ROuxaSl6CWZu+wm76neGTTfXEpiBdkeS+f1PJ2mibwNSwO8GfN+/goh62Lb9B2DTIiJlHTt2HD5y5MgaAAiC4ERmvoqI9gHwJDOfBpNn/EOtdRURUd++fScOGzYsFc1nf8KyrAsbaqW+77+glFqptX4TwMVKqcu01n4sFvt+GIbvMvMzUWIbJqKKgoKCe5ubxuX7/qNEFDQMrIvi+pXjOCOjFKq/JSIbJrnNKmYu79ix4+SGzxEd49/M/ELD8rdBEDha6/tc1212emAzMSxSSj1dUFBwLQAkEonxSqk/O47Tu7n9y8vLB4Rh6Mfj8ZGjR49eEwSBpbWeqpQaAWCDbdsDAaCsrCxfax0w82rXdTcVkEEQ7K21fk8plWPbdrzxsYMg0LZtKwDwPO9uIor1+PjjeQcsWHBax+rq/H1efz0k5r4wc5dfAFABoJyAla35rDvC87z5RLQvTIKT/WEGKp7pOM6Lze0fddNMYuZeAN5WSk1LxwJBYvuwuVe/DCAXwA/JjPvYlec7F8AMmFaCbc4E2U6SqlaIyIjc3Nw7Gr4ZM2bMMmZ+oa6ubtO668x8NjM/xcyv2LZ9k+M4JwH4GTMniOgUIrqzYSrcqFGj1hPRNK31qY3OcdjChQuLmLkoDMMbCgoKniaiz+rq6g7XWicAhLZtD3Mc5xTbtu9prnCP0rUe0FC4A4Bt2y8RUc706dM7T5w4sc5xnBts2z7Ytu0827a/6zjOrxsX7gBARPtpraf6vv/bIAgc27Z9IqopLS0d2pqLRUR7NxTuAFBYWPgYgOTMmTMPbm7/VCp1MoDE6NGj10QxhwD+CDO6/ocN+0WD0L5pmubWtu3Po/SyVjSgEQDw8MMPD2b+9jK5rvtzAOVrDzzwwHfGjXv9neuvP5CYBwA4Ljpff5jpf18w8AwDFzDQqoea7eG67kla6zthFgDKZeahLRXuM2fOPCiVSiUAPAvgzugz+tH/tWgjDHQF8BSA7gDO3NWFeyQBk/HuwjY4V5uRPniRbbYoTIlIYfNms4YBZZseUJlZAQiJSIdhuPmUL5M6dotmN6WUVkoRAGitVU5OTjIMQ8XMqZ35ALm5ua1eMY6ZO8VisYVa66+YuZvneQ9prb9RStXtRAhERM3WOolIR9dqE6UUMTOItijHUgDySkpKOk2aNKkGMDX7MAzXEtHGIAg2eJ73JyLqBeACNkvWbuI4znMAnmtyzNei1w1sBuw5MK1qDwK4l80o6ekA5qZrpHRhYeG9MNOrtioMw6uZ+UrXdd+INr3ved6gsrKyowG8no5YxNYxEIepQQ8GcDqZWRq7HAGazXoRv2Fgvyi97W5PCniRVYhoTm1t7XXM/Dsi4kQicQARnbhhw4bihn2YeQ6A/wXQNwiC7+bk5KzYuHHjxdG0tCeVUr8KguA827brZ82a1aO+vv78MAzHNTrNm4MHD65QSj0ShuEtZWVlSWYeUFNTszgnJ+fxeDx+ZiviZM/zPgiCYLRt27MA07cd9bG3ajnSioqKE5PJZIyIHnNd9zwA8DxvqWVZB9i2/X5rjsHMH3ueN9V13UsBoLS0dBIAGjNmzCfN7R+LxSqTyWRFRUWFl5+fv6qysjK2cuXK65n5UyJ6g5kPIaKwrKxsgta6h9b6kR49enzm+/6TRNQ7DMOTLcs6raCg4OVEIjGPiK6KHqqmFhYW/rw1MTcg4D2Y/OB/YOCwL4444r6eH300KnfNmtHJTp3Cunj80Zy1a+8koGpbx4qmBl4BwNJafxSPx69MpVL3ENF+0diEt2Bq8Q0//0kz1+hApdTiJtsWa60Pwg4U8CUlJZ3y8vICACeyad74v6qqqvGTJ0/eqQfI9irK2/AQTJKmc8kM0GxLD8PMiZ+IdpIgaU9qepI++N1AlGP+RiL6McySj2Dmq5suJer7/nnMfC0R7Q1AEdFyZn6iqqrquiFDhlzIzBcCWA8gh5n/4LrupgF9lZWVudXV1S8DOFhr3UEpFddab4ianm93HGdKa2KdMWNGt3g8PhWmb1cDqI7H45fm5+e3qk85CILHmfkYmJaHvWBaKVLM3MNxnPg23g7ADLLLzc19CabJO2TmOq31iMLCwhaXxEwkEicrpW6EqSF3BTCjqqrq/iFDhnyste5HRJqIuL6+/ppx48bdXVpaeqJlWeOYeXXHjh3vGjVq1IrWxLY9fN+/EcDPuiSTPz79oov2XbPPPnf2+PDDgVYqBZjldR8AUEbAFi0bvu//HsDFzHyqUup9Iro1SmF8y8KFC4sPPfTQe7TWPyOiuwBcx8w3MfMFixcv7tu4sPV9/1YiWtC428X3fZ+IJtu2XRUEQX+t9ckAoLWuLCoq2uI6JBKJI2Kx2AVa6ySAM5l5Wbdu3fJTqVSHurq6p7XW37iuOyy9V699YDPw8zoA15Pps85EDE8DGATgIPq2pXBnySC7NiAFvMgK0UCuGdGo+hxmPtJ13YXRz85KpVJljuPs9NKxDUpLS69SSl0O02I313Gcy8vKylytdTGZRXReJqLz0jmYbPr06X1zcnISUYvAqlgsdvHWZgb4vr/csqz/GTt27KZpbbPvv/+9Y++//9X+7757PICDAayGab7/W+Nave/7X1qWNWzs2LFLAMDzvIkw/fsTXNct833/S6XUFWEY/sl13X0BIAiCRWEYFhcWFs5sOE4QBD2ZeQ4RVTDzB8w8iohWO47zS9/3TwBwBxFN11qTUmoCgF/Ytr2pW6KsrOwarXUxgL8TUQdmztdanxeNiwAzq7KysjW2bXdLy0VuR9hkkrsDwL1kcs1nKo4xAGYCOIPMvPt0kEF2QuwJpk+f3jcMw/8Q0dcA3iWiGIC3Z8+ePTgIgsHJZHImM/vpOp/neXcrpa5RSl2ilBqjlDrS9/0PmfmvRPRrZj6LiLpqrZs2Te+wIAi65OTkvMfMiwAM11o/EIbhs6WlpSe29B4iytFab9ZkvjEv78uXbrjh3zB99afCDH67BMBCBp5l4Cw297AcrfWHjY61n1KqhogalovNYeZ5SqlND01a65VossysbdtfE9EpAD4nooMBlDiO88vomH+Mx+Nn27Z9n+u6U1Op1NnMfHvj94dhOFlrPcRxnCIAVwJYrZT6a6O4NIAwypsgImyWS74dZhT7FRkO50mYWR3tYrCd9MEL0YZycnIma61ziegcAGthBhXG6+vrF0aD+550XXdius5HROO7du2634gRIxqS6xzn+77euHHjMRMmTGjIiX+253mfJRKJYwsLC1/b2XMy8zUA3mmY+gfg/dLS0ngsFrsDZhR9c+/5r1LqDzBjKxAEQRdmPrK2tnYimWs0D8A8BvrCFAgXw+Qkf3/wrFnrPho27HaYQhWpVOrpeDxe3Llz5yejwy8F8BwzVzU69g/QzE08asXY7AErCIKOzLwhSjoEACgqKvrK9/3aadOm5U6cOLFu+vTpBxLRN67rfhYd5/NoCqIVBEEH27brgyA4QwjLmHAAABo3SURBVGudcl1Xpt1FGCiASeL0JICJaWwW3yHRanPTAVzBQB8yuSJ2W1KDF6INEdFoIlKO4yjHcfIcx7GiDHF1juN0cF13TJrPh0aFewOOxWK5TbYtU0odkabTHqyU2mxgXE5Ozj/ZTJNrKc5RYRhe4Hnee57nvcjMy7TWD06YMGGzKVIErIz6Zw8CkA9g2aGet/+ZV1758w9POmn1Mzff/GYsFnsGwMKampqXPc+bz8x9mPkwZh7QcGwAD7mu26om0yhDYZfi4uJN98vo684TJ06sA4Dx48d/AqBT4xkKzHy1UqozMy/wff8trbWvlBq/xQn2UAycDVNrnw+zeEy2DD58CGZ9hgmZDmRnSQ1eiDbEzN2IaEOTbSuJaLPCL0rQczYzd1ZKvdx4QZ7tobVOlpaWnlhUVPQSsClzHimlDobJEtaQandIXV1dWvoctdbPM/P1jbelUqnLACxs6T22bX/OzP2CIBgfhmFehw4dLnIcZ0lL+0fZxmYBmMXA0Fh9/VUHLFgw/sD5849Mde68ILZhw+99z6uOBmtW27Zd6nneuUqp3pZlXdTQX99aRDRz8ODB95eXl99UX19PRPQbIvIb/Vz7vv+a7/vvJBKJi5RSOcx8AzNXMHNlLBbjzp07z2jmYWuPxIANU7i/BWB0c4MnM4WAJWweOg7LdCw7SwbZCdGGgiD4UGu9N4CPiaiSmY8losEAvnEcpxcAeJ73HSJKMPMjRLQOwBhmft513bu3evDmz+cw80PM/CyA9UqpkVrrp4hoFEwB/zmAkQCecxynMF2f0/O8d4moO4B/ENHhWutDOnXqdEjTXPvpFDXfXxK9+gF4EyZhTTkByZ06tpndMZaIRkZT3mY7jjOrcRIkZla+7/+FiM5iZlZKJWzb/s3OnLc9YuCnMAPPFgAYSWa2S1aJ0teCgFZNed0GGUXfBqSAFxk3c+bMc7TWT4Rh+JRSqjrK/T5Sa32Z67r3AYDneZ5S6ibbtv8DmIV3ALxYX19/5rhx47a7BhgtpHOFUqojM0+zbfutOXPm9K6rq7tKa92HiDzHcSrT+0mB0tLSQsuyfqy1rlqyZMldbTX/m4EcAIUwffKHA1gG4B4ADxDwdVvEIJrHwGUA7gbwfwDGpKkAzXYZK+D3JH8G4GU6CCGCIPhlEARJ3/d1EASpGTNm3Nzk51ukUvV9//ZEInFs20XZPjAwnIG5bDKVbWDgvmgRE9GGGFAM3MYAs+lW2ZNmEjwIICOLG0kfvBBpNHPmzIFhGJ7JzIsaJ9dpzLbt22GmBTWLmddVVFT0bZwwh4gGMvPH6Y+4faNvR98PBvALmObhSWxqkH8G8Bw1kx45E6ZNm5bbuXPnoQCwYcOGfzcM4NvdRc3d0wGMhUkZfOUuWLFNNEOa6IVIE8/zHlVKjWLmdwEcSESqT58+Bw8bNmy7btRBEJwUper9FYBqZp7IzHu5rjtpZ2NMJBJjlVITmHlj1A3QJrm+swWbvvlLYfrp+wBYBOAvAGZksrk4ejB8FKZfGgB+xMznua6btvwEmRBd79kAjgZwLQF3ZTikTJBEN0LsznzfH6aUOmvRokW9Hcc52XGc/Ynolerq6k0jrVvbxG7b9nxmvpKZz2PmG4nog8WLF1+ShhgfVkrdDeBfAJZrredHWd/2GASsIKAYJr3wRdHmvwH4lIEp0TKlbU5rfY9lWYWO41zrOM61WmubiLa5QE62SSQS+zZ8zcDxMKPkD4NZhnVPLNwzSmrwQqRBWVnZPVrrXo1HonuedwgRvcDMHxHRD2GSeCgAnzmOs19bxhfl36/u06dPn4YWhdLS0qGxWOx527abXTt+TxAtcHIqgKsAnAkz2t4HcBcBb7dFDHPnzs355ptvnrJtu/GSxvB9/xkiGhXNw89q0VoCv4BZYrjLob7/waDy8sEAPgZQQMC/MxpgZkkNXojdWTKZ/BzAvmVlZf/yfX9DIpH4LBaLFRBRTCl1fDwe/77jONaaNWv6ENGAIAiebsv4Vq9efSwzL2/cXVBUVPRv7OHjcAhgAp4l4KzVffse/tX3vve6jscLAbyVjMdfYWA07+L75JlnnlnPzDnN/KhjQUFB1vfDV1RUnATg8u7dux9sO85hYwsLnx9UXn74iqFD1856+OGY73me7/sXZzrOPdEe/cctRLoQUQLAzVrrpZZljSKiS8MwnMLM6wH8Jz8/fyEATJo06Svf9x8EcF5bxpebm/tOMpnsx8wqyomO8vLy/cMw3GyA2RNPPLFXXV3deKXUqrFjx04jol06GCqRSPxQKXUzEcUBgJn/4DhOuhb5aLXKysrYsytX/pGZH/3u88//bN8FC67sWl3909hXX1UA+IhNM/40AtK+kl5FRcV+APr6vv8JM3+llJrOzJ2Z+ZXG8+yzVX19/QVE5J9+xhnHASihMOy2yLa/qBo7thczOwR0AXC/7/uHOY6z011NbSkIgtEAfh2lkd7IzL90XbdNWnbSQWrwQqSBUmoygOXMnEqlUgEznwjgFSLqGC0oswkzE9p45HaUQe2NsrKyJUEQFHme9/NUKvUOM2/qF/U87666urpPiehqrfUdZWVlteXl5UfvqpjKy8v3tyzrdiIqsG37BAAjiOiXnue1eQax6urqHwH4l+u6Dx71t78t6bd48SVP/+UvI94+//xymIF4N8H00wfR1Lu0dG9WVlbGUqlUwrIsF8CdRLRWa30tgO/369fv+m29Pxt0XL1anXzTTacAqADwRU337icsGjOmJ4D3HMepdBznya5duw4CUJTZSLdPEAQnAji/rq5uuOM4J2qtxxPRfaWlpf0yHVtrZXsB3+LqU0JkkygbXZXruoNc1+3pOE5frfWt0drqgxoG2M2bN29vIrpQa/33to7RcZzhzPxItBiMq7W+yHGcyYBZUIWILk+lUsfatt3PcZwezPxAKpV6dlfFk0wmz9Ja323bdjUA2La9NgzDKUSU1nz8rXQggPcab9hIVLX09NOJgHMAfBdmtP0pAJ4D8D4Dv4qy5+2w6urqQwG8OXbs2Hccx/mr4zindOrU6XtE1HPYsGHZkpu9WdHc9p+dc/nlZ/VetOjg2ry8qQCOmT11qgUgnkqlpjXsO2LEiHXMjMa5+rMdMxdorYsnTJiwAQAKCwu/IKKHYrHYaZmOrbWyvYl+AfasgYBiNxWlgr208TbLsq6GGViz1LKsV3zfR3V1NRHRwsLCQicTcTqOczOAm5tuJ6Jzmfmbc889961G+14WBMFFTfdNFyLqGIvFNiYSiXsAHMnML1mWNZOZO23zzWmmtX4HZqDdww3bLMs6hYjeBgACPoIp0H8HM5/7IgC3AbiRgacBPAbg7wRs3J7zhmHYSSlV03hb165d62tra+M79YF2sWiE/F8BHEVh+NyCa65588ujj74UQKEFdCAinUqlShv2Ly0tHaqUSjV0D+0mOiqlmq4bUUNEbf77uaOyqYDfAKC5C9fQlCkFvchajuNc7/v+xb7vr2HmVwEMZOa9c3Nz9x81atQXmY5vW5LJ5AeWZW020KuysrLLypUrW3rLTtNav5JKpV5SSoGINDMfw8y/iMfj52zrvcXFxbF0pr51Xfdtz/PWep43jYieAXAIgFPr6urOaLxftCjKDAAzGBgEkzinCMAoAKsZCKKf/7M1CXQ6d+78bm1t7V2PP/543rnnnrsaAFasWHEBEc1P12dLJzapf/8A06rxKcz0t3LceScAXNewXxAEU3Jzc98PgmAmEeWEYTg6DMNMr/W+XZj5WWa+BObBD5WVlbHq6uqfKqV2m3EE2VRoHgrgEQC3ApgZbWOkL0aZJid2Od/3b4fpWvqsb9++5w8bNuybTMfUWr7v1wH4h+M4o+bOndtn/fr1i4noI9u2d0k/vO/7y4moL0xB8R4z/4iIcrTWvuu6Wyx8Ey3m8gIRHUFEKWauB1DgOM4WqX13VBAExzPzocy8sl+/fk9tq5nc87zjFPOte7/5Zo/9FyzYa6+33+5CqVRHAB8CKIdZs/6fW8vcFvX13sHMS4mov9b6s27dul08YsSI7WoN2JXYdE38HNGDDIA7ANxNQIu/32VlZT/UWk8EEFqWddf2ruCXDTzPm6yUOjX6vxmstb7Tdd3tTXkui81EusMU8v+FeRqshxTwQmwhCIIuUSKc/YloCRHNsG27fiv7/5iZ/5eZcy3LqigoKLiz6T6lpaUDY7HY8wD6MDOI6GXbtk/aVZ/B8zzWWt8Vi8WuV0oN0FqvBLCGmVc6jrNXM59httY6z3GcYUSky8rK8rXW0/r27dtve7MFpkNpaWm/WCxWAWCMbdvL586dm1O3cuVjPygpWbrfK68MBXAagDjMyPvZMIPQXiBzX9tMSUlJPC8vb0AqlaopKiraZSvubY9o0Z4imBrsUACrYFLN/omAtZmMrS3NmDGjW4cOHXpt2LDhyx1MHywFfCMKwK8BnA7gJEgBL8RmosL9/wA8wMxVAI4mop/07dt3RHM1zmgO8i1KqVuTyeQapdRVRPSJ4zhnbHHwNuT7vmbmKqVUdTT46i0i+jkzL3Mc58Cm+3ue9/XatWv3mTRpUk2jYyxSSv2Wmccx8zlEBGauZeaxLa0FkC6e57kAerquO7XRtkFEdLXjOD9jIA9mKd4xAH4MIBfAOpg8+M8BeJGaDOzLNAYsmNq6C2A0zGdYDDPA8DECarbydtG8jBXw2dQH30DDXIxXAQzPcCxCZB1mPp+Z/+a67vRo0xtBEHSrrq7+Cb7t3tqEiKYopY4ZO3bsB9H7HygrK/s6CIKetm1vdflU3/fPYebzlVKrunXr9tszzjjjy3R9DiJKRs2epbFY7BGt9W3MHIvH4z9tbn+lFOXl5W32AMPMSa31Fcx8rFLqMNu2q3zfv10p9dTcuXP3GjFiRHW64m0mnjgzJ5tsSzKzBQBkmrIfBfAoA51h7mdnRi8bANh0TzwHM6D4dQBLyNwD20z0IPJjAGcAOAtmZsA3MC0OjwGYly0L8ojtk81TFioB/GY739MbwA9aePWDaS4TYnd3iNZ6s0VimPkdAN9rYf9YQ+EOANFI5s+Z+YStncTzvDIA9xPRcq11lzVr1nxQVlaWzofupVprJiInDMN/MPORRLQmlUr9p7mdmfkdZn6k4fvy8vKjlVIHATgGQL5t21UA4DjOL5l55dq1a69r7jjpEobhC0RUNH369M5RfMTMVxHRk033JWADAXMIuISAA2D+ry6DydWeD2AazHz7NQxUMnAHA+MYGMrmvpYWDMQZGMzABAbuYfNQsRImPW8+zIPGOAD9CTiPsmi1PbH9srEG39TJMIV9a5rqB8E8gTanD8zAFyF2d4styzoWm+f3Pg4t5Ptm5mQQBIc3rBxXXFwcY+b9ampqFjS3PwAEQbA3M59WVVXVq2G0ehAEZ0UF7L4tvW97MPNXtbW13+nYsePtRNSLiEqYeQQRdQewRcsCEY1k5rc8z1tLRDVhGHYGcDERTaupqVncZN+1lmVt0Y+fToWFhZ8FQfDn3NzcF3zf/zQIgn0BzLFte9a23kvA+zCvqVEq3ENgHlSOhqmQXAxT6wcAsGna/xAmt/vnMIXyF2i5L7wDTE18b5jKTY/oHAfi24rOOgBvAvgjgGdgBgNm9dx7sX2ysQ9+V7FhnoSnbmtHIbLZnDlzOtXW1s6FaUJ9C8BJRHQ8gJ/Ytr3FaG3f988joru11vdalvWV1voKIlrCzP8G0IWZ5zuO4zdOi5pIJM5XSl3qOM5RTY611nGc7un4HL7vP0ZEU23bfgUAKioq+iaTydm2bZ+wtRStQRB06datW9eG7oIgCJYw82rHcY6Pvu/JzCvi8fiw/Pz8l9IR67bMmjWrRzKZXN/c9d8RjQr9w2CS7BwUvfaGqaz0aOWh6mAGxy2HeaB4L3r9C8B7bd0dsIeSQXZtQAp40W4EQdABgKO1/h4RvVNVVTVr8uTJLd6sE4nEEVE63c7MPJ+IhmutfxOPx6vDMJwAoLvjOJc17D979uzBGzdurHQcZ1NazpkzZw7UWr9o2/ZOZW9rEI1Cn87My2BWITtKa32V67pvbM9xgiDoqbX+FKZQXEdEvZn5767r/iQdcbaVkpKSTnl5ecOYeX1VVdXLW5vnz6b1tSdMnveOMAP4GqyGWRXvazL5RURmSQEPM9DjVzD9QANgRnMuAzAHwI0wzUk7Qwp4IQD4vv+E1vqSwsLCL7a2zfO8fxHRKiK6MwzDfkR0h9b6uqKiopJ0xcLM5Pv+QKVUbMOGDR/s4DQkAEAQBA4zHxCG4RNFRUW71Zzr0tLSQqXUA0qpT5i5IxHlhWF4SmFh4TuZjk3sNBlFD2A6TP/SKACfwDx87APg/Ohnu9XTuBDZiojyGhfkAMDMVZZlHQTTrwsAWLx48Q8OPfTQu7TWf1FKfQPg/KKiotlpjoWnTZv2UTwe77AzhTsA2LbtpyuutmZZVonWerht268BZmqjUmo2gP0zHJrYjWVTDX41zGCQpkkgCGYqyc4O7JEavBAAPM/zAExxXXchYGrRQRC8EI/H8/Pz81e1VRzRfP57AXyHiDYAsLTWk1zXbfOaTiaVlpYOtSzr747j7Nd4exAEa2zbbm1fu8heUoMH8E8AdwK4B6ZAZ5hC/QIA727lfUKI7fM7pdTjnuc9SEQrgiAYB2BuWxbuAMDMtxLR3Iaat+d5g5RS0wD8qC3jyLTOnTuvqK2t7ZjpOET7k03z4MfDZEmaA6AaZuTnXJgpHeMyGJcQ7Yrruu8nk8nTiKiOiPYnoimO49zW1nEQ0dDGzequ6y5m5mVBEOzd1rFkwsyZMw/yfX+Y1nojEdV4nvdXwAyg9Dyvkpnf2tYxhNiabKrBr4ZJUfvrTAciRHsXrVz2aKbjaEYMW1mYpT2orKyMrVix4tEwDGMAPksmk79TSv1Zaz0uCILVzExKqfkACjIdq9i9ZVMBL4TYgzDza57nTXJdtwQAPM87GkAv27aXZzi0XWrFihWXK6VesW37HgAoLi5WQ4YMeZqICmzb/ijT8Yn2I5ua6IUQe5CamprfAhjk+/6bQRD8k4iuJ6IJmY5rVyOi/0mlUmUN30+ePFlrrZ8AcHwGwxLtkNTghRAZEU2LuyrTcWTA17FYrBfMMrIAAKVUb2beo2YPiF1PavBCCNGGtNYPMvMfgyDoCQCJROIoZh5eU1MzP9OxifZFCnghhGhDhYWFrwG4C0AiCII3lFKXaK3H7WyiHyH2ZDaASzMdhBBCiD3KgwC+k4kTSw1eCCGEaIekgBdCCCHaISnghRBCiHZICnghhBCiHZICXgghhGiHpIAXQggh2iEp4IUQQoh2SAp4IYQQoh2SAl4IIYRohyjTAbSh0wHcDWBdpgPZTgcC6AiAMx1IlokDSGY6iCwk16V5cl22RAAsAKlMB5JlLADLAXyVpuN1B3ACgJVpOp5oR+4BMCTTQWSheZAWqOZUZjqALJQHoCLTQWShEwBMyXQQWehCAOMyHUQ6yA1SCCGEaIekgBdCCCHaISnghRBCiHZICnghhBCiHZICXgghhGiHpIDPfiFkGktzNmY6gCwl12VL8jfUvBTMtRGbS0F+X0Qbycl0AFkqN9MBZCm5Ls2T67IlAtAh00FkoVj0EkIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGE2D2NArAQwBoALwI4JLPhZJ1DAWzIdBBZJAZgKoBqAP8EsHdmw8kaJwF4F8D66N8fZTacjLIALGlmex6AJwF8DWBO9P2epKXrIvdgsUvsB3NDOh5ARwDXwty0hdEdwJsAONOBZJFrAcwA0AnA7QAezGw4WeMzAAUA4gBsAJ9mNpyMuRLAa2j+b+ZWAPfApMW+B8AtbRhXprV0XeQeLHaZkwE80Oj7PgC+ykwoWYcAzAIwFlLAN/Y2gMOir7sC+EEGY8kmiwBcCFMrvQBAVWbDyZhhAM5G838z7wEYGH09MPp+T9HSdTkZcg8WbcACcB+AezMdSJb4XwB3RF9LAf+tVTA1sa9hWje+n9lwssZRML8nDa+jMhtOxjX3N/MNTC0V0b/r2i6crLG1e4ncg8UucSpMzexWyOpGgHnafgGmuRWQAr6xJIDbAAwAMAXAq5kNJ2vMw7fX5Y8AnstsOBnX3N/MBny72l4n7JljW1q6l8g9WKQdwfSDycCOzU3B5rWxhteJmQwqS3wBU4gBQH+YWpkw16F/9HUvmH7VPVlzBdkHAA6Ovj4YwPttF07WaHpd5B4sdpkTYEZ19gDQpdFLbE5q8N+aBuA6mIFSv4Np6RDAywBugPn7+QWAlzIbTsY19zfzJ5jCrKFQu71NI8oOTa+L3IPFLnMDmq+pis3JNflWfwDPwkzpmQ/gu5kNJ2sMhBn9vD76d+DWd2/3mvub6QHgKQDLYKbJdW/TiLJD0+si92AhhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEKIHcQtfC2E2A2oTAcghNgt3JbpAIQQQgiRHlJrF2I3JjV4IQQA9ATwOIBVAJYCuKLJzxsX9ucD+BLAV83sJ4QQQogs8hhMAd8NQGcAj6DlPvjVAL4P4BAAz7ZRfEIIIYTYAasA9G/0fX+0XMA/AeBJAAUAYrs+NCGEEELsqGpsXsD3Q8sFPAE4HUACUoMXQgghstqjAGYA6ArTRP8wWi7gP4Zpnh8E4Os2ik8IIYQQO6AngFKYpvr/AjgPLRfwl0b7rQBwQVsFKIQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQojd1v8D8TPU6tqgP8MAAAAASUVORK5CYII=" alt="plot of chunk 9d"/> </p>
<p>The summary shows that all terms in spline fit are significant. Plot shows that the spline fits data well except at the extreme values of \( dis \), (especially \( dis > 10 \)). </p>
<h3>e</h3>
<p>We fit regression splines with dfs between 3 and 16. </p>
<pre><code class="r">all.cv = rep(NA, 16)
for (i in 3:16) {
lm.fit = lm(nox ~ bs(dis, df = i), data = Boston)
all.cv[i] = sum(lm.fit$residuals^2)
}
all.cv[-c(1, 2)]
</code></pre>
<pre><code>## [1] 1.934 1.923 1.840 1.834 1.830 1.817 1.826 1.793 1.797 1.789 1.782
## [12] 1.782 1.783 1.784
</code></pre>
<p>Train RSS monotonically decreases till df=14 and then slightly increases for df=15 and df=16.</p>
<h3>f</h3>
<p>Finally, we use a 10-fold cross validation to find best df. We try all integer values of df between 3 and 16.</p>
<pre><code class="r">all.cv = rep(NA, 16)
for (i in 3:16) {
lm.fit = glm(nox ~ bs(dis, df = i), data = Boston)
all.cv[i] = cv.glm(Boston, lm.fit, K = 10)$delta[2]
}
</code></pre>
<pre><code>## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
## Warning: some 'x' values beyond boundary knots may cause ill-conditioned bases
</code></pre>
<pre><code class="r">plot(3:16, all.cv[-c(1, 2)], lwd = 2, type = "l", xlab = "df", ylab = "CV error")
</code></pre>
<p><img 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" alt="plot of chunk 9f"/> </p>
<p>CV error is more jumpy in this case, but attains minimum at df=10. We pick \( 10 \) as the optimal degrees of freedom.</p>
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