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November 20, 2019 03:59
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# 흔한 실수\n", | |
"- random variable 정의하지 않고 확률을 논하지말라.\n", | |
"\n", | |
"\n", | |
"- correlation(상호관계)와 causation(인과관계)와 혼동하지말라.\n", | |
"\n", | |
"\n", | |
"- 가설 검정이 실패했다고해서, null hypothesis가 무조건 true이진 않다.\n", | |
"\n", | |
"\n", | |
"\n", | |
"## 귀무가설(null hypothesis)\n", | |
"귀무 가설(歸無假說, 영어: null hypothesis, 기호 H0) 또는 영 가설(零假說)은 통계학에서 처음부터 버릴 것을 예상하는 가설이다. \n", | |
"\n", | |
"차이가 없거나 의미있는 차이가 없는 경우의 가설이며 이것이 맞거나 맞지 않다는 통계학적 증거를 통해 증명하려는 가설이다. \n", | |
"\n", | |
"\n", | |
"예를 들어 범죄 사건에서 용의자가 있을 때 형사는 이 용의자가 범죄를 저질렀다는 추정인 대립가설을 세우게 된다. 이때 귀무가설은 용의자는 무죄라는 가설이다. 통계적인 방법으로 가설검정을 시도할 때 쓰인다. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 1, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"from IPython.display import Image\n", | |
"Image('./null_1.png')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Random Variables\n", | |
"랜덤으로 일어나는 사건(random experiment)의 가능한 모든 결과에 numerical value를 할당하는 것.\n", | |
"\n", | |
"예) 동전을 던졌을 때 앞을 1, 뒤를 2로 할당한다면 random variables\n", | |
"\n", | |
"\n", | |
"**But**, 동전을 던졌을 때, 앞과 뒤의 결과만을 본다면 random variable이 아니다.\n", | |
"\n", | |
"\n", | |
"- Discrete(이산)와 Continuous(연속) random variable 두 가지가 있다.\n", | |
"\n", | |
"\n", | |
"## Discrete Random Variables" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 2, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"from IPython.display import Image\n", | |
"Image('./dice_1.png')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"주사위를 굴렸을 때 나오는 눈에 대한 random variable.\n", | |
"\n", | |
"결과는 1, 2, 3, 4, 5, 6 즉, 이산값.\n", | |
"\n", | |
"모든 확률의 합은 1.\n", | |
"\n", | |
"이것이 P(X=x) : probability mass function.(이산 확률 변수에 대함)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## pmf의 평균\n", | |
" $$\\mu = x_1 \\times p_1 + x_2 \\times p_2 \\dots x_n \\times p_n = \\sum_i x_i p_i$$\n", | |
" \n", | |
" \n", | |
" \n", | |
"## 분산\n", | |
" $$\\sum_i p_i(x_i-\\mu)^2 = Var(X)$$\n", | |
" \n", | |
"## 표준편차\n", | |
"$$\\sqrt{Var(X)}$$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Bernoulli\n", | |
"경우의 수가 두가지 밖에 없을 때의 확률.\n", | |
"\n", | |
"ex) coin flip. 앞(1)이 나올 확률을 p, 뒤(0)가 나올 확률을 1-p.\n", | |
"\n", | |
"# Binomial Distribution\n", | |
"Bernoulli trial을 여러번 반복했을 때의 확률. \n", | |
"\n", | |
"예) 동전을 n번 던진다고 했을 때, 앞이 나온 횟수가 x번인 확률. \n", | |
"\n", | |
"$$P(X=x) = \\frac{n!}{x!(n-x)!}(p)^x(1-p)^{n-x}$$\n", | |
"\n", | |
"$$ E(X) =np \\ \\ \\ \\ \\ \\ Var(X)=np(1-p)$$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Possion Distribution\n", | |
"np->$\\lambda$일 때의, binomial distribution의 한정된 버전.\n", | |
"\n", | |
"특정 시간 주기 안에서의 일어난 사건을 다룸.\n", | |
"\n", | |
"$\\lambda$ : 단위 시간 내에서 발생한 사건의 수.(주어진 파라메터)\n", | |
"\n", | |
"$$ P(X=x) = \\frac{e^{-\\lambda}\\lambda^x}{x!}$$\n", | |
"$$ E(X)=\\lambda, \\ \\ \\ \\ \\ \\ \\ \\ \\ Var(X) =\\lambda$$\n", | |
"\n", | |
"np->$\\lambda$는 이미 알고 있음을 가정.\n", | |
"\n", | |
"\n", | |
"예) 기현은 하루 평균적으로 7개의 메일을 받는다고 하자.\n", | |
"그렇다면 어느날 기현이 3개의 메일만을 받을 확률은??\n", | |
"\n", | |
"-> 여기서 $\\lambda$=7.\n", | |
"\n", | |
"-> 시간을 무한히(엄청 잘게) 쪼개서 그 구간을 생각한다면 => binomial" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Continuous Probability Distribution\n", | |
"연속 확률 변수의 값은 실수 집합처럼 연속적이고 무한개의 경우의 수를 가짐.\n", | |
"=> 결과 값들이 무한대의 연속적인 값.\n", | |
"\n", | |
"ex) 시계 바늘.\n", | |
"\n", | |
"시계 바늘을 눈 감고 돌렸을 경우, 정확히 정각에 맞췄을 경우의 확률은?\n", | |
"\n", | |
"=> 이 확률 변수의 확률 분포가 0이상 360 미만의 구간내에서 균일 분포를 가정한다면 답은 **0**이다.\n", | |
"\n", | |
"시계 바늘이 가리키는 각도의 값은 0도~360도 사이의 모든 실수 값이 가능=> 무한대.\n", | |
"=> 따라서 각 경우에 대한 확률은 0.\n", | |
"\n", | |
"\n", | |
"이렇게 경우의 수가 무한대인 연속 확률 변수의 분포를 설명하려면 특정한 값이 아니라 구간을 지정해 확률을 설명해야 한다.\n", | |
"\n", | |
"\n", | |
"\n", | |
"### 누적 확률 밀도 함수(cumulative probability density function)\n", | |
"- $\\infty$ 에서 x까지 구간 내에 존재할 확률.\n", | |
"\n", | |
"$$F(x)=P(X<x)$$\n", | |
"\n", | |
"\n", | |
"### 확률 밀도 함수\n", | |
"누적 밀도 함수의 단점은 어떤 값이 더 자주 나오던가 혹은 더 가능성이 높은지에 대한 정보를 알기 어렵다.\n", | |
"\n", | |
"=> 확률 변수가 나올 수 있는 전체 구간$(-\\infty$, $\\infty)$를 아주 작은 폭을 가지는 구간들로 나눈 다음 각 구간의 확률을 살펴보는 것이 편리하다.\n", | |
"\n", | |
"$$f(x)=\\frac{x}{dx}F(x)$$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Central limit Theorem\n", | |
"많은 수의 independent random variables을 합치면 대략적으로 normal distribution을 가진다.\n", | |
"\n", | |
"ex) 사람마다 가게에서 한달에 소비하는 확률분포는 매우 다양하다. 하지만 사람의 수(case)가 적절히 크다면 이 분포는 대략적인 normal distribution으로 수렴한다.\n", | |
"\n", | |
"\n", | |
"## normal distribution\n", | |
"중간이 $\\mu$ 즉, 평균이 되고, 평균을 기준으로 대칭을 이루는 분포. 폭은 분산에 영향을 받는다." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Summary Statistics\n", | |
"매우 많은 양의 정보를 최대한 간편하게 나타내기위해, 관측 집합을 요약하기 위해 사용. \n", | |
"\n", | |
"- Sample Mean\n", | |
"$$ \\bar{x} = \\frac{1}{n}\\sum^n_{i=1}x_i$$\n", | |
"\n", | |
"\n", | |
"- Quantiles/Percentiles : 데이터의 순서. 확률 분포를 동등한 확률 구간으로 나누는 구분 눈금들. Quartile을 주로 사용 => 4구간으로 나눈 것. 25%, 50%, 75%.\n", | |
"\n", | |
"\n", | |
"- Sample Median : x들의 중간 값.\n", | |
"\n", | |
"\n", | |
"- Sample Variance\n", | |
"$$ S^2=\\frac{1}{n-1}\\sum^n_{i=1}(X_i-\\bar{X})^2$$" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 3, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"from IPython.display import Image\n", | |
"Image('./quartile.png')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"- Range = $X_{min} - X_{max}$\n", | |
"\n", | |
"\n", | |
"- Interquartile Range=IQR=$Q_3 - Q_1$\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 4, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"from IPython.display import Image\n", | |
"Image('./box_plot.png')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Z-score\n", | |
"평균값과 얼마나 거리가 먼지 계산해주는 통계적 예측값.\n", | |
"\n", | |
"$$Z=\\frac{X-\\mu}{\\sigma}$$\n", | |
"\n", | |
"\n", | |
"밑의 분포처럼 내가 어디에 위치하는지 예측할 수 있다. 예를 들어 점수에 대한 분포라고 한다면, 내가 2.5%에 속하는 부분에 속해 있다면 나는 전체중에 2.5%라고 알 수 있다." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 5, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"from IPython.display import Image\n", | |
"Image('./z_score.png')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Covariance(공분산)\n", | |
"확률변수 X, Y가 어떠하게 퍼져있는지를 나타내는 값.\n", | |
"2개의 확률변수의 상관정도를 나타내는 값.\n", | |
"\n", | |
"- 양의 공분산을 가진다. 두 확률변수가 같은 방향으로 움직인다.\n", | |
"\n", | |
"\n", | |
"- 음의 공분산을 가진다. 두 확률변수가 다른 방향으로 움직인다.\n", | |
"\n", | |
"\n", | |
"$$Cov(X,Y) = E([X-E(X)][Y-E(Y)])$$\n", | |
"\n", | |
"## Sample Covariance\n", | |
"$$\\frac{1}{n-1}\\sum^n_{i=1}(x_i-\\bar{x})(y_i-\\bar{y})$$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Simpson's Paradox\n", | |
"작은 데이터 집합을 큰 집합으로 확장시켰을 때, 즉 작은 데이터셋에서 어떠한 결과가 산출되었는데, 이 것을 더 큰 데이터셋에서 예측할 때, 정반대의 결과가 나오는 현상을 말한다. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 6, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"from IPython.display import Image\n", | |
"Image('./simpson.png')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"각 각으로 봤을 때는 Treatment A가 더 효율적으로 계산되지만, 전체적으로 봤을 때는 Treatment B가 더 효율적이다." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Confidence Intervals \n", | |
"sample data에서의 평균이 $\\bar{X}$라 할 때, 이 $\\bar{X}$이 전체 분포의 평균으로 부터 어느 정도 떨어져있는지 알고 싶을 경우.\n", | |
"\n", | |
"=> $\\mu$와 가깝기를 희망." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 8, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"from IPython.display import Image\n", | |
"Image('./conf_1.png')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"전체 분포에 대한 평균 $\\mu$는 1-$\\alpha$의 확률로 위 구간에 있다는 것을 말함." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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CstHc3MzWrVtZsGABCxYsaDWNXwSw9+7dm5/85CfMmDGDuLg47XhyAks5FYM+59GZrlvV+W+PPi2DLIaFmNLnBAMoLi7mueee49NPP6WioqKV+EpISOCaa67hmWeeIT4+XrNIykJNFlWqHVO0R3vPuqo7rVGiSsfZ3A4Vr6D4LgSyVEBgl5u8PMnJkyf55JNPeP/99/nqq69azfIymUzExMRwxRVX8OijjzJo0CCsVqufq0l/Hfrzq/r7/aAvi0ALMBsMBiorK/n3v//N/Pnz2b9/v58g8/l8REREcMMNN/Dzn/+czMxMLW6urfxVqv1StMXZ9Imq3ihRBbQfrwK0Ginqk/2Bf2xDWzEpCoWMvk7pUx7oaW5u5sSJE7z22mssWrSIY8eOaccRxwgLCyMrK4ubbrqJBx98EJvN5meNkkVVoHosf6f4/hHWJ2htMaiurmbDhg08//zz7N69m5aWllZt1P3338/s2bMZMmQIFotFO6YcOycnBdUnb1VcfLSVxkX/OtDgS7UbYPq+L6C7IQssfVCvaogU3wbZLaMXOqIDrKmpYceOHbzxxhusXbuWurq6Vhaq+Ph4rrzySm699VauueYav/xVbQUoq0awayPXByGIhSvYbrdz9dVX06NHD37729+ye/duamtrNZHk8/l49913tcD3IUOGaElj5eOKuqG3iikuXmR3sYycuV/fVql6cxrjU0899dT3fRFdHVlI6Rcx1SfVC7SvQqFHb1HQp04Q9SYoKIjjx4+zbNkyXn31VVatWoXT6fQTSWJ5mTlz5nDfffcxevRov1QL8raBclspui6B2ha57CwWC4mJiWRmZlJWVkZFRQVNTU3atl6vl8LCQpqamsjMzCQ2NtbvOPolhvTxVoqLEznsQF//9Jn69a8vdpSlirYXf5URIz9hjpdXlRf7ie+UxUpxJvQjPJPJpAUby7FP+/bt41//+heLFy9m//79fvsbDAbsdjtDhw7lvvvuY9y4cVowuqifsrg603WIa1F0HfQLNMvCWLZgjRkzBo/Hg9lsZvny5TgcDi1H2alTp1i1ahVms5nf/e53REVFaXnI5GWPAsXbKS5OAs0SlSfDyCEF7RkVLkaUqJLoSKUItFCsPk5FoTgTgWIR5MzaDQ0NHDp0iBdffJF169ZRWloKnK5/QnilpqZyzTXXcO+99zJw4EAsFovfDEEZfZoFRfdDdF5yJyYEkcFgYPTo0bS0tGAwGPj3v//tt31xcTHLly8nMjKShx9+mPj4+FaWBv0MRIVCFk/gb5USnptARoSLuf4oUXUGRIWqrKzkwIEDHDt2jOjoaC6//HKSk5O1iiU3bnBxVypFx5Fdy6ITrK2tZevWrfzxj38kNzeX+vp6bVvR6Q0cOJAf/vCHzJgxg9TUVMxmc6vp8mJKflu5iVQd7fro41fcbrdmgZI/F9bO0aNH4/F4OHnyJOvXr/fbpqSkhH/84x/07t2ba6+9lqSkpICxMQqFfnJWWVkZ+/fv5/jx48TGxjJ06FBNmLfnmbkYU69c9KKqvUA78V1jYyMrV67kD3/4Aw6Hg/j4eJ5++mmtURL7ynl+9CM+UUFFJyc3ZoGCh2XTqvjsYqqYFyrChSwHC8tLzpw4cYJly5bx97//nYMHDwYMFM3OzuYnP/kJ11xzDTExMa0mTcjxWPJ/RfdDbhPayyEm6lBoaChjxozBZDJRVFREUVGRFpbgdrupqqriueeeIyIiguuuu46QkBDN9ayPlQmECkz+fulsd31b6VTkzx0OBytWrGDu3Lk0NjYSExPD3LlziY+Pb5UbT7Z4ymtPBjrfhRro3mVbW3n0HmgUpf9eP+2zvX3bO2egz/bv38/GjRs5cuQIxcXF9OrVi6ioKD+zOXzTeYmOUB/cLnd68ud6gdXetHpF18fr9WpLjoj3Is+U3qIpvz9+/Djz58/n2Wef5cCBA37Z0wHCw8MZP348L774IjfffDPR0dFtBriL1/o6quhe6IOAZWEl/4lZWT6fj/DwcIYPH86f//xnevfu3SrI+OjRoyxYsID169cTFBTkt+C2onvR0b4xUJ94pn1F3dq5cydffPEFhw4doqKigksuuYSoqCiCgoK0xLKiDonXXq9XE1SyN0ffJgrk9rG7W027pKWqrZt6ppvdkf06EpQub+vz+di8eTPr168HwGQyMX36dPr06aNVChEMHBQURF1dHfn5+Wzfvp3CwkJKSkowmUwkJCSQnp5OcnIyo0ePJiIiQqtYavHaCwc5eBhaZy6XGxXRaLW0tFBRUcETTzzBmjVrtGnxgqCgIBISEpg8eTIvvPACoaGhfkJeP6BQIuriQ7Q/goiICK6//np27NjBRx99xJEjR/y2Xb16NT169KBXr14MHDgQaO3yESiXcdfgTP3b2ZRNR/o/0UZt3LiRnJwcLR3H9OnTSUtL044jrOyirXO5XBQXF7N9+3YOHTrE8ePH8flOp3xJSUkhLS2N7OxsevTooXl3RB8a6Lq6W53rcqKqrYe6s9Wr3i0XyE0HUFRUxK5duygoKCAkJISMjAyys7OJjY3VrqmlpYV9+/axYMECVq5cSWFhoVa5RGWRUzH07t2bOXPmcPPNN9O3b1+AVtYp2ZWo6F7I9VW2XoqM6DLNzc0cO3aMe+65h//+9780NjZq34lGrGfPnsyePZvHHnsMq9WqjeqMRqNWv/QWjbauS3HhIcpeLIgtLKXBwcE8+eSTNDY28tZbb1FbW4vJZNLq4ooVKwgJCeFvf/ubVo+MRqOfUG+rzlyMsTLfJx3p/9rbJlAf2l7ZijpVWFjIzp07KSgoICwsjP79+5OdnU10dLRfX+12uzl69ChLlizh3//+N19//bXfOfTnTkpK4o477uDuu+8mLS0Ns9l8wdSlLpmnqiNui29TAIH2ae84BoOBd999l1WrVlFeXk5iYiI/+9nPGDJkCKGhoRiNRqqrq1m+fDlz5sxh/fr11NbWEhwcjM1mIzw8nIiICEJDQ7XGzOPxUFVVxfr16ykqKiIlJYXk5GS/zlF2Eyr3TfdCX06B3HFOpxOAhoYG1q1bx//8z/+we/du7XMx8jMYDGRlZfGb3/yGOXPmEBISoglt0fkBrVxCnR13oegeyGUvEr+azWZiY2Npbm4mNzdXmx0Ip2NlGhoaCAoK0maPBnJLi/fiHPpzKroebbn2BGeKmxPb/uMf/2Dt2rVUVlbSs2dPHnroIbKzswkJCfFrz77++mvuvfde3n33XcrLywkNDSU6OlrrB8PDwwkJCdH6wIaGBjZv3kxOTg59+vQhNTVVa/O6u2W0S1mqzjb+qaOjKbGNbJGSCRRI5/P5aGxs5PPPP+fIkSMEBweTmprKzJkzsdls2vkbGxs5fPgwPp+PxMRELrvsMsaNG8eoUaNISkrCZrNp2bCXLVvGihUraGhowO12s3btWgBeffVVYmJiNJeRLKzaujfdsbJdLLQ1OhOfWywWqqurWbhwIa+88gp79+71szIZDAasVivZ2dk8++yzDB48mODgYO2YIvYAWgsqxcWNvh60tLRw+eWXc8stt1BYWMgXX3yhhS0IS8QLL7zAkCFDGDRoECEhIZrFSlmjugZtucTOJkzmbPpWEWdXW1vLqlWrOHbsGFarlbS0NG688UZCQ0P96obL5SInJwev10vPnj3JyMhgzJgxjBs3jtTUVCIiImhsbGTv3r18+umnrFmzhvLyclwuF3v37uW3v/0t7733Hj179vQT9t2VLm+pgtYz4NrzvZ6NdUt/fPk8DoeDVatWsWjRIkpLS0lLS2Pq1Klcd911WnCe6ODcbjdJSUk8/PDDPPDAA1x11VWkpqZit9sJDg4mJiaGrKwshg8fjtls5tChQzgcDlpaWjCZTGRkZJCWlqbNwjnTdbf1meL7p72GTsQoFBUV8eqrr/L2229z4MABvwbSaDSSkJDApEmTmDt3LpmZmdqoUBxHxCCIz/QB7crCefEiyly4+ITojomJIT4+ni+//JKmpibtO5/Ph8PhoKioiKysLJKSkvxiPM9kOVD16/ygF7jf9r53tE2ora1l5cqVLFq0iMrKStLT07nuuuuYMmVKwNnEHo8Hu93O7bffzsMPP8w111xDnz59sNvt2Gw27HY7GRkZXHvttYSGhpKfn8/JkyfxeDy4XC569+5NamoqYWFh3+n3dQW6pKgS6ANwXS4XNTU1lJaWUlFRQV1dnZZFWB6xixkIdXV11NTUaMHg+tl3suVKJFQU31VUVPDcc89x+PBhXC4XI0eO5MEHHyQhIcGvYlqtVvr168f48eNJT08nJCREu155u6CgIGw2G1lZWSxZsoTy8nK8Xi9Wq5Xk5GTNpSh3nmdyTSrOP4Gsn4HQd26i/h49epSXXnqJ//znP+Tn57far0+fPvzwhz/kiSeeID093S/WQMRYieML9At4q7qhENZuUUeDg4Ox2+1ERkaSm5tLQ0ODVnc9Hg/5+fkkJCSQkpKiLWUTqC4pUdX5tNemyP1BS0sL1dXVrfo/0bfJZSH6P7GNiL9s69yyJ8fj8XDixAn+8Ic/kJeXh9frZcKECdxzzz1+aRRky3t6ejqjRo2iX79+2Gw2zfAgwhTk7fv168emTZs4cuQIPp8Ps9lMSkoKgwcPJjo62u93d0fOq/uvLXeI/nMx8hbB20ePHmX37t3s37+fkydPUlFRgdPpxGq1Eh8frxVoZmYm4eHhOJ1OTpw4wbvvvktVVRW9e/dm3LhxZGdn+1mlAo3uAerq6jhw4AAbN26kvr6e+Ph4Bg0aRP/+/f2E25k6MP3vM5lMxMTEEB4ejsViwel04vF4aGxsDGh9C7TGkuL7QS/wA70WyA2jsAY0Njayb98+XnzxRVatWqUl9JS3HzRoELNnz+aWW24hOTm51cw+eXvxv7vHHyg6j7ZEvhDdsbGx3H777ezatYvPPvuM8vJybRufz8c///lPYmNjiY+PJyoqqtXkGdEmq3rWecjtvjyoh29WT8jLy2PPnj0cPnxYW9+xubmZ0NBQEhMT6d27N6NHj6Zv377YbDacTieFhYUsWLCAhoYG+vXrx9ixYxk8eDDQup7oPTV1dXXs27ePLVu24HA4SElJYdCgQQwYMMAvdYe4xkCvxXv9bzSZTK3ijN1uN/X19X4pFroz33tMVXudktPpZO3atSxbtoz169eTn5+vFaogKCiI8PBwsrOzufPOO5kwYQJms5nt27fzt7/9jYaGBkaOHEl0dDRDhw5tJVDkCiLOe/z4cT755BOamprweDwMGzaMcePGYbFY/KwC+pmC+t8gH1MOQheuPzit8hMSEvySguqtaIqujVxu+jITovmrr77ijTfeYOXKlVoOKyGKzGYzgwcP5qGHHuLqq68mISFBs7YK65SqC4rvitFoxG6389BDD1FdXc2aNWtobm7GZDLR0tJCYWEhy5YtIykpiWnTpmn1TuQgEtYH8B8wqrr57RB9T6CwFq/Xi9PpZNWqVSxZsoSvvvqKY8eOtTpGUFAQkZGRDB8+nB/96EeMGzcOk8nEtm3b+Mtf/oLP59PWBBWiqq1rEf2YqAcOhwOfz8fo0aMZNWqUX+ogvRAT6OuCCHsQ1yrqk8vl0mYxm0wmkpKStLjR7s73Lqraor6+nn/961+888477NmzB6fTSXx8PNdeey19+vQhLCyM+vp69u7dy2effca6desoKyujvr6eMWPGUFBQoOXNSEpKIikpSTNHQusKLWhububIkSMsW7YMl8tFREQEI0aMYNiwYX6CTt6nvSBAeWQnrreurk47ht1uZ9SoUQQHByuLVBemLatqIERDEhQUhNPp5NNPP+Wdd95hw4YNWr0TDVRYWBhDhw7l8ccfZ/jw4djtdoBWbj7VeSk6iyFDhnDDDTdQUVHBtm3b/BaHz8nJISYmhv79+5OZmdmqfQzUBqqA9m9HoIG3eF9bW8uHH37I22+/zaFDh3C5XCQmJjJhwgSysrK0CVC5ubl8/vnnrF69mrKyMhoaGhhfSA2qAAAgAElEQVQ4cCCHDx/WzhMXF0ePHj20Y8srOuivpampiYMHD7J69WoALZHsZZdd1mb/19HfajCczsm3c+dOKisrtXoXGhrK8OHDiYyM/JZ3smtxXkVVoIIIZLJ2Op3k5eXxyiuvcPjwYVpaWhg6dChz5sxh0qRJxMTEYLFYaG5upri4mIkTJ/LMM89w6NAh1qxZg8PhYM+ePVqh9ezZkz59+mjmVDmAU28ZKiwsZNu2bZSUlGAwGMjOzmbQoEFaZyd3boF+j/xgCEuD2O7UqVO8/vrrnDp1Cq/XS2xsLIMGDWLgwIEEBwe3smiJdb4UXYv2XMd6q+ebb77JBx98QG5urp952+v1EhMTw4QJE3jyySfJysrCYrFox1AdleJcINrA66+/ntLSUgoKCqisrNTqcENDA1u2bOGNN97g+eef12JxxFT49kIelPDvOLI40Yd5OBwO9u7dy1/+8hdKSkrw+XyMGjWK2bNnc9VVV9GjRw9MJpMW5jJx4kR+97vfsX//fj7//HNOnjzJwYMHgdNl0rdvX/r06dOq39L3VUajkby8PLZu3aqdd+TIkQwcOBC73d6h8m3P/Sziwj7++GMKCgrw+U5n/7/kkksYMmQI4eHhnXBnv3++15gqPeKhPXbsGB988AF5eXk4nU4GDBjAjBkzmDVrFjabTTuWxWIhMzOT+Ph48vLyWLhwIfv376empoaSkhI8Hg8hISH06tWL1NRUP9+vvnEQHdm2bdtYvny5Zk24/vrrGTBgQKs4lkBiUF/h5HUAy8vL2bBhA0uWLMHpdGIwGLj88su59dZbtWnMQky151ZUdF3kxurkyZP87W9/Y+HChRQVFWnuXjjthomIiOCWW27h4Ycfpnfv3tqMK1H2SkwrOhtRP41GIz169GDy5MmUlpby6quv+gn50tJSVqxYwbhx47jyyiuJiIgA/BPZqrbpuxEo4F/c/yNHjvDhhx9y4sQJAC699FKmTZvGrbfeqvV/gNb/RUdHc/DgQRYtWsSePXsoLS2luLgYr9dLZGQkffr0ITExsc21HcVkGqPRyObNm/niiy808T1t2jSysrK+dXnLbWJtbS2bN29m1apVlJWV4fP56NOnDz/5yU+Iioq6YNq8LvFk6EVEcXExq1at0oTG8OHDGT9+vJbDQogP8T80NJR7772XjIwMjh49Sk5ODidOnMDr9TJw4EB69eqlxUOJP4/Ho1kORCNRVlbG7t27OXToEMHBwfTt25ehQ4eSmJioXWd7biDh9pF9yC6Xi+bmZjZt2sTcuXOpq6vD5XIxfPhwZs6cydixY4HAMxIVXZO2gsNF2eXn5/PSSy8xf/58CgsLtYSLon7bbDYeeeQRHnvsMfr166clatQHfLpcLr/4QVE/5HgG/WcKxZkQ7d7AgQOZNm0aAwcOxGq1anVZzP76zW9+w7Fjx9qc3KP47vh8vlYB2idOnGDDhg3ajPSrrrqKH/zgB9rMcgCXy4Xb7dYmPz344IOkpKSQn5/P119/rQmyfv36kZiYqFnB5fZEFlhms5nS0lJ2797N4cOHMZlMXHrppQwbNoy4uDi/cpfjkDv6G1taWti/fz9PPvkkR48exe12c8kll3DzzTczadIkv3i97k6XEFUCISxqamooKCigubkZn89HVlYWl19+uTa9XFh/hPIODg7W4qxEATY1NQEwbNgw0tLSAP8KJadYEAJt3bp17Nq1C4/Hg9VqZfr06fTs2VPr9Dqyirs87R1OjyY+/vhj5s2bp+UkstvtzJkzhxkzZmgPihw435HzKM4vgYSLENHiv8fjITc3lzfeeIM//elPnDp1ym9bET/wxz/+kdmzZ5Oeng60niwhjiVShSgUnYnIcWaxWBgyZAi/+93vtPADgQjBeP/997V2S7RHQvSrhd+/OwaDQZsFB6fbgurqao4ePaq5Xfv3709WVpa2vZjcImKczGYzmZmZREVF4fF4aGpq0nIgipyJok+Rs5bLg3ifz8fKlSvZvXs3Ho+H6Ohobr/9dpKSkvySUgPttkmyJ0fuv9avX8/TTz/NwYMHaWpqwm63c9ttt/HTn/7UT9BfCJwX91+g+JBAUy9dLhcOh4PGxkbNXRIdHU14eHirWXfieOLhNhqNJCUlER0dTWVlJXC68Rg7dqzmTw7kvxb7GwwGVq1axddff43BYNAqlWw21c96kK1r8nFl68Ebb7zBm2++yc6dOzGZTISHh/Paa68xfvx4bDZbq8otiyvZFXghVbquxNmMjuT6Jt7L5bdv3z7mzZvH+++/r5WZnL26d+/ePPPMM1xzzTV+MXqBGi35utoqe1UnFHoChSUI5Jllot2y2+1MmDCBm266iZUrV1JeXq5t19LSwuuvv056ejq9e/fGarVq5whkWVf1seOIvkg/eaqxsZGamhqam5uB0wtjW61WvwXaZS+N3BcmJSVht9uprq7WvDEjR46kV69emgDTrz8qytHj8bB69Wr27t2Lz+cjOjqae+65h6ioqFYeGrmfCiTO5H7R5XKxePFi5s+fzxdffIHBYMBms/HrX/+aGTNm+CX7lNtL8Xv1fX13GGSeF1Glf9jaeujNZjP19fWUlpZqn4n1zkQCM7lTE8cR34WGhmKxWPD5fISEhDB48GD69OlDaGiotk2gPBter5d169aRn59PU1MTPXr04MorryQ1NbXVArj6QtYfV1xPRUUFCxcu5O9//zsFBQVYLBb69+/P888/z8iRI/0SfcrHlsWfElTnl/YElvxAyw2cmPiwZ88efv3rX/PVV19p9cBsNtPS0kJISAgjR47kvvvuY+bMmWc8l0LxXTiTsJLj9wwGAxERETz55JMcP36cmpoaXC6Xtn9DQwMLFy4kKiqKGTNmtOqQ5f/imPrPFIHRx+b6fD7q6+u12eFBQUGEhYVprjE5hCDQfbbZbISGhlJdXY3ZbGbIkCH07dtX8+DA6TZJNgB4vV4cDgfr16/nyJEjNDU1kZKSwoQJE4iOjta2F0I80Kxk8V6uc263m+bmZpYuXcpLL73Eli1bMJlMJCQkMHfuXMaPH09sbKyfEUFY0sR7kdi0vfrcFelSyT+9Xi/h4eFaRt+goCCqq6u1XCpCxOhdgMI9d/LkSWprawEIDQ1l2rRp9OjRw8+aJJ9bFJbD4WDhwoUUFhYC0LdvX26//XY/F2GgQtVfv893OrdWfn4+ixcv5k9/+hPNzc1ERkbygx/8gIceeogrrrgi4Lpa4vfo74dqnM4t8gOrfy3Ql4fcwDU0NLB9+3aefPJJ9u/fj9Pp1AR2S0sLVquVCRMmcPfddzN9+vRWOdbauy6F4tvSUeumqNMZGRnMmjWLxsZGcnJytO+NRiNbtmwhKSmJoUOHkpGR0epYSkh9e2QLD5w2IthsNq0Nqa6uxul0+nlk5Fnl8qC7tLSU6upqAHr06MFtt91GTExMK/ErXIPC0tXU1MTChQspLi7G5/ORmZnJzJkz/Szoeg+K/jfIuN1uysrK+OSTT5g3bx7FxcWEhYVx2WWX8fOf/5wf/OAHWsC93gIlGzv0yUO7g5UKulieKrGUi91ux2Qy4Xa7aWpqora2lrq6OqxWq6Zchbgym8243W4aGhqorKzE4XAQFBSE2WwmISHBL7hPNpeKzs3lcmkLjVZUVBAZGcmll17K6NGjtVGZHHguCyg9zc3NbNmyhXfffZcPP/wQt9tNQkIC06dP54477mDYsGG4XC7NsiVEoqgwshVNfmgU5xa9abut7/Wu3ZMnT/L555/z/PPPa6k/ZOui1Wrlhhtu4P7772fMmDGtRH2g1wrFuUQWQGJgIOr1jTfeyPHjxykqKqKkpARAs8Ru2bKF+fPn8/TTT2uTfpQV/duj90KI13a7naioKOC0oHU6nVRVVdHQ0EBERITmLtSHr9TW1lJZWanFEgOkpaVpnhtZlMk5EZuamsjLy2PNmjVUVVURExPDgAEDGDZsmF/fFOj6ZYQ4dzqd7N+/n48++oiXX36ZlpYWoqOj+cEPfsDdd9/NpEmT/PbRDzLl/k+gt+iJz7oqXUpUiZsZGRlJeno6+fn5+Hw+9u/fz549exg5cmSreBY4/eCvWrWKEydOaD5Zj8dDdXW131R2GWEtKi8vZ9GiRVRXV+PznV4q5KqrrsJsNvvFw5zJolFXV8eKFSt45513WL9+vRZDc88993DTTTeRmZkJ4CfyxDFMJpPWeIkHQNH1kBPGlpSU8Mknn/D222+zZ88eAL8g0KioKKZMmcKjjz5KZmam9p2cI02hOJ/IHbH8J9rCiIgIrrvuOioqKpg/f75mEQE4duwYy5Yt44orrtDSLAQKT1D1umPIbbzcl5jNZqKiokhNTdXCYPbv38+BAwcYMWKEtr3sqRFutoqKCq2N8ng8lJWVadnwhWtNb2k6ceIEixYtoqGhAbfbzeDBgxk3bhzBwcF+28rWeb24EZ/X1dWxefNm/vnPf7Jw4UJcLhe9evXi5ptv5rbbbiM7OzvgvRDHCPQnvtcvEN6VOa8LKss3KtDncoBkU1MTO3bs0KxVoaGhDBw4EJvN5te5iURp8+bNY9++fbhcLoKCgjAajcTGxjJ06FDNBCqbSw0GAy6Xi7179/KnP/2JiooKzGYzN910E7fddhthYWEBl6QRr8V1u91uSktLWbBgAX//+9/Zvn07oaGhDBkyhMcee4wZM2bQs2dPbT99AyQLQ33+rLa2VZx/5A6ppKSEd955h3fffZe9e/dq24h60bNnT2699VZ+9atf0bNnz4CpQFSAr+J8I8ejBmpbRP4qs9nM4cOHKS0t9etAnU4nhw4dYvjw4URHR2uWfLkeq7rcMWSrt3gvaGlpobGxkW3btuHznV43NDw8nH79+hEaGuq3fUNDA7m5ucydO5fDhw/T3NyseWrCw8MZPXq0X6ZyuaxcLhc7d+5k3rx5VFVVYTabufXWW7n55pux2WyaR0UYF0R/qM/I7vV6tdi7V199lTVr1hAUFES/fv348Y9/zB133EH//v39rkH2/uh/f3uz3wNt39X4Xmb/tefWMhgMpKamMn36dD799FOKiorIz8/no48+wuFwMGnSJJKSkjCbzVRVVZGbm8vixYv56quvSExMJDk5maqqKk6ePMnq1avJzs7G5XJhNptpbm7WAteDgoIoKSlh27ZtHD58GJ/Px2WXXcbgwYOJj4/XrjVQYKAszIqLi3n77bd58803OXnyJD6fD7vdrk2B/fzzz7X95IB7+MbyYTKZyMrKomfPnn7J3ZTF6tzT0XssYqQqKip44YUXWLx4MUVFRa3iSvr378+MGTO4++67SUxM1KwA8nlUygzF94Wod3KnJrdJJpOJwYMH89Of/pSf/vSn1NXVads6HA5yc3N5//33eeCBB/w6SnFsRcfQ55+TLUDp6elMmzaNxYsXU15eTl5eHh999BH19fVceeWV9OrVC6PRSEVFBTt27GDp0qXk5ORoSa5PnTpFVVUVa9as4YorrtCWWGtpaaFv375aCoOioiJycnLIz88HYPjw4Vr/p782cc2iH5NpaGjg/fff55VXXiEvL0+LjR48eDAhISHs2LGDHTt2aJYmedajWDkEIDMzk7S0NCIjI1vVJb2FrCtj8J2HK20v+Ff+XO58Ghoa+PTTT3nttdfIzc2lqakJq9VKnz59iIuLIygoiNraWkpLSzlx4gTJyck8+OCDhIeHs2bNGj799FPgm+RnRqOR6OhofvnLX5KRkYHVamXp0qX8+c9/ZuPGjQA88cQTzJ49m379+vldm15QyaJq8+bN3H777Zrr0WA4PWU0Li7Obx+9pUz+/SaTiWuvvZZ7772XrKysgKJTWTXODYFiA+SYNoHL5SIvL4+//vWvLF26tFUOKoDBgwdz1113ccstt2hrTeoRHVpbFkmF4nzQ3jIpXq+XkpIS5s6dy4cffqilqIHTnVuPHj341a9+xfTp07XEyAI50Fh/HlXPv0E/yAJ/j011dTVLly7ltddeY+/evTidTsLDw0lPT6dHjx4YDKfXBywuLqa0tJTk5GQefvhhTCYTq1evZsWKFfh8Pi699FKSkpIwGAwkJCTw+OOPk5GRQXBwMAsXLmTevHnk5OTg8/l4+umnue222+jdu3ebQeH6QSRAWVkZU6dO5cCBA1pMl9lspmfPngFdiIHqG8BVV13FnXfeqS3e3N75uzLfS0qFtj6Tb7bNZmPatGn06dOH//znP3z22WcUFhaSm5urFagwV994443MmjWLkSNHagHqlZWV7Ny5k0OHDnHw4EEMBgOXXnqplkD05MmT7N69m507dxIUFERycjIjR44kPT29TUuaqBRyegeR0basrEyrHA0NDTQ0NHT43litVk6dOqUp9rYElaLzOdO99fl8uN1utm7dyuuvv86SJUu0pLQCs9lMv379+NnPfsY111yjjfTaOnZ3MGErLmzkTlPfgRoMBnr06MH/+3//j3379pGTk0NjY6PmPiwvL+df//oXsbGxzJgxQ5uRpg+gVrSNfJ8CTaCKjIxkxowZpKWl8cknn7Bu3ToKCgrYtWuXtq/JZCIxMZHbbruNmTNnkp2drYneU6dOkZOTw+HDh7X+Lzs7W+v/ysrK2LVrF3v27MFoNJKamsrIkSNJSUlp81r1n8kCWriDRf/tdrs1C5i8T3uLcZ88eZLm5mbt2KKflbftDnFVXSpQXT+F0mq1MmLECHr37s1dd91FbW0tp06dorCwkODgYBISEkhKSiIuLo6EhAStwkyaNIlLLrmE/Px8ysrKaGpqIioqSjMvGo1Gtm7dSk5ODg6HA4vFwtSpU8nIyNDycrSXD0RW0QMGDOC9997TAv3k33E2vzsiIoKUlBStQrndbi1VhKArV6TuSqC4Bvn+GwwGVq9ezTvvvMNnn32Gw+HwG2WFhISQmZnJH//4R0aMGIHdblflpOhWBOrggoODSUtL495778XhcLBlyxYMhtNZ2L1eLzt37mTFihX06dOHwYMH+03S0C/VpZ6HwAiRIFxh4jNAy7s4ZswYLrnkEu6//35qamooKyujuLiYkJAQ4uLiSE5OJiEhgfj4eC3t0LXXXsuAAQMoLCykqKgIj8dDbGwsffv21VYI2bp1Kzt37sThcBAREcGNN95IWloawcHBftfYkbKLioripZdeorq6Grfb7Wdxa6svDOSpio6O1kJv5HRC+hmrXZ0uJarAPyeFmLkXExNDjx49gNNBci6XC4PhdHp/MaNBPNRutxuLxUJWVhaZmZk0NTX5bSu237RpE9u3bwcgODiY2267jbS0tIBWBNnlp88dFRISwiWXXNIq8PNsfqvsEhQuRH3SUcW5Q1928r3/+OOPmT9/Pl999ZXfKArAarUyatQonnnmGQYPHnzBLbeguLgIFIYxZcoUDh06RGlpKceOHdMSg3q9XtasWYPNZuPll1+mubkZs9msiQO9SBCv1fNxGjnfonzf9S4xr9dLbGwscXFxmlgV/aLZbPZbM08cy263ExkZSWZmprbuqIhfMplMtLS0sHr1aq3/i4yMZNasWSQmJrYqo46UmdlsJi0tjb59+7a5GkSggat+G3FP4JsYqra8Rl2ZLplNS4xuLBaLNnMKvqk0FouFkJAQzZIgj4aMRqO2eKTISBsaGkpwcLDWWe7YsYP//ve/VFZWEhMTw+TJk/1UuihIvalSCCpRuUVhezwe3G63X/JO+S8Q7cVMid/jdrsDWsoUnUeghk3MZlm6dCnPPvss69at08S6KI/g4GBuuOEGfv/73zNy5EisVquWYf1MZa9QdHXkMIwbb7yR6667zq+D83q9VFRUsH79el577TU/a4v4XhxHPQttE0jIyu2R6OMAbVaf1WolJCREC0HRWwjFZyaTidDQUKxWKxaLRRNU27dv58CBAzQ0NBAfH8/w4cPp1auXtgyRvqw6UnYid5loA/VWJX0frv9c/D758+7a53UpUSWbDUXhCMEiBIbRaNTUuT4pp7y9+FwcV3wfFBTE8uXLOXLkCABJSUnMnDmT8PBwP/EkZ8/WB5qLYwqEFaw9U2cgoaW3UsnBnfpGSjVK5w7h7hNlUVVVxapVq7j99tvJzc3VlkwQFlKj0ch9993HE088wciRIzEYTk9PBiV+Fd0f/QBj4MCBTJkyhTFjxvh1dgaDgaNHj/LCCy9QUFBAQ0NDqyVQ5MGn4hvk1CqBEj7L/YI+SaY+ngnQrFfiGHqBJZfJwoULyc/Pp6WlhcTERO644w4iIiK0Y3e0DZO3c7lcmsfIaDRqg0u5/AMJbH2fqBdcsmGhu9SjLiWqZEThCMuTCIYU6K1JQh2LffQFIXJX+Xw+ysrKCA4OJjMzk1GjRjFlyhQiIiK0zlNsL+8vuyX1MxMCiaazGZ3JST/l3/RtRgyKs0OOYfD5fJSWlvLhhx/y4IMP4nQ6/craYDg9qeDRRx/lgQceYNCgQX4Nor7xa+t8auSu6A6I9tTn8zFq1CgeeeQRv7XovF4vLpeLyspKfvnLX3Lo0CHAP6BYxVQFRhY88oBcGAXEd6K/kfsjYRyQB/FiZRHZoCCXkyyyamtrsdvtXHrppYwdO5bJkydr3p1AbVOgUBh9OyZi7cT5RZhNoOMEcjG2dW559ZHukormvKRUOBsCpanXm0Vlt5vP59MCugMFyQl1Lh/faDTS0tLip6zF8fXXom8UArkFxbkC+Yn1yJ/rO2T52uX33yZeS3Ea/SiprW0MBgMFBQW8+eabvPfee5SUlPiNFo1GIykpKcycOZOf/exnJCQk+DUGcgxJe+XVkTqiUHyf6C0JcLqunjhxgrfeeotXXnmFyspKv+fDbDbzv//7v8yaNYt+/fq1ig0KVNfbi6+5WBAiyev1arPnZISAEtuK/kzuG2QRK3s5RP8m9oVv+r/GxkaMRiMhISF+ZSzKq62UBm3VDXGtshDXJwnVW+HEMeS+Whg15FyO3UFIyXQ5UXW+aU+Vt7WtvHxDILOt3uQq76sE0vlBb6lsy3ULpxuDo0ePMnfuXJYtW0ZJSYlf42UymbRFRv/3f/+3lYA6U3I8haI7IbeJ8sQcj8dDVVUVDzzwABs3btSW9hLb9+rVi4cffpg777yTmJgYbR+gw8+FahP9CWTF0QdxyyJFL7JkoaImP50fzusyNd2Bth5q/WhKrsRy7JY8etB35PLn7Z1L0TnoR0TwTYMk3jc1NbFv3z5+//vfs2LFCsrLy/3Kymg0MnToUO69917uu+8+rFar33JC8vECWRYViu5GoIGfqN8hISH07NmTgoICjh8/7uduqq2txeFwEBYWRlZWluai0reBgc6hnpvA6Af9gWJ9ofX9DLRmn7q/5wclXSU6WulkX7i+Q5VHZvqKL/Y9m3Mpvjuym1V2rdbV1bF9+3Zeeukl1q5di9Pp1LaH02U0btw47r//fiZOnEhYWFibLkRVnooLBbnd0s/kMplMjBgxgptvvpmamhq2bt0KoLmetm3bhs1mo2/fvtokjkAxrqDcfx1BH74i3HpthYoI9P2O4vxx0VuqOjpKkhsa/UwMQEsKqR8RiPxZsqVEPq/i3CJbB8W9F6PqNWvW8Morr7By5Upt9owol9DQUK666ioee+wxxo8fj91uB/AT0PI52hqFKxTdlUATZUTgdEpKCk6nk7y8PGpra/3SzVRXV1NeXs6IESO0dVZl2ns+1LMTGH2YgXhdXFzMypUr2b59OxaLhfDwcC31i2xN1++nOHdc9KLqbNCrfxGLs2DBAlauXIndbic2NlabdSHPgJA7XCWozj16d6tsDm9qauKDDz5g/vz5bNy4sZUZPTY2liuvvJJf/epXDBs2jPDwcO07+GZULl7rz6tQdHfkuq5/7fV6sdlsxMTE4PP52LZtm2ahh9Mu9bKyMhobG8nKyiIyMtLPZX6mcyq+IZBlXNynhoYG1q9fzy9/+UvWr1/PgAED6NWrF6GhoQEHffK+inOHElUdRD9Lwev14nQ62bt3L3/5y19Yt24dRUVFREZG0qtXL7+kbWJ/aD9gWtF56KfniobF6/Uyd+5c3n77bfbs2dMqp1lcXBzXX389v/nNbxgwYIA2szRQubUXP6dQdHdk95L8mXiO7HY70dHRVFdXk5+frz1LBoOBlpYWDh48SEJCAomJiZqwAn+h0BGxdbGjX/LHYDidF2/Lli18+OGH7Ny5k759+3Lttddqy9AI5H3UPT4/KFF1FujjpEQ+kcjISHbs2MHBgwc5fvw4QUFBWqCmPMoTxxD/VSU/t+jv74kTJ3j22Wf54IMPOHbsmObyg9MNfXx8PLNnz+ahhx4iMzPTLz/MmRqmtlJgKBTdkUBB0GJQKU+dj4qKIiMjg5ycHGpqajSLlcfjwel0cuDAAdLS0sjIyND2kZ8T9aycGb213e12U1NTw8cff8z777+P2Wzmxz/+MUOGDCEqKkpbLijQvVX3+9yjRFUH0ZtT4ZuONCYmhl69elFYWMju3bu1bLWDBw9u1Snrc3covj1y5ntonc9MDrTNzc3l1Vdf5fXXX+fUqVN+60yZTCbCwsL49a9/zZ133kl6enqrNAmBOgL5/YU64patFPocNfrg4zMtTXKh3ZsLmbbqOPhnAzcajcTExJCWlsbu3bu12bOC2tpaSktLCQ0NZciQIX7H1z+38nllLnQLcEeeE9ki3tzczMcff8yiRYuorq5m1KhR3HrrrSQmJmK1WjUvSaD26EK9h10JJao6SKBpwSJrrclkIjo6mqSkJKqrq8nJySE3Nxej0Uh6ejoRERFaMjSRwl8cS/6v6DhtJRUU7gr5+61bt/L666/z1ltv4XQ6/fYRo+0XX3yRm266icTExDatiYHiFC7UUXdbsxz1a3sJ6wW0tuQKUSu+u5Duz4VMW3Vb/yfqiMVioW/fvjQ2NlJWVkZFRYVf/SktLaWxsZEePXrQp08fPxeiPni6vTpyIdafM6WJlJ8lEQ9aWZXe8SUAACAASURBVFnJq6++ypdffknv3r156KGHuOSSS7Db7YSEhPglEZXLSQWpnx+UqPqW6M3jFouF+Ph4EhISMBgM7Nixgy+++ILQ0FDi4+OJiYnRkq+pafnfHv2oVX4vLzEk3LMbN27kz3/+MwsXLtRWbBcEBQUxcOBA5s2bx3XXXUdkZGRAkXYhiqb20K8ZJjfK8nJP4D8wkJeo0CcgvJju38WCKM+WlhYtn1tNTQ179+6lqalJ287n83H8+HGOHj3KhAkTtGXH2hNTgQYwFxqBrLkC/YBbiNCGhgbmzZvH2rVrCQ8PZ9KkSUyZMoXY2FhCQ0M1K5V+lrIawJ8/lKj6logKK1L9i9FBVFSUZoYtKCjg888/x+FwkJSURFxcHD6fr9VIQl/hldukY8idvnBFiFxU9fX15OTk8MQTT7Bx40a/IFohgq+88koeeeQRbrrpJr9jye5dOTbhYikH2Z0pN85ibS8535fYHk6LLpfLRUNDA06nU1tGSl6n7GK5hxcDop0SKwwYjUaSk5MJDg5m27Ztfmu1ilQL27ZtY+zYsdoARtS1tpIrX8h01Con1gNsamri6NGjPPvssxQXFzN+/HhuvfVW0tLSsNlsWiyVfIwL1ZLelVGi6izQP/hyTI/o0M1mM5GRkaSmpmIymaisrOTrr7+mqKiIpKQkUlNTA8YrXGxm785AH9MjREBFRQWfffYZDz30EHl5eX6CCiAsLIwpU6bw4x//mClTpgD+SfX0WaAFF1M56O+tbKUSCMHp8Xiora2loKCA5cuX8+GHH7J27VoOHTpERkaGnwXwYrqHFzry4EO8jo6OJjo6Wpv9J4Q1nA6wLikpobq6mtTUVBITE7X0My6X66IUAG09F4HanSNHjvDcc8+xa9cu+vfvz3XXXceoUaP83H7KMvz9ozKqnwWyKyRQhm450V3fvn258847CQ8PZ9WqVWzcuJHy8nKefPJJxo4di91uV2thfUf08TsAhYWFfPzxx7z44ouUl5e3mr5ts9mYOXMmDz74IIMGDfJb8V12W4kFTrvjgp6dhbwkhv61mAVWU1PD4cOHWbt2LQsXLiQvL4+WlhZMJhNJSUlcffXVJCYmtlrY9WK8nxca+pUlBFlZWTzyyCOUlJTw1VdfUVtbqz2rbrebDz74gNDQUACGDh2KyWQiODj4jPFFFyrys6AfzIj4xcrKSrZs2cLy5csxGo2MHz+eYcOGERkZSVhYmN/+cj+lP77i3KMsVWdBW7OfZFeJ2WzGYrFoQewiGVtVVRUHDhxg8+bNxMTEkJCQQERERMAKr0YaHUPcH7fbjcFweobf/PnzWbBggSaoxDZms5nk5GRmzZrFo48+SkZGBiaTyS/jvVy++kWTL8byCJQmQrhEy8vLycnJ4aOPPuKFF15g0aJFVFZWavFYRqMRu93OjBkztOD/i9Xqd6GiH9QId7DRaCQ8PJwhQ4ZQUFBARUWFFmMlnrFDhw7R0NBAcnIyqamprY51MdSP9hJ7yuLK5XLx5Zdf8uabb1JQUMD48eOZOnUqAwYMIDIyMmDqF/0x1WDm/KFEVQfRdwj6Dlj+Xggqs9lMcHAwCQkJxMbG0tjYyJ49e9i1axcGg4G4uDiio6PbPXag88OFuV5WoAe/rYSb8nder5etW7fy17/+lWXLllFWVqZ17MKi2L9/f+6++24ee+wx4uLiAuYNC5QWIVDM24WOfrAA/rMtt2zZwrvvvsvrr7/O0qVLqaqq4rLLLmPEiBHaqNpoNBIWFsZtt91GUlKStq/g295L/bMhC+eOWjraCw6Wg/TlbS+Wsj8b5DhEPWazmdjYWFJSUjh16hQnTpygublZe85cLhfFxcWUl5fTs2dPbSJPRwXVhVIe+nZcP7jz+XwcPnyYxYsXs3z5cmJiYrjvvvsYOnQoMTExhISEaFb2s3ElKs4dyv13FsgPvBxbIpAzBptMJkJCQrT9hO87LCyML774gjfffJPKykpmz57N5Zdfrm0nHiq9a1Bu6C9k5NGu/F5uwOX7UF1dzdatW5k3bx47duygtrZW+0649saOHcsdd9zB1KlTCQsL8ysn+V5fiEL1uyK7eLxeLx6Ph7feeosVK1bg9Xq54oorGD9+PGPGjMFisTB//nz27dsH+E/hPpfCVO+elJHzjQmhDd9YN+X4ObkeyPVOJXZtG1l06wPOAcaMGUNzczM+n49Fixb5WaROnTrFmjVrqKur46mnnuLSSy/FZrMFdF+11S52d/RxafrZzC6Xi5UrV7Jq1SpsNhtTp07l8ssvJyYmBrPZ3OYkkPaEleLcokRVJyM3xvJSNUFBQVgsFsLCwrDb7Xz++ecsXLiQkydP8rOf/Yz+/fsTGhrq15jI+YAuhodEFk5yklTRoIrGWDRAJ06c4LPPPuPll1/m4MGDWsoE+R5OnTqVu+66i3HjxhEREQH4u7Uu1jiOM6GfBSnul8fjIS0tjdtvv53MzEyys7Pp168fVquVgwcPavuJ9RHl5KGdQSDLmfgvX2dLSwvFxcUUFxdTX1+PzWYjOTlZm5krBICoa8XFxTidTiIjI4mOjsZisbQ6p8KfMw1CxGdjxozBaDRiNpv55z//6Ve3ampq+OKLL3C5XDz++OOMHDmS8PBwP0uhPqnshVAe8tIz+vQ84jd7PB62bt3Khg0bKCsrY8CAAUyZMoXExETCw8MJDg6+IO7FhYYSVecIn8+nBexarVYtfgfghz/8IVFRUaxcuZLly5drAexDhw71i7O6GB8YubOThZQcY+Dz+Th27BgfffQRb731FseOHdMsD2K7iIgIpk+fzuzZs7nssssIDw9vZZEQqBQW7SPfD4vFwpw5czAYDERERBAWFtaqoxOdglgG6FxYePR1QnRS27dvZ9WqVWzbto2mpiaqq6txuVwEBwdjt9tJTk5m6tSpjBs3joSEBBwOB4cPH+a3v/0tVVVVZGRkMHXqVG666Sa/ySiyO1l/TxTt34/g4GCGDRumDRpXrlypBa8bDKfXsduwYQPNzc088MAD3HDDDYSHh+NyuTRrTCC3bHcuA71o1Fv53G63FtS/a9cuUlJSmDhxIpmZmYSFhQVciqa735MLBSWqzhF6S5XP59NyiQQHBzNlyhTCwsJYtmwZmzZt4he/+AWPP/44EydOJCYmBkDLwH4xIaZgi98tx7kIMXTw4EHmzZvH0qVLqaioaBXPlpKSwtSpU/nFL35BXFyc34juQmqYzyX6eySLmOTkZO27tuL/DIbTucDO1f3Vi+66ujoWLFjAkiVLyM3Npbq6utW5RezJxo0bmT17NjNmzCA2Npbdu3ezceNGampq8Pl81NXVtbIQq3rSGr2lt73nKTQ0lMsuu4ynnnoKh8PBV199xalTp/xmueXk5OBwOKisrOTee+/FZrNpgkog2sTubrUKFAco2jqApqYm1q5dy+bNm3E6nWRnZzN58mRsNhs2m82vfVR0LZSo6mRk861wl4gORmRUF+6F0NBQIiMjeeedd8jLy+Opp56itLSUH/3oR9jtdm37i+XBaS99gcFgwOl0cvDgQR577DF27NhBY2Ojtq3FYsHtdtO3b19mzZrFT3/6Uy0/khyPoY+PkYWBiplpjbgfIlu9HOt2JsufXvh0Bj7f6Wn5csdaX1/Pn/70Jz7++GOKioowGAykpaVxzz33MHz4cOLj46mqqmLdunX8/e9/58SJE/ztb3/D4XAwffp0CgoKtFxmKSkppKena9crsoVfaLE85wu5LXQ4HOzdu9fPei8szEJQ7Nmzh5dffpkTJ07wzDPPYDQatfxLEDiWtTsSSEyJ3+hyuTh27BjPP/88RUVFjB49mv/P3pvHRXXd//+v2WfYZoZd2QVZAoiIoKigRo0axURNbBajiTHVbmnTtI+0adqP7aNNP00+TfOwbfJNYzZrEk1ijMHUteISd0FQWVzYQWBg2Idl1t8f/M71zJ07w6CoQM7z8fDhMHPvuds57/vezvtkZWUhMDAQarUacrmcpS2MYJhSNczwQ1b8JGiFQgGFQgEAGD9+PObNm4eIiAi89tprKC4uxptvvonGxkZs2rQJJpMJCoVizAiSwaDzZUwmE+RyOWe5lZaW4uOPP8b/+3//D93d3XZFBYEBQTRp0iQ8//zzeOyxx6BSqQTd6kLJtAxh6FwWfi0ikjcFOK63SPalvVzDCSkYSV7UJSUl2Lp1K3Q6HZc8//vf/x6ZmZl2ylB6ejoef/xxrFq1CleuXMG5c+cgEolQUlLCKVXBwcGIjIx0OBZ/jbrR7CW5G9D3h4y5zs5OFBYW4tixY2hubgbgmCNntVpRVVWFjz76CLW1tXj11VcRFRVlV5jX2XFGM/QamfX19cjNzUVRURG8vb0xa9YsLnyqUqk4bx0xML5rxvdIh5lfwww9vZVf3Zb+5+3tDa1WCz8/PyQkJOB//ud/MGfOHHR3d+ODDz7A008/DYPBwAl0oankQh4BPvz8pHsB/xycnRPt+SCJwiLRwBT93NxcvPHGG2hvb7cr2AkASqUSmZmZ2Lx5M1avXs0prUSY0wnvpE2Gc0gfJR4a4nE1Go126ysCN5fQ4M9CIsqIs37Lf+6D9V/ymUC8jpWVlXjrrbfQ1tYGi8WCjIwMrF27FnPmzIFCoeAWPCfLSUVHR2PDhg2IjY3F1atXcfDgQRQUFKC/vx8ajQYTJ05EaGgoN2PNmTeO4Ry+h5LIQplMxuVV0feW1PUDbnr6W1tbsXPnTjz22GP48ssv0d/fD2DAc+hOnxpNkFQRm82G/v5+5Ofn491334XVakVOTg7S09MRGBgIb29vu/AnKd3DGFmwJ3KHcDUbBhhIRJTL5dBoNNzL6yc/+QnGjRuHr776Cnv37sX69evx0ksvISUlBSqVatCXzmDHv5cIKTR0WI6/HfFEXb9+HX//+9/xxRdfwGg02u0nEong6+uLGTNmYPPmzRg/frzggqKurFkW8nMNuTdEOeH/JiTUbTb72ZvkO/425H+z2QyTyWS33Alpn1bYiLJNexv1ej2OHTvG9Y0pU6YgKysLwM2SGqQt8iJ64okncPjwYezatQsNDQ3c8VJTUxEREQGJRMKVkKAXhWY4wn9e/O8A+2fd29tr1xfGjRuHadOmIT8/HzqdjlOeyLgtKCjApk2bcPXqVTz99NMIDg62a1PIWBpJ8pB/LvQ94iuDIpEI586dw549e9DU1ISwsDAsWrQI8fHxXD0qWr6R9klBXsbIgClV9wg6J8THx4cbNCR5dtu2bdizZw9sNhvWrl2L2bNnw9fX107IC+UE8RWIkfAyoPPM6BcUrdCQcgjkJdjb24v8/Hz88Y9/5BJYJRIJl6NmtVqh0WiwcOFCbN68GVqtljseX1EbCfeAcRPSF4CBKfX5+fm4ePEient77fo1UWyAAaUuPDwcjz76qF3IyGAw4MaNG9yLJTw8HBMmTHDob/QY8fLyglqthoeHB/r6+jhlLj09HZGRkZw3gO89Yf3o9iC5peSzSDSwtFdiYiLWrVuHd955BydOnOAmDBDlubS0FJs3b0ZhYSF+9rOfISkpias3Ryu+tKIhJGPuJs68ZkKeeSLDu7q6cPDgQRw8eBB+fn5Ys2YNoqKi4OPjA5VKxc2E5MMUqpEFU6ruIcTyJkJBo9EgOjoaCoUCPj4++PDDD3Hw4EF0dXWho6MDOTk53MxAOgGUr0TxvUE091LAEGWIvCzJ96SGDTCQG9XQ0IC8vDz8+c9/xo0bNzjrlg49Wa1WTJgwAVlZWfD19XV6TIKz2TaMuwN/Agd5EdTW1mLz5s04fPgw+vr6uG3J2oL0SyQjIwMrVqzgfu/o6EBDQwPXp7RaLby8vLhjES8av6aVRCKBv78/NBoNmpqaIJFI4OHhgdTUVERFRQlOaGDcOrRHhl8awWq1QqlUIjs7G+Hh4di6dSt27tyJmpoaiMViLteNpAAUFhbi+eefx4IFCxAREWGXc2qxWLg+M9LDYvw+abFYsH//fhw7dgy9vb2YOnUqFi1ahJCQEHh4eAh6qOj9GSOHkd3zvgPQoSxvb2+u/ohMJoOPjw8+/fRTXLhwAa2trWhra8OaNWugVqvtViTnF8cjn0cKdF4KEaxE+NHeCJPJhKKiInz++efYtm0bt5YceYnSoUGRSASVSgVPT08AEPTgMUYGfIucfj6+vr5YsGABtFotjEajnaJNXqgkzBgfH2/3cqHDhnTf4udB0X1BqN6RQqHAzJkzERMTw+X88JXwkTSeRhv0veQX6KXHdmJiIn7yk59g4sSJ+OCDD1BQUGCn1BqNRpSXl+Pll1/G2bNnsWLFCkybNo0LCZKwLT+fayQ+O7r2ltVqRWNjI7788ksUFxdj4sSJWL58OYKCguDp6elSQRyJ1/ZdhylV9whaqBDBQiwsEnogda1yc3Nx6tQpvPHGG2htbcXq1asRGRnJLYNDt8kfZCNh0PFn3JHQDjCgIFmtVpjNZuzduxcff/wx8vLy0N7e7pATRb9oAXuBTFu+5Dd6O8a9g1ZySNI7eSYhISH40Y9+xE3KoJ91b28v90IRi8V2Xgmz2QyVSgWNRsMdo7OzE319fQ79gn7+VqsVUqkUbW1tXAFKuVyO+fPnIygoiNuONlbo62B9aejQso48T77SQxTg0NBQPProo4iNjcX777+PAwcOcDMFiSJiMBiwY8cOXLx4EQ888ACWLl2KjIwMKJVKuz5EH5sc/14iZOxZrVZ0dHRwxrNKpUJGRgaysrK4qunuLEPDGDkwpeoeI5SsTao/SyQSzJw5k1vaZv/+/di8eTPnsUpJSeEGnTsxfODeJmyS66TPwWKxQK/XY9u2bdi+fTvKysq4ZFVy7jKZDIGBgdBoNCguLhb0SjhL4gecJ7Cyl+TdgVZ4+WvqkTCdj4+Pw+QCDw8PB28TUcjEYjFUKhXUajVUKhX6+vpgNpuh0+nQ1NSEcePG2e1HEIvFqKqqQkNDA3p6erhz8fb2FqxHRVdUH6me4JEO30PNV3bpsL7NZoNGo0FmZiYiIyORlpaG7du3o7CwkKvQDwwo1ZcvX0ZNTQ1OnDiBJUuWICcnB9HR0VCpVA4pEPf6efHzXwm9vb24evUqPv30U+h0OsyfPx9z586FRqOBh4eH3cxIxuiAKVX3CL6Apgc+ybXy9fWFWCxGamoqPD09oVarsWPHDuzYsQPNzc1Ys2YNFi5cyE3HJW2NNPgvUmDgGg0GAwoLC7Flyxbs3bsXra2tnIAlSKVSLFq0CMnJyaiurkZJSYldG85WZ2chwJGF0DOiFRYADv8Tr5bQLEKijPn6+iIxMREXL16E2WxGaWkp8vPzsXTpUq6/0cc0m83Izc1FdXU1147FYkFzczOMRqNd3xqJY2k04kw20YYWnW8HDJRZiIiIwHPPPYekpCTs2LEDubm5nNeK7NvZ2YkzZ87gypUrOHLkCHJycrBw4ULExsZyxxkJz5HOKQPA5QxWVFTg448/RkVFBcLDwzFjxgykpKTA09OTm7zEb4cwEq6L4QhTqu4R9EtCaKYKCXMQC/q+++6Dp6cn/P39sXXrVhw6dAgdHR1ob2/HqlWruERvvkVN2nU3wXEoyhltwfOLI9LnwrcabTYbmpubsWfPHrz33ns4f/48jEajnVdCLBbDy8sL69atw6OPPgqTyYSPPvrI6fHdcfczIeQezvoOYF/1nr7nQlY4XdCQNhj4x+H/JvTc+EoZOV5oaCieeOIJXL16lXvBBgYGIj4+HhMmTLBrq6OjA2fOnMG2bdtQUVHBHd9sNuPs2bN48MEHER4ezr38+KFlxu3DV3IB4Rpg5L6rVCrMmjUL0dHRyM7Oxrvvvov8/Hz09vbaKeVtbW3Iy8tDSUkJDhw4gAULFmD16tWcx5/vbRTKtRIKzdFRAKGIAF+20d/x+w7xsJLixm1tbcjPz8fnn38Oq9WKxYsXY+rUqfD29oZKpeL2ceWNZ4w8mFJ1D3EVI6ctNjrXSqVSwcvLC59++ilOnToFvV6Pzs5OPPnkk9yyLDT8XCahYw0H/BlTALgaQ/yX8JUrV/DOO+8gNzcXtbW1sFgskEqlnBUnl8sRHh6OX//615g9ezZCQkJw+fJlh+sRguUdDC8kIRwA94zKy8tRXFwMvV7P5T9ZLBbcuHED169fBzCgUPX09GDXrl24cOEC93IQi8VISEhAfHw8tFqtoMJEw1e0+LmIQUFBWLZsGRc6bm9vR25uLurr65GTk4PJkydDLBajoaEB+fn52LFjB+rq6pCUlAQfHx/U19ejvLwchw8fRnx8PFpaWqBUKtHW1obs7GwuBEnn/TCGhtBz5csiVwnlMpkMYWFhWLlyJdLT07Fr1y5s27YNZWVlAGBXU6yhoQF6vR75+fnYvXs3HnvsMSxcuBDh4eHccekQMgBu9iitdAkpRO7A35cuVEzCnyQ39OzZs9i5cye6urqQlpaG9PR0RERE2K3txz82k2kjH6ZU3WOEwlT0wCHKFAmFkCKMSqUSu3fvxvHjx/GnP/0Jvb29ePTRRxEaGmpnEdGz4viWl9AAHeqgFcozIcnndFKqzTZQJfnIkSN44403cPnyZXR3d9t5C8jU9uzsbLz88stc0VP2Mru38O//22+/jf3790On03HfkZcVyYcDBjxD//znP+32F4vFmDZtGn75y18iKyuL69d8xduVokUfUyqVIiwsDO+//z5++9vfIi8vD21tbThy5AjOnDkDLy8vzjNgNBrR09ODqKgo/OxnP0NAQAC++OILlJeXo6enB2+//TY++OADSCQShISE4PXXX0daWhq8vb2Zl2CYEPJo0s/a2UQTMrklJiYGGzduxLx587B9+3Zs377droArMDBLsKmpCc3Nzbhw4QJ27NiBlStX4uGHH0ZAQACkUqldTh+RlcDNVAV6QoSQQu2O7KRzCQkSiQQmkwnNzc04fvw4Dh8+DB8fHzz++ONISEjgcgRZ7anRC1OqRjjE+0NmPonFYkRFRcHT0xNeXl7w9vbGV199hVdeeQVtbW144oknEB8fD+DmbBs6jj+c8BVCukwCPyeluLgYH330Ef7+97/bLTVBe7j8/f3x3HPPYf369QgJCYFYLOamYNMJrsDguQUs92D4IM+ZhPPUajUXviDQLybgZr/t6Oiwa0smk3H1pAA41KJyBzqERJT3+Ph4fPjhh/jiiy+wdetWFBcXo6urC11dXdz5hYSE4LnnnsPGjRsRFhYGkUiEgIAA9PT0YPfu3dz2JPTs5+dnN35YP7pzEIWaXzqFXpKF9BO1Wo2UlBQkJCTg0UcfxT//+U/s3LnToSQHMKDYHzlyBKdPn8a7776L73//+1i6dCmCg4MdFBe+8sQvVuxOKJhW1vjt0fvu3LkTBw8ehI+PD+bNm4dp06YhICCAS+NgfW30wpSqEYCrAUTc0mSgajQadHR0QK1WIz09HWq1GkqlErm5ufjrX/8KnU6HH/3oR0hMTLSbjk6/GFy52m8lp4oIH349FYvFgt7eXnz66ad47733cPbsWcHrlsvliI+Px+9+9zvMmzcPPj4+3Da0kOEnsQvlawl9zxga9DMlfwM3c0o2bdqETZs2cb8RLwL9jITy64hiRi+ITPcZd71BzvJcvLy8sHbtWqxduxYmkwkNDQ2oqqriqrGHhobaJUYDQFpaGv7973+jsbER1dXVMBqN0Gq1CA8Ph1arZQrVXYBWkPkTdgD7CvxEEZLL5ZDJZJg2bRpSUlKwZs0a/O1vf8OZM2fQ2dlpV3rFZhtYHqeoqAg//elP8dprr+H73/8+Hn74Ya7YKz3Zh59APxTofC1+/pjVakVfXx/Ky8uxf/9+XL16FSkpKXjssceg0Wjg7e0NpVIJkUjEee7pe8T64OiAKVUjHDpGT15ApCCcVCpFUlISgoOD4eHhgf/+97/4/PPPUV9fj1deeQWpqalQKBR2LyDSJnD7Lwoh4QcMuMy7u7tRXV2N//3f/0VeXh5aWloc9pfJZAgKCsL999+PP/zhDwgODuYEGV1Rm35xu3PuLLn49uAv7UIgz4V85uePCL2AyDR44mkg+STkhUFePPxn5uo5C+UJkmORApBk9lhERASn7JnNZgdPAHmRjx8/HiEhIQ4JzXSRRtanbh2hsB/9G2BfdR+4qTCTvD06H4r2BKlUKixYsAAzZszAvn378Mknn+Dbb79Fe3s7gJvpCORYdXV1eOWVV7BlyxYsXrzYbjkYshQMOZYzL6qz/kCPG773lrT59ttv49KlSwgPD0dWVhZiY2Ph5+fHFbal8wiFEvsZIxumVN0jBlMOaBc4baUQlzhZukAmk8FkMmHdunXw9vbGgQMHcOrUKfzkJz/BH//4R2RkZECr1doJCVeDdCgDmAhKs9nMeR8MBgMqKytx6NAhvP7669Dr9XZWI0GtViMjIwOPP/44Vq9eDQAOlhkdegHscxPINkzg3Hno5F3A0XMg9MIk39GzUoGbypW7icpCCcP8EAv5XiaTcYVkhaqp08nIJFeG5NfQ25LrIy9z1sfuDrSXh4bID6IwE+iVGWy2gSKuDz/8MLKzs3Hy5Els2bIFpaWlaGxstFvqihyjpqYG//rXv/Dvf/8bS5YswYoVKzBp0iQEBgZys65ppYZ/Xs4MAf7fZJuOjg6cO3cO+/btQ1tbG2bPno3FixdDo9FAoVC4HR0gsH45MmFK1QiHCHWSdE4rGlKpFF5eXlzi+mOPPYbAwEDs2rULly9fxosvvogXXngBCxYsQEhIiEMOAf0ScTXDZDAXuFQqhdFoREVFBfLy8rB7924cOnTI6QsxJiYGOTk5WLlyJaZNm+ZgqdLww5VCLnmWRDz8kHtOXkK08kRCg/zCmMTKppff4D9/oWnqgPBUe3fOjz4+Uabofk4bEXTxUb4yRc6DhC9ZLtWdwdVYpcc/7Skkz5NW5gmkvxGFy2KxwM/PDzk5OXjggQdw8OBB7NmzB6dP7gtMJgAAIABJREFUn0Z1dTW6u7shlUq5dQIBoLu7G9u3b8fXX3+NjIwMLFy4EDNnzkRkZCQCAwOdlorhX4+QkkX+NhqNuH79Ov7xj3+gpaUFKSkpmD59OiIiIuDt7W23kga5fsbohClV9wh3Eh5p6ERNvndApVJBq9VCLBZz66h9+umnOHPmDF5//XW0tLTgkUceQUREBLdKPOBYbNGZS9uV4DAajdDpdDh+/Di+/PJLnDx5Eo2NjQ7XIhaL4e/vj8zMTDz11FPIzMxEQEAAd22DhZKE/naVCMoYHoTyOvj3nK+s0/3UWXv83+jQLmnXFULeA75XjO/1oMeQ0DkBsMvxYjOwhg9aCeZ/z1eC6d9cbSu0D62AqVQq5OTkICsrCwUFBdi3bx9OnTqF0tJSdHZ2Ohyjt7cXR48exZkzZxAREYG5c+di1qxZSE5ORnh4OLy9ve3kEx2GpI0COieLKPI3btzAiRMncPDgQXh6emL+/PmYNm0aZxST0B//nISS6RkjG6ZUjRKEhBFw0xIn03AlEgnS09Oh1Wqh0Whw7NgxbNmyBU1NTXjmmWe4BHa6PdpzwFduANjlOND5Bg0NDTh37hz+85//YN++fWhubnYI9dlsA8n1KSkpWLp0KR555BGMGzeOO4ehFlnkW6qM7xauFC+h3CzGyIHOw7tbxxOJRNBqtZg7dy4yMjJQWlqKI0eO4NSpUygsLERtbS0Aey9ZX18fysrKcPXqVezatQtTpkxBZmYm0tLSMHnyZPj7+7uUWXxjtbe3F6dPn8b27dths9lw//33Y8qUKRg/fjynVPENABbmG70wpWoU4EwI0dYfsbB9fHwglUqhUCiwfv16aLVaHD58GJ999hlaWlrw4x//GElJSfD09OTapr0+dIiHDr3RwrCtrQ3Hjx/HgQMHcPz4cRQXF9t5B+h8lsmTJ+OBBx7gqgWrVCrBbV3le7Hcqe8Gw/GMWT8ZffBD/MPZJnAztOzt7Y2pU6ciNTUVS5Yswfnz53Hy5EmcPHkS165d40q90GFsnU6Hffv24dtvv0VkZCQmT56MjIwMTJs2DTExMfDx8XGYKUvnv4pEIpSVlSEvLw/FxcUYP348Fi9ejLi4OK7Ip6u8LMbogylVYwSSqEtc5BKJBEqlEqtWrYJarcaBAweQm5sLnU6HX/ziF8jIyIBareb2JS5suj36s0gkQmdnJ06fPo0vvvgCZ86cQVVVFbq7ux2EgkQiQUBAAB555BEsWrQIqampCAgIsJvRR29PhJirvC5X181epAzG6OROj12+553IyYSEBMTExGD+/PkoKSlBfn4+Dh06hKKiIuj1em5bouR0dnbi0qVLuHz5Mg4cOIDY2FguL2rGjBkICQkBYB9iFovF6Orqwt69e3HkyBGo1WosXboUiYmJ8PPz42oP0sofgRU8Hr0wpWoU4I7gIUoRGaQkaTMmJgYKhQJqtRpfffUVjhw5gvb2djz//PNYtGgRfH19HRQq4KbFZLVa0d3djXPnzmHnzp04ffo0KisrYTAY7PIKCP7+/sjKysKaNWswdepUBAQE2OVx0YmlZF9+PgL/mu922IAxcmEKNMMdaHnBn+hDSm8oFAqEhIRg3LhxyMjIwJIlS5Cfn4+8vDzk5eWhvr7eLqRMjMKmpiY0NTUhPz8f33zzDWJiYjBt2jTMnTsXSUlJ8PX15VIkjh49imPHjqGlpQWpqalYsWIFxo8fDw8PD24JMiFjkoX/Ri9MqRoD8BMcySwSUrlaLpdDLpdDq9Vi69atKCkpwauvvoqGhgY8++yz3BpsfCVJLBbjv//9Lz777DMcPXoUjY2NnGeKngFG6g4tWLAAK1aswJw5cxAREcFNSaanPZPzI0IHuJkc7ExpcqZQMWHDYIwO7oVhxE8qJ7lLJJ+TyB+JRAIvLy8kJiYiJiYGCxcuRHV1NQ4fPowvv/wSV65cgcFgsEuJsNkGCopWV1ejuroaZ86cwSeffILExETMmTMH8+bNQ0REBD7++GNcuHABUVFRyMnJwYQJE6BQKBwm59AzaJnxOLphStUowh3Fgm9ZyWQyaDQaSKVS+Pj4ICgoCJs3b0ZxcTHefvttNDY24pVXXuEKitpsNnR2dqK4uBivvfYaCgsLodPp7NZ0o9cSVCgUuO+++/Dzn/8cs2bNwvjx46FQKLhthXIGaOXPlYeKwWAwbgU6pEZ7wo1GI5cmQcsei8UCmUwGlUoFhUIBf39/JCcnY+3atTh79ix2796Nffv2QafTOchhq9WKrq4udHZ2orq6Gnl5efjrX/+KkJAQlJaWQqlUIiMjA7Nnz+aiBlKpVDDER8qRACwEOFphStUYhJ7iS08zt9lsSElJwe9+9zu88847OHLkCD755BM0NDTgtddeg4+PD/Ly8vDRRx9h//79MJlMdrP5SEiRWHipqalYvXo1nnrqKS5BnlhgdPImOSeh//nn7ex6AOGZf7Rlx1znDMbIRmgM38nSFfwyDHQqAg0/RYEYpJ6ennjooYewaNEi1NbW4uuvv8a///1vXL9+nSsoSstbs9mMrq4udHd348aNG5wsqqysRHFxMWJjYx2S2ulUCyFvFb/kjTMD1JWsY0br3YMpVaMIZwOCnztAksWBmwvOenl5QaFQcHH8DRs2IDAwEDt27MDnn3+O0tJSdHV1QafTcSE+vsVks9mgVCoRFhaG9evXY/ny5ZgwYYLgCu4k9EfnDLga0EIK0WC/sSR1BmN04M74vpPHvR0kEglUKhViY2Px4osv4mc/+xmOHTuGzz77DAcPHkRTUxP6+/vt1ialFS2DwYCDBw8iLy8Pv/nNb/DEE0/goYceQnx8PDw8POyS2+kwIEmroO9df38/J8Ppeljkd2fXzeTk3YMpVWMMkghOu7mBm4NVqVRCq9Wir68PU6ZMQX19Pfbt24dLly7ZLc0B3CxzIBaL4eHhgaioKDz22GN48sknuVXebTab4OKf/MF+q4OaX/OFD5uOzGAw7gZEvkilUsyZMwdz5sxBY2Mj9u3bhy+++AJlZWVoaWlBT08PbDYbt4QY2c9kMqGurg5/+ctf8NZbbyE5ORkLFizA4sWLERYWBh8fHyiVSu54dCFTWn7TIULGyIMpVWME/mwXuVzOrRNIFhQ1m83Q6XS4dOkScnNzcfToUVRVVdktx0EncIrFYgQFBSEhIQELFy7EihUrEBUVZafo0Ivv8pMt6f/dxR0XNoPBGF24GrujyYtCRwMAIDg4GOvWrcOaNWtQUFCA9957D1999RVaWloEFyYn8tBgMODkyZM4deoU/va3v2Hy5MmYP38+0tPTER0djcDAQHh6ejosyyW0zBML7Y0smFI1ynDm4hWaNSISiWAymdDc3IzKykpcvHgRe/bswalTp9DR0WEXmqOrpZME9ClTpuB73/seFixYgOjoaC6Rnb8OHAkxkvNztQgpg8H4bjKaS6MQRYpfa4++HuJtstls8PX1RVZWFnQ6HXQ6HZqbm9HR0WHXHqGzsxPHjx/Ht99+i6CgIKSkpCA7OxtTp05FcHAwxo0bB7Va7ZBSQa9lyZbrGjkwpWoU4UoY0R4hUluqoqICJSUlnEVUVlaGvr4+bmYgUYCAgUFJcq4sFgukUikyMzNx//33IyoqymEaMg0/2ZK0x2AwGGMB2iMkk8lQXFyMsrIyyOVyZGVlwcPDA3v37sWJEycAALNmzcLLL78Mq9WKqqoqFBUVobCwEOXl5aitrUV/f7+dzCbKWUNDAxoaGnDgwAGo1Wqkp6dj6tSpSE5ORkxMDCIjI6HRaOwKjPK5nXQLxu3DlKpRwmDWnc1m42L2RUVFOHfuHC5cuIALFy6gvb2dCwECN13YwICA8PDwwOTJkxEfHw8vLy9UV1fj2LFjeOedd9Db24vVq1cjJSUFcrkcMpkMJSUl6OnpQWBgIEJDQ+1Cf3QeAOFODXBniepMoDAYjDuF0WjEvn37sG3bNnh7e0OtVkOtVmPnzp0oKytDQkICli1bhsDAQKjVam7dU51Oh/z8fOTn56O0tBSlpaWoqalBX1+fwzGsViva2tpw6NAhHDp0CAEBAbjvvvuQnJyMuLg4JCUlYeLEidxKFQCb4TdSYErVHYCfX0QrM4PBnyXjyuogCemtra0oLCzEuXPnUFRUhJKSElRUVMBsNtsNNLqCuVQqRXR0NKZPn44pU6ZgypQpCAoKgtlsxtWrVxEQEIAvv/wS27dvR3NzM1avXo0FCxbAarXijTfeQF1dHR566CE888wzkMlkDkvPkGPeqqufvx/tVXNnXyZYGIyRhytP90get3SYz2g0wmAwoLe3F2azGefPn0dtbS0uXboEjUaDadOmISMjAzKZDDKZDFKpFHK5HJGRkYiMjMSSJUtQUVGBsrIyFBcX48KFCzh37hx0Oh3MZrPdO4Mcl1RxP3bsGDQaDSZOnIjExEQkJiYiISEBkydPhlarhUwmc/r+Id42egIS3/jl59fSbdCzyl3J+JH6DO8WTKkaZtyZMuyqE9KDifxGd2iLxQKbzQa9Xo/Lly/jxIkTKCgoQGVlJaqqqtDV1eXQJv1ZIpEgMzMT2dnZSE9PR2JiIiIiIiAWi2EymWAwGCCRSODt7Q2NRoPPP/8cBw8eRGtrK9rb27Fo0SJcv34d+fn5CAwMxLx58xAdHW1Xl2q4B9V3fZAyGKMd/ixk+vvRML7p1AqTyQSlUgmFQoH29nZcuHABeXl56OjoQE5ODuLi4rBnzx4UFRVh5cqVyMzMRHBwMCfLlUol4uPjER8fjwULFqC+vh7Xr1/H5cuXcfbsWRQUFKCmpkbwPKxWK/R6PVpbW1FQUAAfHx+EhoZiwoQJiI+P5xaMDgsLc1CSyOoW5FpI9EJo5jaBNmbpiUwkhYThCFOq7hB0nRI6qZDW9IUECn/GHGnDZrNxHqnDhw/j4sWLqKysRENDA1pbW50en1gjoaGhmDt3LnJychAZGYmIiAio1WqIxWK7c/Ly8oJUKoVEIkFOTg48PT2xZ88eFBQUoLm5GY2NjdBoNPDy8kJdXR0uXbqE8PBwrngeLTz5BUDvxD1mMBijn9GgXJHyMTabDZ6enlCpVKioqMDp06fR0tKCyMhI1NfX48MPP0RVVRWam5s5j1JwcDDXDq2UeHl5YeLEiYiLi0NWVhZWrlyJ2tpalJWV4dChQzh16hT0ej1nTJN3A1keTK/XQ6/Xo6ioCN7e3ggKCkJERATi4uIwc+ZMTJs2DePGjeNKNdA1sQDY1TMUqjdIv6dcFR5l3IQpVcMMXZDNlUJBKx205UDykkjnbWtrw+nTp3H48GGcP38edXV1aG1tRU9Pj6ArnY6vy2QyZGdnY8mSJZgxYwbCwsKg0Wggl8sdCnsCN9fgUyqV8Pf3BwA88MAD0Gg02L17N44cOYK//vWviIuLg1wuh16vx5UrV7BgwQK7Nsnx+dd7uwNxKIUD70ZOF4PB+G4hEg2sUqFWq+Hh4YHe3l7U1tbCYrHgxo0b3CLMoaGh+PGPf4ysrCz4+/tzChlRiISMabVaDS8vL4SHhyM9PR3Lli1DS0sL8vPzcfjwYXz77beora2FSCRyKDQqFovR2dmJzs5OlJeX48SJE9i1axcCAgKQmJiI7OxszJkzB7GxsXblbojRLjR7UGimITHC6dmQ/Ov4rsOUqmGGb3GZTCZOUSKdkWxHlyYQiQYW+rRYLKivr8e3336LAwcO4Pz582hoaIDBYEB/f79DnRR6Jh/5PGHCBKxcuRIPPfQQxo0bB61WCw8PD4dzI+3QFolUKkVvby8uXryIl156CVKpFKGhoQgPD8ecOXNw8OBBLvG9t7cX165dc5rrxCwbBoNBwy+pMFrkAjlvmUwGg8EAhUIBlUrFla2x2QYWWJ44cSLmzp2LBx54AOPHj0dQUBBkMhnMZjO3jBdRimh5TCtJJBdLqVQiODgYcXFxWLFiBZfysWvXLhw7dgwNDQ0wm81cWI+mv78fOp0ODQ0NKC0txX/+8x9otVpERkZi2bJlWLBgASZMmGBXbNRsNnNKEu25Eio2yiYIOYcpVXcAIYWH9tSQquckYdBiseDatWvYu3cvDh48iKKiIuj1ejvrgLYs+McSiUQICgrCkiVLsGrVKkyfPh1KpZJblZ2s10e7emmXLjlX0hZZILS8vBx6vd5O4QoICEBrayssFgva29tRXV0Ng8EAuVwOpVLpUIxuOGrSOKttw78G+t4zGIzRwWh4GRNZbrFYoFQqodFooFAouPIzarUaK1euRHZ2NiIiIricVBIZIDKcyEShZWb46SIkciCRSKBUKuHl5YXQ0FAsWbIEra2tyM/PR25uLnJzc6HT6bgQIXlH0OsRdnZ2or29HbW1tTh+/DiUSiWSkpKwaNEiPPjgg0hISOCURADctZJcXuaRch+mVN0B6LwiWskgVc1NJhM6OztRVFSEvXv34sCBA6isrOQWL+YrBnxFSiqVQqVSYfz48Zg2bRqWL1+O2bNnw8fHxy78R5aPIf8IEonEzoNGBANJQpTL5UhLS+M8ZefOncP58+dx5coVdHV1cddkNpvR2tqK4uJipKWlccKD4Cxv7G7ABj2DMfIYrUYPbXyazWb4+fnBz88PoaGhmDlzJpYtW4awsDD4+vrC29sbnp6e8PLysstZJfCNTtI2HbmgFS2yrVQqhUwmAwAEBgZi8eLFePDBB/Hmm2/i9OnT+Oqrr3DkyBFUVFTAZDLBbDZzOWBEDpN3gsFgwOnTp3H69Gn8+c9/RlxcHBYvXoz58+cjKSkJGo0GUqmUU+xobxUdvhzJMzbvFWNeqXI2iN31brjqMPzQFj+nyGg0wmg0oq+vD+3t7aipqcGZM2eQl5eHwsJCtLa2Csav+R4pqVQKpVIJT09PBAYGIiMjAwsWLMD06dMRHh7ucL50kTpn50x+o6fJ0rP3xGIxPD09kZqaisTERHzve99DS0sLysrKkJ+fj2vXrkGv10MsFuPy5cuYNGmS0/vkLoOFCp09J6HvWdiRwRgZ0OVhXOVFjpYXtEwmg5+fH7faREhICNRqNby9veHl5QWVSiXonSIIfUdDG+JkQWV6Wzp0aLPZIJfLMXPmTGRnZ6OrqwuXL1/Gvn37sG/fPjQ1NaGzsxO9vb0wmUwA7O+zzTawSPPFixdx8eJFvPnmm4iKisKcOXM4BcvPzw+enp5QKBTcOQg9q8GerdDfzhgN/cAZY16pouF3JgK9rAr9G7+Oh1B7tFXR39+P7u5udHV1oaOjA3V1dXb1o+rr6+00fn5SO93xZDIZvL294e/vj5CQEKSkpOD+++9HZmYm1Gq13bIwtBVFcNYpXXmSyLkoFArOG+bj44Pe3l709fXB398fkZGRyM7ORm9vL/R6Pbq7u+Hv7895uviD51YHh9B+/LwB4mnjfzdarWEGY6zDl7VE1o2WMUvkpVqtRlJSEpfCoVQqoVQquZp9fPnHV6RcefEHm5BDZD8NSSnx8vLC9OnTMX36dPz+979Hfn4+jhw5gpMnT+LatWtob29HS0sLjEYjd54kQiKRSGA0GlFWVoYrV67g3XffRVhYGGbMmIHs7GxMnjwZQUFB0Gq1UKlUXHoJPy+Xfq8JTVgCHEOdY6k8w5hVqpzNRCMPk/YEkfg1nexN9hNSxMj//f39aG9vR3NzM9ra2lBXV4eSkhJcunQJV65cQUVFhd3+/Hof9GebzQYfHx/4+fkhODgYkZGRSE5OxsyZMxEfHw8/Pz8uP0po9XIadyyIwbxzJKlSLpfDx8eHcyX39/ejr68PfX19iIyM5Kqse3p6ctforBDo3WI0WzkMxlhntChQNLShLZPJIBKJoFQque9JqMwdY9LVNrdjFNJFPcnfU6ZMwdSpU9Hd3Y2qqiqcPn0ap06dQnl5OW7cuAGdTofu7m676AhRdiwWC6qqqlBdXY3PPvsM/v7+mD59OjIzMxEbG4vIyEiMHz8eWq3W7rj89yT9/qS/4ytig9230cKYVapo6IdJXvp0oiCZdUcncvMtCYvFgu7ubjQ3N6O+vh4tLS2oq6vDtWvXUFpaiuvXr0Ov18NoNHIdVCguTmvvcrkcWq0WoaGhCA0NRUxMDJKTkzFp0iRMnDgRCoXCwZoh7mCCOzlL7gxw8pke0PR9IiUTVCoVl/hOrpEIGbI9rSgOJafKnVDrUPZhMBiM4YbIPII7M+Pc+W0o2whBcrKESh94enrivvvuQ2JiIlavXo2KigpcvnwZhYWFKC4uRmVlJWpqamAwGByuieTa6nQ65Obm4quvvkJwcDCSkpKQmpqK5ORkTJgwAZGRkdBqtZDL5U7Ta/jRnbHImFeqaDek1Wq1K+MP3Azx8ZMGTSYT9Ho96uvrUVdXh7q6OtTU1KC6uhq1tbWoqalBa2srjEajg9bNd/kSpUoikUCtViMiIgIRERGIjo7GxIkTERsbi+joaPj7+zvErYGb3jXi4qXbvZsdlAgTcg/5iyfTSiPfIrkdRqNly2AwHHEW2hrpxpGraADfM8OHn091pyAz9gj8PF1yfKVSiYSEBCQkJOChhx5CU1MTLl26xC0SfeXKFZSXl0On0wkeRyQSccvm5OXlwcvLy27JnNjYWMTExCAqKsouVMl3KvCjQCO9D7jLmFWq3PF60J29u7sbNTU1qKqqQlVVFWpra1FXV4cbN27gxo0baG5uRmdnJ6fY8JUGOpxIOojVaoVGo0FkZCTi4uIQExODsLAwTJgwAeHh4Rg3bhy8vLzslCPayyOk4dMDREiBGa77JpRYyYcOQ/IL2t3OIp9CQkgoyXWsDEIGgzGyccewu1feF2dpIPzf+d+JRCLI5XKEhIQgLCwMCxcuhE6nw/Xr11FaWoqKigoUFBSgpKQEzc3NXIkFWnkj5XdOnjyJkydPQqvVIiwsDNHR0YiNjcWkSZOQnJzMlZkQeh+MNaN5zCpVBH4yOJlq2tTUhIqKCly9ehXl5eWoqamBTqdDS0sLlyNFZku46gD8pDxfX19uHaakpCSEhoYiJCQE48aNg7+/P9RqNaekuFKQyHd8pYJW4u6lhTfYcYca+qP3ux3GksXDYIwF3MnxHEs4M0iH2wAWgp/OQZ+TzXZzpjc/ogIMGMlBQUEIDAxEZmYmuru7UV1djYqKCpSWluLChQs4c+YMdDqdXfSE9o51dHSgs7MTly9fhkwm4xS2+Ph4pKamIj09HXFxcVw+Gn1OY4Uxq1TxBy5dyKy4uBjvvvsujh07hra2NnR0dKCvr89usUm+sgPYJxjabAPVdf39/TmNnCxOHBgYCF9fX/j6+kKlUjlUPCft0edEt0sfC4BDAiH9+VYHpyurxhmDKZRC7d5pBYcpUAwG407jzIPPx5lHaKiK5FBChnzFjf7emVzmFx+ljXZizJPipcnJyZg3bx50Oh1u3LiBq1ev4ttvv8XZs2ft6ivyK7AbjUYu8nP27Fns2bMH48aNQ2hoKKZPn45Zs2YhKSmJ82CNFVk+ZpUqGv7DCg8PR1tbG0pKSgRnKNDQf8tkMkRFRSEhIQFTpkxBcnIyoqKi4OXlxf1TKBR2oS/SsYXWVhJSioQ6lpBb+Xa9QMPhQRKydobSvlCb/OdBL50gtNah0P78lddHOs7u7a1uxxi93IlnPJw5PbcSgqfTLYSWtCIvZYb7uJLH7uStCT1Hel/6d5IL7OPjg5iYGGRkZCAnJwfNzc24evUqjh49isOHD6Oqqgo9PT3cPnTSfF9fH+rr61FfX4/CwkIcP34c7777LsLDwzFjxgwsXrwYKpUKra2t8PHxQXp6ut25EUWNluv8pHe6fte9lItjWqki1WNphUksFsPHxweJiYmIiopCRUUF9xuBPBRvb28kJiYiNTUVaWlpmDRpEkJCQiCXy6FQKCCXyx2Kswm5X+kOeysJ3M4GgzsCbigWkjPhO5igp38nQlPoO/p7ocHLz1Uj98tkMqGrq8vhHMxmMwwGA9rb2yGXy9HX18f9JjSbk3+tQnlr9G+DbSt0X4SWERK6VlffD9Ye/5ycXYNQ2/xn4e59GewaXF2HUJ8QOrY7/cTZ+Qrtxz/uYM/QlZIvdO8GO/5Qz9/ZmBjs3F0ZgkL9xdX+rvqE0LZC98TZ57a2Npw5cwa9vb0ABsa4TqfD7t27ce3aNZd1AYUUMlf3+Fb6r7N9XV2rszYG+0wbiIONWWefb+V63R1jg/Vb4OYKIb29vbBarfD394fBYEBPTw/6+/vtlsshiEQDpRr0ej30ej2qq6tx/vx5vPPOO9zz9/b2RkpKCp599lnMnDkTPj4+dvsC9o4GfimJe43I5qwXj3L4HY2UAFAoFPjlL3+J/fv3o7KyEt3d3ZyCIJVKuYUylUolJBIJZDIZN0WUeEDIApp8ZY08dFeCgfzGLwJKb0PjznbOXiD8bW91OyHBIXSuwwk/6d1qtXLlKkgcXyKROBTCo1dVd/c8+Un1zj4Pp/Uz1HvnTl6KO8mfQrVkBmtrsPN157j3Iq/Gmff5Tp/HrYTW3W3P3TZu9zkM5zWQtkgeDl/2EK+GK0PTWT91dU6uPDdDaYd/Hbe6/+0wXG3f6vN3tR1fVtJ5v86gPVnkb75RrVAoMGnSJDz99NNYtGgRwsLCAAy+TM699t6PaaUKsK/carMNrFe3dOlSnDp1SrAmB4FfY4qPkPdpLOHOC2k4j0Mfy9mA5p8Tf0DTnkFXA3qkcrfu+WjlVnJThuOYAHsmt4urZ0fWH2WMfvjKDn+2PL2dkJymv6f7TExMDB5++GH84Ac/QEBAALfqB1HMSOFVOv+Y/v9uMqaVKqElEQBgyZIlOH78uINS5UyA8h+00DZCs/eEGKqlMJIfz51+ybnrnbHZBiYN0AmTztzhI5HhetbD2WfcbWss9Ofh9qLdimfpbrXn6iVzq14od/cj2zozSIW8DyOxv3wXGEpqCj+8B8DpcxVqn/ae85Ui+rNYLEZgYCB+/vOfY/ny5QgPD+cgDFxtAAAgAElEQVQUN3pb0q/uVW7VmM6pEovFMJvNdhozAIc1i8jv9EOlEfKM8DuKu56R4XJF3yrDKaBdhY3o4/CVW2fnw4dYsHT4gD8w6dpeEonELo/KHQYbdMPhZha6J0LtuXOOdFtCyr8rBrsGd++Fs+MP5VycbeNqv8GEsztez6Geqzv99laO4e7zd+c4/LZu5Xpc/T7UfuHsHAF745M2VqVSqUP4h/7f2TMf6rW4+/tQjuHuuB7K8x5MqRyucx+udvlykh81IN+TsB//ndrX14eOjg60tbWhp6fHwSgm/ebGjRv4zW9+A5VKhVWrVsHPzw/AzbyqkcCYVqrIYAXsB3VycjJMJhN6enocKs4CN1/WQkU56ZwdulYHfQzShhDuvJhvZZC6s82tKAa3+vLg7zeUlzndBsmdEokGFv4kFexJYqJUKuWW0CHXCNxcdHQwQTDY/XB1He5eq7N9XV230L7unK+z8yY4m0k62HbOzsndmanO7pWra3DVlqv2hNp2dd9cXetgx3LWJ4Suw93jutse/SKjZ0W5OqehjEuh8xKSJ+4+W9JfiPFKp1iQUA69nTvn4Wy8CW3nrD13x8Tt3NOhPJOh/u7suELfuyPvhO6/q/vMz3ESap/0FRJRsFgskEql3N9NTU04e/YsTp8+jZKSEtTV1aG+vp5rh+4bJpMJHR0dMBgMnFJFlDVn13U3GbPhPxq+16K1tRW9vb2cMOK7pPnw17QDMKgAILjq7PT/zj7f6v7Ojn+rQnWwl5QrhhJC4ruS+fsSxZa/RI6QAuzOebp7HbfrlRlKe0NhOJ4Dvw13PWBD9boOpnAMpa3bbWew9ga7J3fiuLf6InC3rVvtc66eP22oCY1Xkcg+z8VVuM+dfjLUaxjsnt6KJ2io7Qm1JRQyc8atXoM7+94uQsfmP2O6D9Df8z2WZrMZfX19qK6uxqlTp3Dy5ElUV1ejpqYGTU1NMBgMUCgUmDx5Mn77299i9uzZUCqVdsuk8d8L94LvhFIllFNDK1F0Mvu91HAZ7jOcLyUGg3H3YWOYQUMnp1ssFphMJpSUlKCsrAxVVVXo7OyEl5cXsrOzMWnSJGg0GgD2fYaOSN0rvjNKlRDOLCvG6GAoeTMMBuPe4GqcMvnLoCEOEP5kBX4kwpkiJeQBu9t8J5QqBoPBYNwbmPHDcAdnIVF+0jqtXJH9iDI1WA7Z3WBMJ6ozGAwG497ClCmGO9CeKWceTFp5ohUssh9/+3sB81RRMIuKwWAw7i4j5WXIuLcIqSJCtSFpjxT5jZTeGWzW8t2AeaoYDAaDwWCMCGgPFL+wpzP4K6CwRPURDvNgMRgMBoNxZ+GXLALsZ+q78mo6m+F/t2FKFWNYGcpMy8G+d9U2U3AZDGGGs27RUGrMMRgMFv5jDCOuBLCz3wazPhgMhvsIFcul/x+sULFQG67aZ+OVwbCHKVWM22Ywa3YodWpcwQQ4g3HvYEENBmNwmFLFuC1uVdAyAc1g3HnIWntDWSLoVpaDYTAYAzClijHsuEogFAoxuPJgMe8Ug3HruAqvuxpbQtPYB9uHwWAwpYpxB3BVuG2w7V0JbZZ7xWAMDaFCioB9EUV32uB/5i+GzGAwBmBKFWPYoAWuUKE2Zx4rehV7JqAZjFtjKCE7Z8qQUKK7qxm9DAbDHqZUMVwymHdIJBKhv78f+/btQ0NDAwwGg+DSAe6EHSZPnozExEQEBATYfT8SCroxGKMB/nijjZn29nYcPnwYDQ0NMJlMnBFDGzU0YrGY247OzcrKykJsbCx8fHzsjinUBoPxXYMpVYxbgniYenp6UFZWhj/96U+or6+HyWQCYJ8gSy986Yply5ZhzZo18PPzc6iky1+5nMFgOIev6Oj1euTl5eHll19Gd3e3w9i0WCzcmKV/I99LJBKuvcbGRqxduxYJCQlsPDIYPJhSxXDAmeUpFAbQ6/U4cuQIysvL0drayu3jrLotP9THXxRTJpPZrUBuNpvt1nRiCbMMhj3EwCHjRigHqrGxEefOnUNVVRWAAQOHP0ZppYrAT1hXKpVQKBQQi8WwWq12yhaDwWBKFcNNhBQqsVgMHx8fxMXFYfLkyWhvb3cI1dGKk81mg8ViQUdHB/R6Pfr6+gAAUqkUJpMJmZmZiIuLc3hJ8AU7U6gYDHv4Rgdgb8io1WrExcUhKSkJACCXy2G1WmE2myGTyQDcNGCkUiksFgtqa2vR1tbGLVZLjjN//nyEhYWNiMVrGYyRBlumhuESV1OqrVYrJ3BJyMBqtdopVrTl3N/fj7q6OqxZswaXL1/mQoUeHh7YuHEjnnvuOURHRzscR8ijxQQ4g+EIbcDQYTwSyhMKwdPheZFIhI6ODpw8eRIbN26EXq/nxmlYWBiee+45/OAHP4BGowEAO68yG5MMBvNUMQbB1fIytNIkEolgMpkgFoshl8sBgFOwJBIJenp6cPbsWXz/+99HXV0dt21wcDAefPBB/OpXv4JGo3GYAUgvr8H0fwbDOfyEc6JIkTElFos5o0TI8JFIJOjq6sLevXvx29/+Fo2NjVw78fHxePLJJ/HrX/+aG+8sz5HBcIQpVQxBnOVE0Z4rvveK5FfQ30ulUnR1deHrr7/G66+/jsrKSkilUkilUoSHh+ORRx7BH/7wB0ilUs5SJkgkEodjWiwWSKWs2zIYzqDHC+1JIiF1YGBs8ZWitrY2vPfee3jvvfdQU1MDYCDHMTY2Fs888ww2btwIk8nEhQvpYzEYjAHY22kMcSfX0ePXnaLbIcKaJK9aLBZOwdLr9di+fTu2bt2Kixcvcvka0dHRWL9+PdavX895toTqVPFDf3eyrIKrqeHOCig6a2OwBH9XbTAYtwI/95CMQ/I3/ZlsT7xZOp0OW7ZswY4dO3D16lWuraSkJLzwwgvIycmBh4cH1747iy/fDfjX42r8Dbb8DhuLjOGA5VSNAYQK9PGLbhqNRvT29nL5EYMJENKeSqWCQqHgvEN865c+Nh2qs1gsaGtrw/vvv49PPvkEFy9e5I4bHx+PF154AcuWLUNgYKDDMd1dSmO4cVavB7h5P92pKD2UYolMkDNuF6GxT0/0sFgsAAaUKuINpuXCjRs3sGXLFmzbtg11dXUABmb5JSYm4ne/+x1mzJgBrVbrcNx7XayXzh2j0wP4ChX9/e1MemFjleEOzFM1RuDnOQA3cypMJhMKCwvxzTffoKenZ0jtRkdHY+7cuUhISLBLcqUVKSLA6dyqhoYGbN26Fe+//z6qq6sBDChoEydOxK9//WvMnj0b/v7+3P50Qi0597uN0JRyAj9UQgt02gMgVJOLn3vGt5yZsGYMB7QhRbzGtAfZbDYDuNnPTSYTSktLuXHa1dUFANBoNMjIyMCvfvUrTJkyBV5eXiPKM0WPIzqkKeRpJnW2ANiVgHBmHDnLE2NjlOEuTKkaI9BTnomwAQaEhV6vx3//+1+8+uqrQxaK0dHR0Gq1iI+P5xQI0i59bFqZuHbtGj766CO89957aG9vh81mg7e3N6ZMmYIXX3wRmZmZXDVmoWu42wKMvhYhb5WQsKW9cnzrH7DPL+PnhdG5Y0xYM24XZ55VWuEg3xGPs8ViwdmzZ/Hhhx/is88+44wtrVaLefPm4Yc//CEyMzPtPNT0se6lcsU/NlGW+DOTAdh9T98ToTSCwYoTu0oPYDAITKkaY/Bd3SKRCBKJBFKpFBKJhLNW3cXDw4NLTKUVJ9oqJse12WzIz8/Hxx9/jI8//hgdHR2wWq3w8vLCnDlzsHHjRjzwwAMAbip/xJJ0lu9wp4WXUEI+/7i0YmQwGFBRUYG+vj4EBQUhNDTU5UtNKJTJz21hMG4Hui/Ryj6/7xFF32q14vDhw3jvvfewd+9e9PT0wGazQaPRYPny5Xj66aeRkZFhVyeODrOR49wrLysxZOjrpMea2WxGZ2cnysvLIZFIEBoaCn9/f4d74uwaaM8Wv8o8gzEYTKkaAxDBR7v3SV4TAPj6+iInJwf+/v7o7u7m9htMibFarYiJiUFqair3Gz1Fm8/p06fxwQcfYPfu3ejo6IBIJIJcLseyZcuwbt06zJw50yH3gbYanSXD3y2E8sTo3xobG7F582YUFBTAZDJh+fLlWLduHVQqFTd7kfZUCd0n2hpmQpox3NB9VyjsbLVasXfvXrz11ls4ceIEenp6IBaLoVQq8cwzz+Dxxx/HpEmTOA8VbWTwDZ972X/5xo/ZbIZUKoXNZkNRURE++OADFBYWQi6XY+PGjVi6dCk8PDzsjDihCTeuJp/Qx2NKFsMZTKkaAwjl8xCXOAnZxcbGYsKECYO6uGksFguUSiWkUqmdcObXjDKbzcjPz8cbb7yBI0eOoL29nTuXdevWYc2aNUhNTYVMJhvxuQp8hYqcX21tLfbs2YMtW7ago6MD06dPh1arhVwu5xRY+t4QIS9UYZ4ch8EYDuj8IcC+r9FGUHt7O06ePIk///nPuHjxIgwGA0QiEby8vPDzn/8cjz76KCZMmACZTMYpYBKJhPMM0Z6qe5Wk7mz8ECWwvLwc33zzDT7++GN0dnZi4cKF0Gq1nLed9taR9ujxy895dGVEMhhCMKVqDEGsLQB2a3IRwcFfp8uZoOALLCJYyP5ms5mz9rq7u3HhwgW8+OKLKCsrQ39/P6RSKTw8PPDUU09h48aNiI6O5hQqWvDTYQUy/ftuCy8hJY/+jiT6nzp1Cps3b0ZbWxt8fX3x5JNP4sEHH4RUKrVTMpubm1FaWoqioiLU19ejubkZHh4eGDduHCIiInDfffchPj4eKpXqrl4nY+xCh6eIDCBKPember0ex44dw0svvYSamhpuTEdGRmLt2rXYsGEDp3zQYWrSPmAfFhspigadI2U0GrFnzx5s3boVPT090Gg0+OEPf4jp06dzBo5EIoHFYkFdXR1KS0tRVlaGmpoadHZ2wsvLC8HBwYiJiUFycjJiY2MdrvFWZg0yvlswpWqMwU9MFXJzC33mQ4cM6GKbdJsGgwFHjx7Fiy++iJqaGhiNRgBAaGgocnJysGnTJqjVajtljhbUZrMZNpsNMpnMISGWn0g6WKIsPYVc6Fqc3RO+V8pisXDnRDh58iR27dqFa9euQSqV4tlnn0VWVha0Wi3EYjH6+vpw8uRJfPrppzh58iSamppgMplgMpm440kkEshkMigUCixfvhwbNmxAUlISrFYrV6eLPxPSnefEYBDofkIbKO3t7di5cydXfJdsGx8fj8cffxw//elP4eXlJdgWP1zmysPK99YKyR86xA/Yr5TAn4HHL1xKz96jPefk2Lm5ufjmm29QVVWFwMBA/OIXv8CUKVPg6enJeeqOHz+OTz75BBcuXIBer4fRaOSW7yHKmVwuR1BQEJYvX45nn30WkZGRd7Q+HmOMYWOMeqxWq9N/FovF7t9Q2zSbzTaLxWIzm822/v5+7nuDwWD717/+ZZs4caJNKpXaANgkEoktJCTE9vzzz9s6Ozsdjm0ymWwmk8nu3Mxms8Ox6O9tNhv3navt+P8IJpPJbhvSjtlsdviNbp9ca2Njo23Dhg02pVJpUyqVtrS0NNuVK1e47Zqbm225ubm2oKAgm1QqtYnFYptEIrH5+vra0tLSbImJiTZ/f3+bRCKxAbABsIlEItvq1attR48edfns+NfCYAhB+kl/f7/NZDLZjQuDwWDbtGmTLSwsjOt/AGzR0dG2N99809bX18dtzx8n/HFLtiHjz5ms4W9Dt2U0Gu22J+dLj03+OHX2O71NU1OTbd68eTapVGrz8/OzrVixwtbV1cXtX1tba/vHP/5hE4vFNpFIZBOJRDaFQmELDg62paWl2RISEmw+Pj42kUhkA2ATi8U2uVxue+mll2yFhYXceTMYg8E8VWMAV56MW/Fy2ASmHhML1Gw2o6+vD2+99Ra2bduGiooKLqQXFBSE559/Hhs2bICnpyeAgVAhbV0K1ZQxmUxcqILO3aBnGdL7CHlxyHZkH3JMcjxijdLnQu9LW+QAuBDKP/7xDxw6dAgWiwVJSUn405/+hKCgIO7+tLa2Yv/+/ZDJZMjOzsaiRYuwcOFCJCUlcUvqNDc348svv8Sbb76J6upq9Pf34+uvv0ZUVBQyMzMdwi0Mxq1AcqEIXV1d+J//+R98/fXXuHHjBtfPIiMj8cc//hFLly7lwmJChUKBm8V+CfzJHHQCPO11oscd2Y+kIJB1P4k3jb/0DT2G+eObnzdmNpvR1taGX/3qVygtLYVIJEJaWhp++ctfQqFQcG3W1dWhoKAAWq0Ws2bNwpIlSzB79mxER0dzOVXNzc1499138cEHH6C6uhpGoxHvv/8+kpKSkJycPGKS9BkjG6ZUMRzgKz+0MOnt7cXbb7+Nbdu2oaSkhMvh8vHxwYsvvogHH3wQJpMJbW1t3D50sjYttOlq7UajkUuIF1K8CPQSODYqvGDjhRPIcjlkWRxyTLPZzAlw+qVAF0kkxzl27Bh27dqFyspKTJw4EQ899BBXEoKELoODg/HMM89g3bp1mDBhAry9vTmFjLQdEBCARYsWwWAw4Be/+AUAoLOzEx0dHbBYLJzwp19UTGgzhgJtFJjNZtTV1eGf//wnPv30UzQ1NQEYGBt+fn74y1/+gqlTp6K7uxsGg4EbI/Q4AMC15enpCYVC4WCUAANj22QyQS6Xc0YN+UfKuNDj0fb/pxPQ45Ou9UZfDz/HkjaWyLFbWlpw4MAB7Nq1C+3t7UhLS8Py5csxbdo0AAMGm0QiQXh4OJ577jm88MILiImJsVO4gAHZEBwcjEcffRRdXV34v//7PwBAa2srWltb0dvby/IgGW7BlCqGU+gZMiQnIS8vD2+//TZXJV0kEnGLI587dw4VFRUAbgp5IlDJtgS5XI7s7GwsXrwYCoUCcrnczqolApdW6sjSN21tbejp6UFnZyeMRiPUajW8vb0RFBQEb29vThhLpVJcv34d3d3dUCgU8PX1RWBgoJ33i54lSY7d39+P8vJybNq0CdXV1fDx8cHcuXPx7LPP2l2bSCSCp6cnUlJSuH3JtRKvAfHUqVQqaLVa7rh02QvyQhlJCcCM0QWtvDQ1NWH//v3YvHkzTCYT159UKhUiIyPxzTff4PDhw1wfpj1MFovFLtdRqVRi6dKlmD59OpRKJYCb3mfSV4nCRc7DbDajvb0dra2t6OnpQXd3N6xWKzw8PKBWqzF+/Hh4eHhwy+b09/ejsrISBoMBnp6eCAgIgK+vr9318Q0si8WC7u5unDt3Dm+88Qa6uroQGBiIRx55BCtXruTuBcnVDAoKQnBwsENOF3+sKZVKeHp62il6RDlkMNyBKVUMpxDLlXhcWlpa8Mknn6C9vd1BEF++fBnFxcV2worMtKG/oxWP3t5ezJgxgwunEUHND/9ZrVbodDoUFRUhLy8PBQUFKC8vR3NzM2dJx8bGYvny5Vi6dCni4uJgsVjQ0tKCV155BWfPnkVCQgLWrl2LVatW2YUYyXGIABWLxaioqMCWLVuQn58Pm82GnJwcrFq1CuPHj7e7P3Q79HXxl8UgYcLy8nLOUh8/fjzGjx8PpVLpYP2Te8//jsEYDJFIhMrKSuzatYvz9pC+3dfXh8LCQpw/f95uH35f43tLg4KCkJKSAplMZhe24/dNk8mEuro65Ofn48iRIzh79iwaGxvR2toKi8UCtVqNiRMnYs2aNZg/fz7CwsJgMplw5coV/PSnP0VtbS2ysrLw1FNPYe7cuYLHoM/t4sWL+OKLL1BSUgKJRIJVq1ZhwYIF8Pf3566Z782mE+FJe7Qsa2hoQG1tLYCBcUwKhyoUClYGheEWTKliOECEB7/yt8ViQXt7O8xms4MXi/5H5zeRbYggI0IsJCQEMTEx8PX1dRDi5DPx4uTn52PXrl34+uuvceXKFajVaoSHhyM2NhZisRj19fUoKChAaWkpWlpa8MMf/hBarRb79u1DUVERbty4gSlTpuC+++5z8EwBN71GNpsNDQ0NOHToED766COYzWakpqbioYcewrRp0+zqdJHzJP/TZSbIPSRKZW9vL0pLS3HgwAFu2xkzZiAtLU1wRhXtSWMw3IFWGIxGI1d8l1YaLBYLN0OPwB9zdF+0Wq2IjY1FREQEvL29HWYB00aESCTC0aNHsXPnThw6dAhVVVXQaDRcGRGj0Yja2lqcOnUKV65cQU9PDx555BGYzWbs378fhYWF6O3tha+vL6Kjo12u0We1WlFZWYmvv/4au3fvhkwmQ3p6OlatWoWkpCTBGb6kHVrZ4l+L0WhEQUEBTp8+zW23bNkyxMXFsbA8w22YUsUYFCJQgoKCsGHDBsyZMwf9/f3c71KplAsZ8JPKAeEqxNHR0cjIyODKCQjtI5FIkJ+fj3feeQd79uyBwWDAxIkT8b3vfQ/p6ekICwuDSCRCWVkZXn31VVy/fh1Hjx5FTEwMHnzwQezYsQMNDQ0YN24cJk+ejNjYWJfX19/fj/3792Pr1q3o7u6GVqvF+vXrMXPmTCiVSodp3OSlQrdBe76Il4osZl1UVMRd+6JFi5CWlvb/tXfnsVFXax/AvzOdmZa2dKXQjS7sRSwVpaCRVbDsWyQIQSUVYzBiNIrGmLgByk1YNIJoZIkCNlVZVEKxKgJasSxSbYE20GChLS2VQjtLh3ZmzvsHnp9nfp2Wcu+89w73fj/JhHb2aeYcnnPOc57TrpAqR8P0rzAYDOjfvz+efvppnDt3TltSB9rnEKrBhppPKO8LAEOGDNHqPKnXq491Op0oLi7G2rVr8fPPP0MIgbvuugsLFy5ERkYGEhMT4XQ6UVRUhNWrV6Ourg6FhYVIT09HTEwMdu7cievXryM9PR1Dhw5FSkqKNqjS51caDDdKuXz++ecoKCiA0+lEWloannvuOQwePBgWi6XdYE4NhuRzymVRmWJgMBhQVFSEb775BuXl5QgODkZ6ejqmTZuGtLQ0DnSoyxhUUTu+RrLAjcNW586d+//2umqn73K5YLfb8f7776OwsBBWqxX9+vXDq6++ivHjx3vlJ6WlpaG0tBSffvop/vjjD/z444+Ii4vDiRMn4HA4MHXqVIwePVrrcH0FMUII/PTTT9i7dy9KS0sRERGhLVMkJCT4DBZV6pKfOiouLy/Hjh07sG/fPng8HkRHR2Pp0qUYO3YsIiMjAXS9dhiRL/oZlJSUFCxcuFD7/Wa71royU6rfsCJvb21tRXV1NVasWIHjx4/D6XTivvvuw7JlyzBx4kSvGlcxMTE4c+YM8vPzUVZWhqKiIiQmJqK0tBQulwtTpkzBsGHDtCVL+TrqMrvL5cL333+PvXv3oqKiAikpKViwYAHGjh2rbRLR1+qT5Eyd0Wj0mnVra2tDWVkZNm7ciCNHjsBsNiM1NRWvvfYahg0bhvDwcLZL6jIGVRRQZIdus9nwxRdf4MiRI7h8+TIyMjLwyCOPYNasWdroEoCWKJudnY39+/ejsbERFRUVyMvLg81mQ8+ePTFq1ChtqU2fEC5HxA0NDdi2bRsOHz6M8PBwjBgxAkuWLEFycjKAvwsbqssl6nKm/pw1l8uFyspKrFmzBoWFhWhoaEBKSgqWLl2Khx56CL169fqP/Y3pf8vNAgJ9Lt+tLHNdvnwZu3fvxtGjR2Gz2XDvvfdqgxG1jQFAeHg4Ro4cif3798Nms6G4uBhhYWFwuVxISkrChAkT0L9//3bvSf58/fp11NTUYMOGDSgtLUVUVBRGjx6NxYsXa4GPr2VJ+bnUMg8yL6y5uRm///47li9fjqNHj8JqteKuu+7Ck08+iRkzZiA4OJi5jnRLGFRRwFBzHZqbm7F582bU1tYiKCgIQ4cOxfz587XlQn1OV3x8PIKDg+FwOFBeXo5z585BCIHZs2dj5MiR2mGq+p1+QgjYbDasX78eRUVFaGxsxPDhw7FkyRKkpqZqHbF+9KsGZrLOjuxom5qacOLECaxYsQK//fYbrFYr7r77bixevBhz585FaGiotvzCzpkCSWczWfqZKoPBgKqqKmzduhUOhwNmsxmjRo1CTk6OtvtVHYSEhIQgKSkJBoMBVqsVJSUlMBqNCAsLw+LFi3HHHXcgJCSk3eySfK3a2lqsXbsWx48fh81mw4wZM/DYY48hMTHRq03ql9T1n0sGW/X19Thw4ADWr1+P3377DdevX0dOTg5yc3O9ZtmIbgWDKgoYMshpbm5GRUUFzp49C4fDgT59+iAzMxNJSUlawq26U1ANcGRiuMViQVpaGubOnYuMjAwA8Mp3kkHStWvXcOTIEeTl5aG6uhqDBw/G7NmzMXHiRJjNZrhcLu39qXVy1JkquZTgdrtx/vx57N27Fx999BEqKyvR2tqKWbNmITc3F2PHjkVoaCjzpiig+fp++rqusbERZ8+e1QYwskhmr169vNqHWrCzW7du2vK+zWZDaGgo7rzzTjz66KNITk72eRyM2+1GfX09Dh8+jG3btsHhcODuu+/GjBkzMGLECK14sCRrYMmBjvreZb9RUVGB7du3Y8eOHbh48SI8Hg9yc3OxcOFC3HPPPQgLC4MQwqtQKVFXMKiigCFnn65evYqSkhLY7XavzlpO4ctihTI4MplMWn0q4MZ/AFFRUVi+fDnuuOMOrdCfmjwuSz1UVlZi+fLlqKmpAQDk5ORg4cKFMJvNXlvSAe/ZKnUpUc5UFRcXY/PmzdizZw+uXr0Kk8mE119/HXPmzEHfvn1hsVg4O0X/Naqrq1FWVqa1pczMTPTp0wfAjaU6WRBUtjd5zp66JDdo0CCsXLkScXFxXhtAZFAkA6KioiKsWbMGTqcTISEhePTRRzFt2jQtSFNLm6gDHbWoqGzH33//PT744AMcOnQITU1N6NmzJ9544w3k5OQgISHBK0CTBYnl+2XbpZthUEUBQ10+Ky8v14Km+Ph4xMfHe90HgDaCdLvd2jZtAEhISMC0adMwefJkryRTuSzgdDphNptx+vRp5O3fOeQAAAxDSURBVOXlobi4GACwaNEizJ49G/Hx8V7F/3x1pOrhsR6PB1u2bMG7776L06dPw2QyISMjA+vWrUNWVhaio6PbVYfWfxaiQOErSd2XP//8E1VVVdoMblpaGmJiYmAwGGA2m7122Mm2V19frwU3AwcOxMyZMzFmzJh2Celq7mNxcTG++uornDp1CmazGbm5uRgzZgyio6O9djfqqflhHo8H1dXV2L59Oz788ENcunQJQUFBGDNmDFatWoXBgwdrNePU2W/9Dkmim2FQRQFDnflxOp1a5xYWFoaIiAivCuQySJHVz998801UVFQAAGJjYzF8+HCEhIS0O24nKCgIoaGhuHbtGgoKCrB582aYzWakpaVh/vz5GD58OIC/R7iy/pT+DEG5Lbu0tBRr1qzB119/DafTifj4eEyfPh0vv/yyVvJBjrzV+lb68gxEgaSjnCT1eqfTCbvdDuBGu4iIiEBYWJj2/Zb5j0IIOBwOnDhxAsuWLcOlS5cAAElJSRg0aFC7QY/avhsaGrBlyxbs2rULERERSE1NxZIlS9C/f38tAFLbpn7GCrhRZPiHH37ABx98gIKCAgBAcnIycnNz8cQTT2gDNvkcwN81+vT1stS/D9su+cKgigKGfueRPPLCZrPBZrMB+PtcQiEE7HY7jhw5gpUrV6KyslIbGcs8Dv02cPkaLpcLn332Gfbs2QO73Y7Y2Fi88soryMzM1Jbo1NGpmvgqO9tLly5hz5492LJlC06dOqUdu7N48WJMnz4d4eHh2uvJx8nf1YRaotuV/A7LJXKbzQaHw9GurEFjYyP27duH999/H3V1dV65jfoSJ+rMksvlwqZNm1BcXIy2tjb0798fb731Fnr37u21A1i2J3UTiuwDqqursWXLFuTn5+P8+fOIjIzEyJEj8eyzz+L+++/Xjt7R7+pTy7uo1xPdDIMqChiyA+vevTv69u0L4EZnVl5ejpKSEvTt2xchISGw2Wyora3Ft99+i/z8fJw8eRLjxo3DpUuX8Mcff8DhcKCmpkZLWpfLEbIzP3bsGHbt2oXjx4+jR48emDVrFiZNmoQePXpo70N/8LL8VwiBY8eO4cMPP0RhYSEuX76M7t27Y8qUKcjNzcWAAQPQ1NQEq9UKAO3ysTweD3r27Kk9N1Gg6WwjhRpc9OzZE+np6dos7NGjR5GVlYXk5GQEBQXBbrejuroaO3fuxJdffona2lrk5OSgsrISFy5cQHNzMxoaGrR8q6CgIO2cvZaWFhw/fhx5eXk4c+YM+vTpg5kzZ2LSpElex0qpy4SSDPBOnDiB1atXo7i4GFarFQkJCZg6dSoef/xxxMXF4cqVK16BkxpAWSwW7bQH7gKkW8GgigKG7Lji4uIwcuRIxMXFoa6uDkePHoUQAo2NjUhMTERlZSUOHz6MU6dOAQCmTJmClStX4r333sPly5fR0NCAAwcOID09HS0tLejXrx+GDBmCHj164MqVK9iwYQNKSkoQFhaG7OxsvPDCC4iMjPTqYOXOIbV0gyx0+OKLL+LXX3/VknEjIiJgMpmQl5fntbQnHyefR24ff+aZZ9C7d2/uKKKAp989JwkhkJycjKysLERFRaGpqQkHDx6ExWLBhQsXEB4ejvPnz6OwsBDnzp1DVFQUFixYgKVLl+L5559HXV0dqqqqUFBQgIiICFitVgwdOhQDBgxA9+7dce7cObz66quoqqpCVFQUHnzwQSxatAgAtJkxdWZbDngMhhsV148dO4Ynn3wSNTU1cLlcCA4O1malPvroI7S2tnrNsqlBmslkQnJyMp555hltOZPLfdRlgihAuN1u4fF4hNvtFvX19eLtt98W2dnZIjIyUhiNRgFAABBms1mkpKSIKVOmiDVr1oiqqipx/fp1sWPHDjF+/HhhNpsFAGEymYTFYhEvvviiqKysFLW1tWLVqlUiPj5eGAwG8cADD4hdu3aJtrY20dbWJtxut3C73cLlcgmPx9Pu0tDQIDZt2iRSU1OF0WgUBoNBGI1GERQUJAwGg/b+5EXeJygoSBiNRmGxWER6erooKSkRbW1t2vMSBRpf33/ZPtRLRUWFePnll8XAgQNFt27dBACtLRiNRtGnTx8xb948sXXrVnHx4kXR0tIi3nnnHZGVlSVMJpN2f4vFIjZu3Chqa2tFWVmZWLZsmdZu5s2bJ7777jutbbpcLu1n2WfIn9va2sTZs2fFqlWrtOeXF7WNGgwG7SLvZzQahdFoFN26dROjRo0SV69eFa2trV6fl22WboYzVRQw1PPHYmJisHTpUmRmZqKsrAw1NTVobm4GACQmJmLAgAHIysrCoEGDYLFY4HK5MGHCBISHhyM7Oxv19fVwu93alH+3bt3w888/Y/369bhy5QoGDhyIqVOnYsKECV6jUPVMNDU3RAiBkJAQZGVl4emnn8a1a9e88ruEbiSrzk7JxwcHByM1NVUrgKh/DNHtJj09HcuWLcOwYcNQUVGBuro62O12BAUFISEhARkZGbjnnnu8ZmYffvhhxMbG4vfff8fVq1fhdrvRu3dvjBkzBi6XC9999x0++eQTCCGQlZWlFfBVqecUAt5LlpGRkcjOzsYrr7zSroSDfrlQKInuwI12Gxoair59+/J4GvqnGIToZAGd6N9IBicAvJbexF+7h6xWKwwGAyIiIhAcHNxul498TEtLC5qamuB2uxETEwOTyYSDBw9i3bp1OHDgAEwmE1566SU88sgjSEtLa1c+QXakLpdL24WkHpIMwOv+alDVUaKrfH/6JcWOSjYQ/Sd19b8FtZiux+OB1WpFS0sLjEYjYmNjvYrlyueVZ/g5HA44HA643W7tvvn5+di4cSN++eUXhIeH4x//+AemTZuGpKSkdu/NV06VvE2+jlqqAfBeOlSpfYC6MUXfztUdvES+cKaKAoqvrdsGgwFhYWFe53vJ69XZHtkBhoWFabkQLpcLZWVlKCgowOHDhwEAc+bMweTJk5GWlua1Y0ilbuuWt6udrX7nnq8AS+3g9fW11I6dHTQFEn3b8/VdVYMN9SinqKgoREdHe+Up+SIL9qpt+tChQ9izZw9OnjyJ2NhYzJ07VzvQXLYrfVCjDmbU9+2rXfvKdVQ/r68ZLfX6jv5ObL+kYlBFAcNXRyl/V29X//U1U6R2/Ha7Hbt378bOnTshhEB6ejqeeuopDBkyxCso03fW+hmkzsofqI/Rj5p9dfi+np8oEHUUOOiXzPQMf5U40H/39e1Itt3m5mZ8/PHHOHjwIEwmEzIzM/H8888jKSmp3Xmd+te7WTtS+wV936I+vrPP2JXXIQIYVFEA6qzT1AcnN+tsrVarVpsmJiYGc+bMwdChQ7WzvdTH6kfo6s9d7VD1j+vo/TGookClb28dBU3qcr3+sb6CFvFXqRIZbMlLa2srGhsb0atXL4wbNw4DBgzA5MmTkZCQAIvF4lWQs7P32lG/0ZUA6p/B9ku+MKeKbludfXXlbU6nEy6XS0tYDQ0Nhcfj0epWqUsKHQVV/8o0f0fPSXS7uFm7UPn6juuTyuV1at5TW1sb7HY7PB4PTCYTQkJCYLFYvJbg1OX3joKjjvoEtj36d2FQRbetznIm1NtkdXX1cFR5HzX5XH0eX6/Djpno1qltUh4+ruooUNO3Z185VWyTFGgYVNFtxdeoubOvcFtbm9dhxnI5Q57pJ3cD6fOxOMNE5B/qbJN+I4d+U4e+DarBk682ybZJgYZBFd1WbjWoAryXGtxuN0ymv1MJO0pyZ1BF5D+ynfmaHVbbl3qsk9oGO9t1SxRIGFTRbasrOVXqLJS8vrNdheykifxLDaj0u3PV+lHyvvogq7N2yfZKgYa7/+i/hn6JQAjRrl6NGkh1ViaBiPxH39587eiT7VdNbO9KKROiQMKZKiIiClhd3WVIFAg4VCciooDFAIpuJ1z+IyKigMbAim4XnKkiIiIi8gMGVURERER+wKCKiIiIyA8YVBERERH5AYMqIiIiIj9gUEVERETkBwyqiIiIiPyAQRURERGRHzCoIiIiIvIDBlVEREREfsCgioiIiMgPGFQRERER+QGDKiIiIiI/YFBFRERE5AcMqoiIiIj8gEEVERERkR8wqCIiIiLyAwZVRERERH7AoIqIiIjIDxhUEREREfkBgyoiIiIiP2BQRUREROQHDKqIiIiI/IBBFREREZEfMKgiIiIi8oP/A6NIpqII5L5hAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 7, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"from IPython.display import Image\n", | |
"Image('./conf.png')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"$\\alpha$를 알 경우에 $Z_{\\alpha/2$를 구할 수 있다. 또한 반대도 가능.\n", | |
"\n", | |
"$Z_{\\alpha}$에 대응하는 $\\alpha$값은 computer look up table에서 찾을 수 있다.\n", | |
"\n", | |
"\n", | |
"standard normal은 mean=0을 기준으로 대칭이기 때문에 $Z_{\\alpha}$와 $\\alpha$를 알면 반대쪽도 알 수 있다.\n", | |
"\n", | |
"Z : Z-Score에 해당." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 9, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"from IPython.display import Image\n", | |
"Image('./conf_2.png')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# 가설 검정(Hypothesis Testing)\n", | |
"룰렛이 있다고 하자.\n", | |
"\n", | |
"이 룰렛에서 당신은 검은색에다가 돈을 걸었다.\n", | |
"\n", | |
"만약 룰렛의 확률이 공정하다는 가정을 한다면 당신이 이길 확률은 18/37 = 0.48이다.\n", | |
"\n", | |
"즉 48%로 이겨야 한다." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 10, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<IPython.core.display.Image object>" | |
] | |
}, | |
"execution_count": 10, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"from IPython.display import Image\n", | |
"Image('./gamble_1.png')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"하지만 당신은 20번의 내기중에 4번 밖에 승리를 하지 못했다.\n", | |
"\n", | |
"위의 가정대로라면 당신이 20번 중 4번 승리할 확률은 0.0082이다. 즉 1퍼센트도 되지 못한다.\n", | |
"\n", | |
"여기서 \n", | |
"\n", | |
"null hypothesis : 룰렛이 공정하다.\n", | |
"\n", | |
"\n", | |
"alternative hypothesis : 룰렛이 공정하지 않다. (우리가 증명하고자 하는 가정)\n", | |
"- 즉, 어떠한 이유에 의해 이길 확률이 0.48보다 낮다.\n", | |
"\n", | |
"\n", | |
"다시 이번에는 당신이 20번 중에 6번 승리하였다고 하자. 그렇다면 그 확률은 0.073이다.\n", | |
"\n", | |
"이 값을 **p-value**라고 한다.\n", | |
"\n", | |
"## p-value\n", | |
"어떤 가설(null hypothesis)을 전제로, 그 가설이 맞다는 전제 하에, 현재 구한 통계값이 얼마나 자주 나올 것인가를 의미한다.\n", | |
"\n", | |
"즉 위 예제에서는 20번 중 4번 승리하는 사건이 얼마나 자주 나오는가? 를 의미한다.\n", | |
"\n", | |
"위에서 p-value는 0.0082가 나왔으므로, 즉 20번 중 4번 승리하는 사건이 나올 확률은 1%도 채 되지 않는다는걸 의미한다. \n", | |
"\n", | |
"이 의미는 1%미만의 확률로 나타야할 사건이 지금 나타났다는 것이다. 즉, 룰렛이 공정하다는 null hypothesis에 의심이 가기 시작한다.\n", | |
"\n", | |
"따라서 $\\alpha$를 정하고 $\\alpha$보다 작은 p-value를 가지면 null hypothesis를 기각하고 alternative hypothesis를 따른다. 그 반대는 null hypothesis를 그대로 고수한다." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Z-test 와 t-test\n", | |
"- z-test는 위와 같이 전체 정규 분포에 대한 variance를 알 때 사용한다.\n", | |
"\n", | |
"\n", | |
"- t-test는 정규 분포에 대한 variance를 모를 때, 정규분포에서의 sample에 쓸 수 있다. \n", | |
"\n", | |
"\n", | |
"- t distribution은 normal distribution은 아니지만, 비슷하게 모양을 가진다.\n", | |
"\n", | |
"\n", | |
"- n의 값이 충분히 크다면 variance를 몰라도 t-test 대신 z-test를 사용할 수 있다. (central limit theorem)\n", | |
"\n", | |
"\n", | |
"# t-test\n", | |
"- sample이 두개면 **two-sample t-test**.\n", | |
"\n", | |
"\n", | |
"- independent sample이냐 paired sample이냐에 따라 두가지 방법으로 나뉜다." | |
] | |
} | |
], | |
"metadata": { | |
"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": "3.7.4" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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