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main.py
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main.py
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{
"cells": [
{
"cell_type": "code",
"execution_count": 342,
"id": "f6dd9c2e",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 343,
"id": "16f16ee1",
"metadata": {
"scrolled": True
},
"outputs": [],
"source": [
"datos_matrix = np.matrix('0.2 0.6 1.2 1.9 2.8 3.5 3.7 4.3 4.9 5.7 6.1 6.5; 2.36 2.55 2.89 3.34 3.98 4.87 5.65 6.83 7.92 9.44 11.04 12.89')\n",
"datos_matrix\n",
"\n",
"datos = pd.DataFrame(datos_matrix)"
]
},
{
"cell_type": "code",
"execution_count": 344,
"id": "b8db0982",
"metadata": {
"scrolled": True
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>X</th>\n",
" <th>Y</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.2</td>\n",
" <td>2.36</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.6</td>\n",
" <td>2.55</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1.2</td>\n",
" <td>2.89</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1.9</td>\n",
" <td>3.34</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>2.8</td>\n",
" <td>3.98</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>3.5</td>\n",
" <td>4.87</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>3.7</td>\n",
" <td>5.65</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>4.3</td>\n",
" <td>6.83</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>4.9</td>\n",
" <td>7.92</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>5.7</td>\n",
" <td>9.44</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>6.1</td>\n",
" <td>11.04</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>6.5</td>\n",
" <td>12.89</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" X Y\n",
"0 0.2 2.36\n",
"1 0.6 2.55\n",
"2 1.2 2.89\n",
"3 1.9 3.34\n",
"4 2.8 3.98\n",
"5 3.5 4.87\n",
"6 3.7 5.65\n",
"7 4.3 6.83\n",
"8 4.9 7.92\n",
"9 5.7 9.44\n",
"10 6.1 11.04\n",
"11 6.5 12.89"
]
},
"execution_count": 344,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"aux = pd.DataFrame(np.asarray(datos).transpose())\n",
"datos_dataframe = aux.rename(columns={0: \"X\", 1: \"Y\"})\n",
"datos_dataframe"
]
},
{
"cell_type": "markdown",
"id": "aaaa18a7",
"metadata": {},
"source": [
"# Punto a)\n",
"\n",
"Grafico de la nube de puntos:"
]
},
{
"cell_type": "code",
"execution_count": 345,
"id": "b012cef7",
"metadata": {
"scrolled": False
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f8165d5f970>]"
]
},
"execution_count": 345,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(datos_dataframe['X'], datos_dataframe['Y'], 'o')"
]
},
{
"cell_type": "markdown",
"id": "15dce45a",
"metadata": {},
"source": [
"# Punto b)\n",
"\n",
"Recta de minimos cuadrados:\n",
"\n",
"Expresion aproximante:\n",
"$$P(x)=A_1*x+A_2$$"
]
},
{
"cell_type": "markdown",
"id": "0b265350",
"metadata": {},
"source": [
"Sistema de ecuaciones normales:\n",
"$$A_1\\sum_{n=0}^{11}{x_i}^2+A_2\\sum_{n=0}^{11}{x_i} =\\sum_{n=0}^{11}{f({x_i}){x_i}}$$\n",
"\n",
"$$A_1\\sum_{n=0}^{11}{x_i}+A_2*n=\\sum_{n=0}^{11}{f({x_i})}$$\n"
]
},
{
"cell_type": "code",
"execution_count": 346,
"id": "54f30a43",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Xi</th>\n",
" <th>Yi</th>\n",
" <th>Xi^2</th>\n",
" <th>Xi Yi</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.2</td>\n",
" <td>2.36</td>\n",
" <td>0.04</td>\n",
" <td>0.472</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.6</td>\n",
" <td>2.55</td>\n",
" <td>0.36</td>\n",
" <td>1.530</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1.2</td>\n",
" <td>2.89</td>\n",
" <td>1.44</td>\n",
" <td>3.468</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1.9</td>\n",
" <td>3.34</td>\n",
" <td>3.61</td>\n",
" <td>6.346</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>2.8</td>\n",
" <td>3.98</td>\n",
" <td>7.84</td>\n",
" <td>11.144</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>3.5</td>\n",
" <td>4.87</td>\n",
" <td>12.25</td>\n",
" <td>17.045</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>3.7</td>\n",
" <td>5.65</td>\n",
" <td>13.69</td>\n",
" <td>20.905</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>4.3</td>\n",
" <td>6.83</td>\n",
" <td>18.49</td>\n",
" <td>29.369</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>4.9</td>\n",
" <td>7.92</td>\n",
" <td>24.01</td>\n",
" <td>38.808</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>5.7</td>\n",
" <td>9.44</td>\n",
" <td>32.49</td>\n",
" <td>53.808</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>6.1</td>\n",
" <td>11.04</td>\n",
" <td>37.21</td>\n",
" <td>67.344</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>6.5</td>\n",
" <td>12.89</td>\n",
" <td>42.25</td>\n",
" <td>83.785</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Xi Yi Xi^2 Xi Yi\n",
"0 0.2 2.36 0.04 0.472\n",
"1 0.6 2.55 0.36 1.530\n",
"2 1.2 2.89 1.44 3.468\n",
"3 1.9 3.34 3.61 6.346\n",
"4 2.8 3.98 7.84 11.144\n",
"5 3.5 4.87 12.25 17.045\n",
"6 3.7 5.65 13.69 20.905\n",
"7 4.3 6.83 18.49 29.369\n",
"8 4.9 7.92 24.01 38.808\n",
"9 5.7 9.44 32.49 53.808\n",
"10 6.1 11.04 37.21 67.344\n",
"11 6.5 12.89 42.25 83.785"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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"<div>\n",
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"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Xi</th>\n",
" <th>Yi</th>\n",
" <th>Xi^2</th>\n",
" <th>Xi Yi</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>41.4</td>\n",
" <td>73.76</td>\n",
" <td>193.68</td>\n",
" <td>334.024</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Xi Yi Xi^2 Xi Yi\n",
"0 41.4 73.76 193.68 334.024"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"xi_2 = pow(datos_dataframe['X'], 2)\n",
"xi_yi = datos_dataframe['X']*datos_dataframe['Y']\n",
"\n",
"tabla1 = pd.concat([datos_dataframe['X'], datos_dataframe['Y'], xi_2, xi_yi], axis=1)\n",
"tabla1.columns = ['Xi', 'Yi', 'Xi^2', 'Xi Yi']\n",
"\n",
"tabla1_sums = pd.DataFrame([sum(tabla1['Xi']), sum(tabla1['Yi']), sum(tabla1['Xi^2']), sum(tabla1['Xi Yi'])]).transpose()\n",
"tabla1_sums.columns=['Xi', 'Yi', 'Xi^2', 'Xi Yi']\n",
"\n",
"display(tabla1, tabla1_sums)"
]
},
{
"cell_type": "markdown",
"id": "f1f3d91d",
"metadata": {},
"source": [
"Planteo de las ecuaciones normales:\n",
"\n",
"$$A_1*193.68+A_2*41.4=334.024$$\n",
"$$A_1*41.4+A_2*12=73.76$$\n",
"\n",
"$$A_1=\\frac{334.024-A_2*41.4}{193.68}$$ \n",
"$$A_2=\\frac{73.76-A_1*41.4}{12}$$ \n",
"\n",
"Formulas de Jacobi\n",
"$$A_1^{k+1}=-A_2^k*(41.4/193.68)+(334.024/193.68)$$\n",
"$$A_2^{k+1}=-A_1^k*(41.4/12)+(73.76/12)$$"
]
},
{
"cell_type": "code",
"execution_count": 347,
"id": "92d9fc48",
"metadata": {
"scrolled": True
},
"outputs": [
{
"data": {
"text/plain": [
"'T de Jacobi'"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.00</td>\n",
" <td>-0.213755</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>-3.45</td>\n",
" <td>0.000000</td>\n",
" </tr>\n",
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"</table>\n",
"</div>"
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"text/plain": [
" 0 1\n",
"0 0.00 -0.213755\n",
"1 -3.45 0.000000"
]
},
"metadata": {},
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{
"data": {
"text/plain": [
"'C'"
]
},
"metadata": {},
"output_type": "display_data"
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"text/plain": [
"'A Inicial'"
]
},
"metadata": {},
"output_type": "display_data"
},
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" 0\n",
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"data": {
"text/plain": [
"'A a las 100 iteraciones'"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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" 0\n",
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"metadata": {},
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],
"source": [
"T_Jacobi = np.matrix([[0, -41.4/193.68],[-41.4/12, 0]])\n",
"display(\"T de Jacobi\", pd.DataFrame(T_Jacobi))\n",
"C_Jacobi = np.matrix([[334.024/193.68],[73.76/12]])\n",
"display(\"C\", pd.DataFrame(C_Jacobi))\n",
"\n",
"A_Jacobi = np.matrix([[0],[0]])\n",
"A_Jacobi_anterior = A_Jacobi\n",
"display(\"A Inicial\", pd.DataFrame(A_Jacobi))\n",
"\n",
"for i in range(0,100):\n",
" A_Jacobi = T_Jacobi*A_Jacobi_anterior+C_Jacobi\n",
" A_Jacobi_anterior = A_Jacobi\n",
" \n",
"display(\"A a las 100 iteraciones\" ,pd.DataFrame(A_Jacobi))"
]
},
{
"cell_type": "markdown",
"id": "b332a944",
"metadata": {},
"source": [
"Recta aproximante hallada:\n",
"$$P(x)=1.564444*x+0.749333$$"
]
},
{
"cell_type": "markdown",
"id": "b24c15c2",
"metadata": {},
"source": [
"Graficos - Recta de minimos cuadrados hallada por aproximacion + nube de puntos"
]
},
{
"cell_type": "code",
"execution_count": 348,
"id": "6093341a",
"metadata": {
"scrolled": False
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f8165dde9e0>]"
]
},
"execution_count": 348,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(0,6.5,100)\n",
"\n",
"y = 1.564444*x+0.749333\n",
"\n",
"plt.plot(x, y, '-r', label='P(x)=1.564444*x+0.749333')\n",
"\n",
"plt.plot(datos_dataframe['X'], datos_dataframe['Y'], 'o')"
]
},
{
"cell_type": "markdown",
"id": "0837790f",
"metadata": {},
"source": [
"# Punto c)\n",
"\n",
"Parabola de minimos cuadrados\n",
"\n",
"Expresion aproximante:\n",
"$$P(x)=A_1*x^2+A_2x+A_3$$"
]
},
{
"cell_type": "markdown",
"id": "f59c0ea5",
"metadata": {},
"source": [
"Sistema de ecuaciones normales:\n",
"$$A_1\\sum_{n=0}^{11}{x_i}^4+A_2\\sum_{n=0}^{11}{x_i}^3+A_3\\sum_{n=0}^{11}{x_i}^2=\\sum_{n=0}^{11}{f({x_i}){x_i}^2}$$\n",
"$$A_1\\sum_{n=0}^{11}{x_i}^3+A_2\\sum_{n=0}^{11}{x_i}^2+A_3\\sum_{n=0}^{11}{x_i}=\\sum_{n=0}^{11}{f({x_i}){x_i}}$$\n",
"$$A_1\\sum_{n=0}^{11}{x_i}^2+A_2\\sum_{n=0}^{11}{x_i}+A_3*n=\\sum_{n=0}^{11}{f({x_i})}$$"
]
},
{
"cell_type": "code",
"execution_count": 349,
"id": "cf51d562",
"metadata": {
"scrolled": False
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Xi</th>\n",
" <th>Yi</th>\n",
" <th>Xi^2</th>\n",
" <th>Xi^3</th>\n",
" <th>Xi^4</th>\n",
" <th>Xi Yi</th>\n",
" <th>Xi^2 Yi</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.2</td>\n",
" <td>2.36</td>\n",
" <td>0.04</td>\n",
" <td>0.008</td>\n",
" <td>0.0016</td>\n",
" <td>0.472</td>\n",
" <td>0.0944</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.6</td>\n",
" <td>2.55</td>\n",
" <td>0.36</td>\n",
" <td>0.216</td>\n",
" <td>0.1296</td>\n",
" <td>1.530</td>\n",
" <td>0.9180</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1.2</td>\n",
" <td>2.89</td>\n",
" <td>1.44</td>\n",
" <td>1.728</td>\n",
" <td>2.0736</td>\n",
" <td>3.468</td>\n",
" <td>4.1616</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1.9</td>\n",
" <td>3.34</td>\n",
" <td>3.61</td>\n",
" <td>6.859</td>\n",
" <td>13.0321</td>\n",
" <td>6.346</td>\n",
" <td>12.0574</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>2.8</td>\n",
" <td>3.98</td>\n",
" <td>7.84</td>\n",
" <td>21.952</td>\n",
" <td>61.4656</td>\n",
" <td>11.144</td>\n",
" <td>31.2032</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>3.5</td>\n",
" <td>4.87</td>\n",
" <td>12.25</td>\n",
" <td>42.875</td>\n",
" <td>150.0625</td>\n",
" <td>17.045</td>\n",
" <td>59.6575</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>3.7</td>\n",
" <td>5.65</td>\n",
" <td>13.69</td>\n",
" <td>50.653</td>\n",
" <td>187.4161</td>\n",
" <td>20.905</td>\n",
" <td>77.3485</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>4.3</td>\n",
" <td>6.83</td>\n",
" <td>18.49</td>\n",
" <td>79.507</td>\n",
" <td>341.8801</td>\n",
" <td>29.369</td>\n",
" <td>126.2867</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>4.9</td>\n",
" <td>7.92</td>\n",
" <td>24.01</td>\n",
" <td>117.649</td>\n",
" <td>576.4801</td>\n",
" <td>38.808</td>\n",
" <td>190.1592</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>5.7</td>\n",
" <td>9.44</td>\n",
" <td>32.49</td>\n",
" <td>185.193</td>\n",
" <td>1055.6001</td>\n",
" <td>53.808</td>\n",
" <td>306.7056</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>6.1</td>\n",
" <td>11.04</td>\n",
" <td>37.21</td>\n",
" <td>226.981</td>\n",
" <td>1384.5841</td>\n",
" <td>67.344</td>\n",
" <td>410.7984</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>6.5</td>\n",
" <td>12.89</td>\n",
" <td>42.25</td>\n",
" <td>274.625</td>\n",
" <td>1785.0625</td>\n",
" <td>83.785</td>\n",
" <td>544.6025</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Xi Yi Xi^2 Xi^3 Xi^4 Xi Yi Xi^2 Yi\n",
"0 0.2 2.36 0.04 0.008 0.0016 0.472 0.0944\n",
"1 0.6 2.55 0.36 0.216 0.1296 1.530 0.9180\n",
"2 1.2 2.89 1.44 1.728 2.0736 3.468 4.1616\n",
"3 1.9 3.34 3.61 6.859 13.0321 6.346 12.0574\n",
"4 2.8 3.98 7.84 21.952 61.4656 11.144 31.2032\n",
"5 3.5 4.87 12.25 42.875 150.0625 17.045 59.6575\n",
"6 3.7 5.65 13.69 50.653 187.4161 20.905 77.3485\n",
"7 4.3 6.83 18.49 79.507 341.8801 29.369 126.2867\n",
"8 4.9 7.92 24.01 117.649 576.4801 38.808 190.1592\n",
"9 5.7 9.44 32.49 185.193 1055.6001 53.808 306.7056\n",
"10 6.1 11.04 37.21 226.981 1384.5841 67.344 410.7984\n",
"11 6.5 12.89 42.25 274.625 1785.0625 83.785 544.6025"
]
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