Write set of string consisting of any number of a including null string, followed by any number of b including null string, followed by ...
September 29, 2020
- Write set of string consisting of any
number of a including null string, followed by any number of b including null string,
followed by any number of c including null
string.
- Convert the given regular
expression to equivalent DFA?
- Using pumping lemma, prove that the
following language is not regular where
![](data:image/png;base64,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)
- Explain decision problem?
- Write the statement of Arden’s
theorem.
- Construct finite automata equivalent
to the regular expression-
![](data:image/png;base64,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)
- Construct a regular grammar
generating the regular set represented by
![](data:image/png;base64,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)
-
Find the regular expression for the
following automating.
- Set of
string consisting of any number of a (including null) followed by any number of
b (including null) followed by any number of c (including null) is equivalent
to
![](data:image/png;base64,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)
- Convert the
given regular expression into DFA –
![](data:image/png;base64,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)
- Calculate regular
expression from the above transition system-
![](data:image/png;base64,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)
-
- Prove the
following language is not regular -
![](data:image/png;base64,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)
- Define pumping
lemma for regular sets.
- Find the
regular expression corresponding to the following DFA
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAh0AAAC2CAYAAAB9JD/jAAAgAElEQVR4nOzdeVzN6f//8WMf6wzGNjNZBsPYMvZ9m8xIIctJewqhyD6WQsluSFK2ZkJKQjFRKGv2LUW0UJQWbSral8fvj8+389OohLSY6367XX/ovJfr5HTO87zf1/W6JAiCIAiCIJQBSXl3QBAEQRCE/wYROgRBEARBKBMidAiCIAiCUCZE6BAEQRAEoUyI0CEIgiAIQpkQoUMQBEEQhDIhQocgCIIgCGVChA5BEARBEMqECB2CIAiCIJQJEToEQRAEQSgTInQIgiAIglAmROgQBEEQBKFMiNAhCIIgCEKZEKFDEARBEIQyIUKHIAgVVlpaGvHx8SQmJvL69WsyMjLIyckhLS2tvLsmCMJHEKFDEIRykZubS3Z2NllZWWRkZJCRkUFmZqbs8ZycHLy8vJg/fz4WFhY4OTlx9epVnj9/ztmzZ8nOzpa1vLy8cnwmgiCUlAgdgiCUC19fX1xdXdmyZQva2tpoa2szf/582eNnz57F2NgYVVVVJk+ejLq6OpqamixcuJAjR47g6uoqa8nJyeX4TARBKCkROgRBKFPXrl1jzZo1DBw4kEGDBqGlpcXs2bP5+++/cXFxkW2XmppKbGws0dHRBVpcXByRkZEcOHAAPT099PT0MDIywsHBgcjIyHJ8ZoIgvI8IHYIglJnr169jamqKpqYmioqKGBkZYWtry4kTJ4iLiyMxMbFEx8nOziY8PBxbW1tsbW2ZMmUK06ZNw97envDw8M/8LARB+FgidAiC8Fmlp6fj4+ODpaUlixcvRlNTEwcHB65fv05AQAARERHEx8d/8HFzcnKIiIggIiKCv/76i61bt7Jv3z7OnDnDtWvXCA4O/gzPRhCETyFChyAIn010dDSWlpaMGjWKSZMmYWZmxrFjx3j58mWpnic8PJyQkBBCQkK4ePEiLi4u3Lx5s1TPIQjCpxOhQxCEzyIiIoKdO3cilUpRU1PD0dGRe/fukZqa+lnPGx0dzaVLl7h58yZv3rwhICCAoKCgz3pOQRBKRoQOQRBKXXJyMsePH0dbWxsLCwvu3btHbm5umZ0/JiaG0NBQwsLC2LBhA5aWljx58oScnJwy64MgCO8SoUMQhFIXEhKCra0tFhYW3Llzp9z6ERgYiKGhIRoaGmzbto03b96UW18EQRChQxCEzyA8PBxvb+9yDRwACQkJHDt2jBkzZjBjxgyePXsmrnYIQjkSoUMQhC9aSkoK7u7uuLi44OLiQmhoaIHKp4IglB0ROgRB+Gj5pcwreinyjIwMjh07hrOzM9OnT+fOnTsVur+C8KUSoUMQhI+SmZnJP//8g6GhIXp6ety/f7+8u1SszMxMjIyMUFVVxdbWlufPn5d3lwThP0eEDkEQPkpmZiZHjx6lVatWrFq1qlJUAjUwMOCHH35g9OjR+Pj4lHd3BOE/R4QOQRA+2Js3bzh//jwuLi6sWbOGhw8fVopxEvb29qioqDBu3DjmzZsngocglDEROgRB+CBJSUkcP36coUOHMn/+fAICAipF4AB48eIF8+bNQyqV0rNnT3bs2FHeXRKE/xQROgRB+CBPnjzBwMCAOnXqsHr1alJSUsq7Sx/Ezs6OqVOn0qZNG+bMmcOLFy/Ku0uC8J8hQocgCCUWERHB1q1b6dmzJ+rq6vj6+pKVlVXe3fogwcHBLFu2jDZt2qCgoMDp06fLu0uC8J8hQocgCCWSnJyMg4MD3bt3p2/fvhw/frxMS5uXpnXr1tGrVy8GDRqEvb19eXdHEP4zROiogGJjY4mOjpa1kJAQrl27hqenJ97e3vj6+spaRESEbLvPvZCW8N/m6+vLjBkz6NixIzNmzODatWuVttbFunXrkEqlSKVSEToEoQyJ0FGB5OXlkZSUxK5du9i0aRObNm3C2tqapUuX0r9/f7755htatWole7OUSqVYWlqyZ88etm3bxtmzZ4mOjubVq1e8evWq0t1rFyo2d3d3pFIp2tra/Pnnn+XdnU9iZWWFpqYm2traODs7l3d3BOE/Q4SOCiA3N5e0tDTi4uL4+++/kZOT46uvvqJ+/foMHz6c6dOnF9q0tbWZNm0aurq6/PTTT/Ts2ZPFixezZ88e9uzZw+HDh3n58iXp6emV9hupUHHkhw5zc/Py7son8/Hx4Y8//sDc3BxfX9/y7o4g/GeI0FEB5IeN8ePHU716dRQVFZFKpWzdupWQkJBC98nNzeX48eMkJydz8eJFFi5ciFQqpWvXrkgkEllr2LAhLi4upKenl/GzEr40InQIgvCpROgoR2FhYezevRt9fX20tLSQSqWMHTuWoKAgkpKSSE1NLXZFzIyMDPLy8sjMzCQlJYWkpCRu3LjB3r17Wbt2LWPGjGHcuHFoaWkhJyeHjY0NsbGxZfgMhS9FQEAAGzZs+GJCx59//knHjh3p1asXDg4O5d0dQfjPEKGjnISEhODu7s7SpUvp3r07Bw8e5NmzZzx79ozs7OyPPm5GRgavXr0iLi6OZ8+e4e/vj1Qq5auvvqJFixZYWloSFRVVis9E+C84evQoOjo6GBsbc+rUqfLuzidbt24dSkpKjB07VgwkFYQyJEJHOQgODsbW1pZ169axd+9eduzYQVxc3Gc5V1ZWFvfv32f16tU0a9aMH3/8EXd3989yLuHLFBgYiIGBAT179mTjxo0kJiaWd5c+mZi9IgjlQ4SOMhYcHMwff/zB6NGjsbS0JCwsjOjo6M9+3vDwcI4ePcrEiRNRUVHBxMSEK1eufPbzCpXfzZs3MTIyQkFBASsrq/LuTqkQoUMQyocIHWXk8ePHHDt2jJkzZ9KqVSt+/fVXPD09y7wfjo6OdO/enSZNmrBw4UKxvLfwXjdv3sTU1JRZs2bh5uZW3t0pFSJ0CEL5EKGjjFhbWzN8+HAaNGhAt27dsLS0LJc1Hy5duoSqqio//fQTKioqHD9+/LOc5/Xr1yLQfCFOnDiBkZERJiYm3Lhxo7y7UyryQ8esWbM4efLkB+37+vVr/Pz8cHd359SpUzx+/JigoCC8vb1xd3cnLCzs83RaEL4AInR8Zrm5uYSHh6OkpES9evXo1KkTVlZW5bbI1OPHj9m+fTtTp05FKpWW6uXyhIQE/P398fT0ZMeOHZibm3P79u1SO75QPszNzenbty+GhoZfTOjYu3cvCxcuxN7enmfPnpVon6SkJAICAvjnn38wMzNDKpUyefJkNm7ciJOTE7NmzWL48OFs2LChxMcUhP8aETo+o+zsbCIiIrC1taVhw4a0bdsWa2vrcp898vjxY9k3vU2bNvHq1atPOl5iYiLBwcG4urpiaGjITz/9RK1atWjXrh0zZ84kNjZWFCerpF69eoWqqioSiQRlZeUvInQkJCRw7NgxDhw4wKNHj0q0T2RkJM7OzkybNo2hQ4eioKCAmpoaRkZGGBkZsX//fmbNmkXnzp0ZMGAAhw4d+szPQhAqJxE6PqNXr15ha2uLoqIiTZo0YceOHbx8+bK8uwWAg4MD48aNY/r06Xh4eHz0cV6/fo2bmxv6+vr8/vvvdO7cmQYNGtC6dWtGjx6Njo4O9vb2ZGZmlmLvhbJy6dIlhgwZwldffYWGhgZ+fn7l3aX3Sk9PJy4ujpiYmELXI3Jzc2PhwoVYWlqWKHTEx8ezbt062rZtS82aNWnUqBHy8vIsX76c06dPy9rq1auZOXMmRkZGX8S0YkH4HETo+Exyc3N5+vQpioqKVK1aFVVVVUJDQ8u7WzKHDh2iZ8+e/PDDD6xYseKjjpGZmSkLHHJyctSpU4e+ffuir6+PoqIibdq0QSqVoqGhwZs3b0r5GQhl4dq1awwfPpxu3bqxf//+8u5Oidy9e5cVK1YwZ84cvL2933ncxMQEa2trXFxc3hs6srKysLCwoHXr1tSsWRN5eXlMTEy4fPlyodvfunWLp0+flsrzEIQvkQgdn0lsbCzbtm2jatWqSCQSQkNDK9Qthvv376OtrU2VKlVQUFD44P2zsrJkgaNJkyb079+fNWvW4OfnR05ODtnZ2Tx69EiEjkouLy8PbW3tShU6HBwc6N69O61bt2bNmjXvPH7mzBlcXFxKFDrOnz9Pnz59qFKlCpMmTeLWrVvk5OQU+becl5dXof7OBaGiEaHjM3n58iV79+5FSUkJJSWlCld+PCsrCxcXF3755Rfk5eW5ePHiB+9/7NgxpkyZwoYNG/Dz8yM5OZmsrCzZNtnZ2cTHxxMfHy/eiCsxHR2dShU6Dhw4QLdu3ahWrRp9+/bl0qVLsse8vLyYO3cuurq6eHt7F3i9/tu5c+fo06cPNWvWpGvXruzfv1/cJhSETyRCx2cQExODk5MT06ZNQ0dHh6CgoE8qbf65uLu707dvX7p06cLp06dLvF9qaipeXl4cOXKEgIAAXr58Kd6Mv2AbNmxgzJgxlS50SCQSunXrxpkzZ2SP/fHHH/z444+MGDGC8+fPF3uc5cuX07RpUyQSCZqamty5c+dzd10QvngidHwGd+/eRV1dnS5durBr165iF20rT/fu3WPhwoUoKiqyfv36Eu2TnJyMp6cnxsbGGBsbEx8f/5l7KZQ3a2trpFJppQkdPj4+jBs3DolEwpAhQ4iNjSUrK4srV67QqVMnevfujYODw3tfu4aGhjRu3Jiff/6Z/fv3k5KSUkbPQBC+XCJ0fAZXrlxh6NChfP/99xw/fpzc3Nzy7lKhgoKCWLZsGW3atOG3334r0T6hoaEYGhrSoUMH1q5d+8nTbYWKb+HChQwePLjShI6EhASsrKxo06YNI0eOJC0tjYsXL6KgoECtWrUwNjYu0WBPQ0NDBg4cyNy5c/H19S2DngvCl0+EjlIWHx/Prl27aNWqVaUIHcbGxtStW5dx48aVaJ9Hjx4xatQo6tWrx927d4u9Jy5UfmFhYYwdO7ZSjekA+Pvvv+nUqRPq6upcuXKFRYsWUaVKFTp06MCpU6d4/fr1e49haGjIkiVL8Pb2/iIWuROEikCEjlIWFBTE3LlzkUgktGnTBj8/v3IdRJmdnU1ISAheXl4EBAQUqFuQHzrq16/PpEmTSnS8t0PHgwcPROj4wh06dIhffvml0oUOOzs7fv75Z4YMGYKGhgbdu3enXbt2qKioyKauv3z5kpCQEFn7d5XgTZs24eXlxePHjwkJCSEhIaFE546NjSUkJERWkycjI0OURheE/yNCRynLDx21atVi2LBh5d0d0tPTcXFxQVtbmzVr1hQozxwVFcXGjRtp0qQJnTt3LtHx8kNHzZo1P2pMR2xsLGlpaR+0j1B+LCwsaNWqVaULHY6OjrRv3x6JRIJEIqFGjRr069ePCRMmcOLECUJCQnBzc2Pr1q2y5uDgUGDF51OnThEfH8+VK1fYvXs3R44c4cGDB0W+5mNjY7l//z5OTk5s3boVNzc34uLieP36tRiEKgj/R4SOUpYfOr755ht0dXXLuzukpqZiY2ODpqYmUqmUy5cvk5GRIXv81q1bTJw4kUGDBpXoeCEhIWhoaMjezM+ePVviEJGYmMiRI0cICQn5qOcilL3t27fToUOHShc6Nm/eLHuNvt2UlZWRSqXs27cPW1tbVq5cycqVK1myZAnLli0rsPLztWvXSE5Oxt/fn82bNyOVStHU1MTW1pbr168TFBREbGwsgYGBPHr0CEdHRwwNDVFUVGT48OEYGhri4+NTjr8FQah4ROgoZfmho1q1avTs2bO8u0NiYqJsCW+pVIq1tbXsakdWVhZBQUHs2LGDBQsWlPh4+/fvp127dtSvX5/hw4dz5swZ4uLiCr3VkpubS0pKCtHR0Rw+fJh58+Zx8+bNUn2Owudz69Ytfv3110oVOjIyMli7dq0saFStWpV69epRr1491NXVMTIyIiAgoMA+UVFReHh4FKjp8bY7d+6gqakpO46cnBy6urrs2bOHMWPGoKioyIQJE9DW1qZfv360aNECVVVVcYVDEP5FhI5SFhISwsKFC2nRogXz5s0r7+7w6tUr1NXVkUqljB8/ns2bNxMcHExubi6PHz/GyckJKyurEoeOfGlpaUyZMoVvvvmGKlWqYGxsjJ+fH2/evCEtLY20tDRSU1OJiYnB3t4eDQ0N1NXV2b17d7mtsCt8uJycHLS0tCpV6Lh37x6amppIJBKqVKnCt99+i46ODjo6Ojg5OX3UjCtfX1/WrVuHjo4OWlpaqKuro66ujqqqKvXr16d27dooKiqyY8cOXF1dcXV15d69e5/h2QlC5SZCRynLzc3l4sWLTJgwoUKEjrS0NJycnNDS0qJx48bUrFmT+fPnExQUxKlTp1BXV0dNTe2DQ0d+RVNtbW0aNWpEjRo1qF27Nj179kRLSwstLS2UlJSoU6cOderUQUVFhT179hAVFSWqk1YiV65cYdiwYZUqdBw8eJDu3bsjkUho2rQpc+fOJSMjg4yMDLKzsz/q9Zebm0tWVhYZGRmEhobi5OQkaw4ODjg4OBAREUFWVhbZ2dlkZ2dX2FlrglCeROj4DK5cucLMmTNxdXUt766Ql5fH69evcXJyQl1dnW+//ZbBgwfj4eHB9u3bqVu3Lj169MDNze2Dj/vmzRtiY2N59uwZR44cwdramkWLFiGVShkyZAi1a9emdu3aKCsrs3v3bqKjoytsoTShcJcuXWLOnDmoqKhUitCxf/9++vbtS82aNfnuu+/Q09Pj+PHjpXqO7Oxs3rx5804Tr+3CxcfHF7lAnvDfI0LHZ3DlyhWMjIw+qLT455aQkMD8+fNp1qwZffr0YcuWLcyaNUtWtbGwS85+fn6cO3eOsLAwIiIiePDgQZHHT0lJIT4+nvDwcM6fP4+VlRUWFhZs3bqVoKAg4uLixJtyJZScnMyff/6JVCrFwsLinbEQFcnff/9N//79qV27NoMGDeLAgQOEhoaKAnblKCYmBltbW4YNG8bly5fFVU5BhI7SdufOHZYtW1bhQgf8b/XNDh060LBhQxQVFRkyZAgSiYRff/21wHZ37txh1qxZDB06FA0NDc6ePcvr169LXKfgzZs3vHjxghcvXhSYgihUTtbW1vTp0wdNTU1u3LhR3t0plK+vL6NGjaJOnToMHToUJycnUdCrnEVGRnLo0CH09fX59ddfMTExEbecBBE6StvJkyeRSqUsWbKE58+fl3d3CggPD2fKlCk0atSIxo0b8+2339KoUSNmzpxZYDtNTU0aNGjAb7/9xs6dO0tUMlr4cllbW9OhQweUlZUrXOjIy8vj4MGDrFy5kpEjRzJhwgQcHR3FmkAVQFBQkOwq2ZgxY+jVq5e42imI0FGaXr58iZ2dHb/99ht6enrl3Z1C5Rd7yp9O2LJlS8zNzYH/zVR49OgRgwcPRllZGVdXV/FtUcDV1ZXx48czderUChM60tPTCQgI4MGDB+jq6iKVSlm0aBEeHh4icFQQb4eO33//ncaNG1fI1baFsiVCRyny9/dnzZo19O3bl+HDh5d3dwr179DRqFEjdHV1iYiIIDs7m7t372Jvb8/ly5dJSkoq7+4KFcDNmzcxNTVl9uzZ/PPPP+XdHeLi4nBxcWHWrFls2LCBZcuWYW1tzYULF0p8C1D4/GJiYjhw4ADKysp0796dnj17iisdFcTz588LFIksSyJ0lKIrV65gaGiIvLx8idcyKWv/Dh0SiYQuXbpUuPEnQsWRHzqkUilWVlbl2pfU1FROnjyJvLw89erVY968eZw7d67AmkJCxeHj48PQoUNp0KAB+vr6InSUktTUVCIjIwu0u3fv8uzZMyIjI3n48CG3b98uspmZmXHw4EF8fHwIDg4mJSWlzPouQkcpcnV1ZcSIEXTv3p2tW7eWd3fekZSUxPz582nRooUscNSvXx9lZWWuX79e3t0TKqiKEjrS0tK4c+cOs2fPplatWvTu3Ztz586JRQcrMBE6SkdKSgoJCQlERETg7++Ph4cHu3btKtCUlJTYuXMnLi4umJmZMWPGjAJt2rRpssrUderUQSKR0K1bN4yMjHB2dub+/fs8e/aM5OTkz/pcROgoRY8fP8bS0pIVK1ZUuA/xtLQ03Nzc6NKlS4FFsH7//fcKc59eqJjeDh1bt24lPT29zPuQmZnJnTt3sLCwYOjQoXTu3Blvb+8y74fwYUTo+DSpqanEx8dz9OhRbGxsmD17Nl27dqVTp07o6+szc+ZMdHV10dXVpX379uzatYuTJ08W2pydnTE0NMTQ0JCOHTvSrFkzmjRpQoMGDahRowatWrVi6tSpHD58mPj4+M929VCEjlKUl5dHYGBghfwQd3NzQ19fn+bNm1OtWjWqV69O586dsbGxKe+uCRVcfuiYNGkSCxYs4OLFi2Xeh7t372JmZoaqqipqamosX768zPsgfLi3Q4eurq4IHR8gOzsbV1dXpk6dSvPmzalevTq1atWiW7duLFu2DB8fH5KSkjh27BjHjh374C8D58+f59ixY5iYmNC9e3dq1apF9erVadq0KXp6ehw5cuSzjPsQoaMUBQQEcOzYsQoXOvLy8pg1axZNmjRh4MCBqKioYGJiwtWrV8ttMJFQeeSHjh49ejBs2LByCR0HDhxATU2NRYsW4e3tXeKVjYXylR86qlSpQvPmzcXslRJKS0vD1dUVPT09VFVVGT9+PBYWFty5c4eUlBTS0tJkJf2zsrLIysr64MJr2dnZZGVlkZaWRkpKCvfu3WPdunWMHz8eVVVVdHR0OHLkCG/evCnV5yZCRyk6evQo+vr6mJmZVZiVVJOTk5k7dy5NmzZl8ODBnD17lhcvXhAfHy8Ch1Ai6enp/PXXX8jLyzNo0KAiQ8fdu3fx9PTE09OTR48eER0dzY0bN3jz5g3u7u4sWLCAefPm0a9fP9TV1Zk3b16BpeT/7fLly5ibmzNv3jw2btzIhQsXiI2NFYGjEvHx8WHChAlMmjSJXbt2ieJgJZCUlISrqyv6+vqoqqoilUrZtGkTDx8+JDMzk9DQUPz9/YH/jfXI/5vz9PT8pAGhmZmZPHr0SDbNWVVVFX19fYyNjZk3bx779u0rldpTInSUIkdHR/r374+iomK5fBv8t+joaBYvXkyTJk2oWrUqy5YtIzw8vLy7JVQyjx8/Zt26dcjLy/PTTz+9M5j02rVr/Pnnn8yfPx9DQ0M2b97MvXv3iIiIwM3NDW9vbw4fPoytrS3a2tooKCgwduxYpFIphoaG7N69mwsXLnDhwgU8PT0xMzPDzMyMvn378t133zF06FDWrl1bbBl+oWIKCgrCxsYGBwcH4uLi3nk8MDCQCxcuEBwcXA69q3iCgoIwNjZGXl5eNuhTKpWyY8cOTp8+jZ2dHWpqaujp6eHn58erV69wcXGRtU8t+Z+RkUFkZCR37tzBxsYGGxsbdHR0aNeuHe3atcPc3JzQ0NBPOocIHaXI0dEReXl5Bg4cWO6hIywsjGXLlvHdd98hkUgwMDDg7t275TIIUKg8srKyuH79uqz9/fffqKur06lTJ7755htatmzJwoULC2xjYmKCpqYmpqamuLm58fDhQxITE0lNTSU8PLxAu3nzJlevXsXe3p7Zs2cjlUoZPXo0AwYMYMCAAfTp0wc5OTnk5OSoXr06nTp1kk2LFXVjKp/810BRyyEkJCQQHh4uihDyv+KSO3bsoFmzZtSuXbtA6DA0NGTBggXo6+szatQo9PX1uXz5MllZWQX+vvJncj158oTDhw/j7Oz8UYEuOztbdszdu3ejrKxMo0aNGDFiBHv37v2kKtUidJSiihI6QkJCMDU1pWXLltSuXRs9PT18fX3F7RShUAkJCVy6dAl7e3v27t3L8uXLZU1XV5chQ4bQtGlT2RRreXl5JkyYINtmzZo1HD16FF9f3xJPt4uKisLZ2Zm1a9cydepU2rRpU6B2jEQi4eeff8bGxoZ79+6JRdu+IA8fPiz0tRIWFoaLiwuPHj0qp56Vn5iYGFxdXVFVVaVOnTr06tWLSZMm0bFjR8aMGYOdnR2nTp2SNR8fH168ePHOcU6cOIGpqSlqamr06dOH3r17M3nyZExMTHBycsLX1xdfX18OHjyIvb099vb2eHt7F7tGVlhYGLt372b27NkMGTKEvn37smrVqo++4iFCRymytLSkRYsW5Ro64uPj2blzJ126dKFfv36Ym5vj7+8vBnAJhYqPj8fT05PFixcX+Ga1fPlyVqxYwZ49e3B0dGTLli3MmDGDESNG0LJlS7766it69uyJqakpN2/e/KhxFpGRkfj7+3Px4kU2b97MqFGjaNu2rSx0jBo1qkKvaisULyEhgZs3b3Lw4EHWrVsna7q6uuzZs4eoqKgC21+/fh1VVVVmz55NUFDQf2r8x+XLl9HT06N169Y0bNhQ9nc4fvx4du7cSUxMTIHtk5KSePz4MY8fP+bBgwe4ubnh5ubGyJEjqV+//jsBvmnTpkydOlV2G0ZXV5fevXvTtWtXRo0axdq1a7lw4UKhQQbg6dOn+Pv7M3fuXDp27IiysjKWlpYf9TknQkcpWrp0KRKJhO7du+Ps7Fym546NjSUsLAxPT0+MjY1RU1PDxcWlTPsgVA7R0dGEhYWRnJzM48eP2bRpEzo6OpiYmGBjY4OtrS1Xr17l1q1bBb6N5q+loaKiwrBhw1BSUuLGjRtkZmZ+cp9evXrFhQsXWL9+Pa1ataJq1ap07dqVu3fvfvKxhfIRHR3N/v37GTp0aIEPwP79++Pq6vrO1Ss/Pz/U1dX59ttv2bZt23+m6FtwcDCmpqa0bt2aOnXq8Msvv7Bs2TJsbW25du1agUCfkJDA/fv3sbe3l9XcmD59Or1796Z3796yol9vt7p16zJkyBD+/vtvbt26xa1bt7Czs2PChAkMGzaMYcOGMWDAAJSUlGRXRIqagenm5sb06dORSqUoKSmhrq5ORETEBz1fETpKUX7oaNmyJWZmZmVyzri4OAICAti5cyfr16/H3NycLVu2iEF3QqHi4uI4dOgQ27dvx9fXlz7+eMsAACAASURBVIiICA4cOMDatWu5d+9esfu+ePGCY8eOYWNjw+XLl7l+/foHT9N7n4SEBAwNDalZsyYSiQQ7Oztxa6USy58yK5FIqFq1Ks2bN+f48eO8fv36nW0jIiIwNzenfv366Ojo/CduB4eFhWFiYkKrVq2oXbs2/fv3Z/v27YXOfnz27Bn29vbo6Ojw008/UatWLeTk5OjevTvdu3fn+++/p0uXLowYMYIBAwbQrl07mjdvTteuXQv9PPL19eXy5ctcvnwZIyMjGjRogEQioUGDBowfPx4/P793rjY9efKE3bt3M23aNAYOHEi7du04efLkBz1nETpKkZmZGbVr16Zt27Zs2bKlyO1SU1NJTEx8p7169eqD3sRfvXrFoUOH0NDQoGvXrowfPx5bW1sePnxYGk9H+ELk5ubKXmOnTp3CyMiIKVOmyCp6RkZGFhs43rx5Q2JiYplMVU1LS+PUqVN8//33VKtWjV69emFvb8/Lly8/+7mF0pWRkcE///xDjx49kEgk1K5dm0WLFhU5IPjp06csXryYOnXqMG7cuC8+dKSkpLBixQrk5OT46quv6NGjB9bW1oVu+/r1azZv3sxPP/3EV199hZycHCNHjsTCwgIvLy+8vLxYsWIFrq6uxMfH8/DhQ2xtbZk5cyZSqfS9X4LPnDmDsrIyDRs2pH79+tSpUwdlZWUeP378zhWn0NBQ2eDSrl274uDg8EGfXSJ0lKLDhw/Tq1cv+vXrx5kzZ955PCMjg6SkJM6ePctff/2Fo6Mjhw4dwt7eXnbvPCUlhVevXhUII/nFYN68eUNSUhLp6enk5uZy+vRppk2bxg8//MDSpUs/eSqT8OXJzc0lPj6eAwcOcPjwYVxcXFiyZAm7du0q0eslMzOTS5cusX//fm7fvi07Zlpa2jstJydHVmwoLS3to2+7ZGVlMXfuXJo1a0bVqlWRSCSsX79e1OeoZAICApg5cyYSiYQqVarw/fffFzm2LDs7m0uXLjF8+HDZt+0veRG/jIwMPDw86NOnDzVq1KBPnz6sWbOm0CscGRkZnD59mnnz5iEvL0+/fv34+++/S3Qeb29vDAwMiv0S/Pa2mpqa/Prrr7LqpIqKiu+MvYH/rVJra2vLxIkTUVVV5eDBgyX+exehoxT5+/ujq6sru72Sl5cnS395eXl4e3szd+5cfvzxRzp37szSpUvZunUrw4cPp379+qirq+Pk5FSgKIxUKmXVqlW4uLhgZWXFjBkzcHd3lx17/vz5qKqqcuXKlXJ+9kJFFB8fj729PZMnT+bgwYMcOXKE2NjYEu9/6dIlFi1ahFQqZd++feTl5RETEyMLMIcPH5a1yMhIbt26Jfv31atXC/wNfKi5c+fSpEkT2TgpR0fHjzqO8HE+5f8OwN3dnb59+8pCRFFrr+Tl5REUFMSWLVsYNmwYVapU4euvv/6iQ4eHhwezZs1CTk6OHj16FDkGMC8vj9OnT2NkZIRUKmXt2rWywmAfIv//srgWEhKCpaUlqqqqKCoqysJiSEhIoce8ffs2CgoK1KlTB3V19UJvmRVGhI5S5O/vj7m5OSoqKsyePZsTJ07g4eFBbm4uZ8+e5ejRowVCh5qaGhoaGkycOJFx48bJQsfBgwdxcHDA2NiY1atX4+TkxM2bNwkNDWXHjh1oa2szffp0jh49iqOjI0+fPv3PDLoSSi46Ohp7e3s0NTVloSMuLu6DZgVs3LgRNTU1pFIpWlpaTJs2DX19fWbNmsXBgwfR0dGhWbNmjBkzBj09PXR1ddHS0kJLSwtdXV3++OMPzp0791H9P3HiBB07dkQikVC9enXU1NTw9fX9qGMJHyY7OxtjY2OmTZtGYGDgB+8fEBDAhg0b3hs67t+/j56eHo0bN6ZevXo0b94cdXV19u/f/0XPuFu0aBGTJ09mzZo13Llzp9D6Sbm5uXh6emJkZETLli2ZPXv2R81EvHnzJtOmTSvQnJ2dOXHihKxt2rQJc3NznJ2d2bZtG4qKilSvXp3Ro0fj4OBAQkLCO8eNiIjAzMyMKlWqUK9ePZycnEoUPETo+ETXrl1j/fr1LFy4ECMjI7S1tZkzZw4nTpwgKSlJNvo/JSWFpKQkoqKiCAwMJDg4mOfPnxdo4eHhvHr1iqSkJNm2sbGxJCUlERwczMmTJ9m1axdjxoyhYcOG6Ojo8PPPP7N9+/Zi51kL/z0RERHY29ujp6eHtrY2f/31F7GxsR8UOK5du8bgwYP5+uuvZa1jx47MmDGDw4cP8+rVK54/f87Dhw8JDQ3l+fPneHh4sGTJEtlVulGjRtGpUyeWLFmCh4fHB90iSUlJYd68eTRv3lx2tcPe3v4jfhvCh8rKymLKlCmyK1wf+v6Snp7OkSNHUFFRoVevXlSrVo2GDRvSpUsXjIyMGDhwIF27dqVdu3ayAYzNmjVDQ0MDZ2dnkpOTS32QckWQlZWFiYkJ6urqBUqbFyYnJ4e5c+ciJydHv379OHny5AeNcwkODsbExIQff/yxwN/w119/jYaGBtOmTaNnz560bNmSpk2boqKiwqVLl0hISCAgIIBNmzahpqaGvr4+jo6O70zbjYyMxMbGhiFDhlCjRg3s7e1LVKdHhI4PkJiYyKVLl2Rt48aNsvtsQ4YMQSqVMmDAAHr16oW5uTmXLl2SXWL+VFeuXGH27NloaGjw7bffUrVqVcaNG0eDBg348ccf2bp1a5FzrIX/nitXrjB9+nTmzp3Lw4cPefny5QfXPVi/fj0tW7YsMP2uZcuWmJiYEB8fX+g+ycnJPHnyBE9PT1auXImKigr9+vWTjaJfunTpB02xc3V1RVNTkyFDhtC5c2fmzZv3Qc9B+Dj5oaNNmzZ07NiR6dOnf/B6UnFxcXh5eTFnzpwCryFlZWV+/fVXhgwZQvPmzWndujXq6urs2rWLx48fF1ou/UuQnp7O2bNnad26Nc2aNcPDw6PYCtE5OTno6+szYsQIVqxYQVBQUInPFRgYyMKFC2UVqb/55htGjRqFqakppqamXL9+nX379qGmpib7P1i7dq1skG9OTg4vXrxg586d6OjoMGPGjHeuMmZkZHDz5k0mTJjA8OHDcXBwEKGjNMXFxeHg4MCQIUP49ddfWbRoER06dEBJSYmhQ4diZGSEs7MzdnZ2LFmyBGtra9zd3QkPDy+V0BEVFcWlS5fw8vLCzs6OOXPmsHHjRhQUFGjQoAEdO3Zk3LhxWFpaflKJWqHyi4yMZO/evUyfPp2DBw+WeL/U1FSuXLmCtbU11tbWTJkyhWbNmr0z519JSem995VTUlJ49OgRhw4dYtSoUbL9v//+e5YtW1bi12hMTAxr1qxBKpXSpUsXxowZ80FvvsLHycnJwdraGgUFBfr06UOHDh2YMmUKR48e5ebNmyW+5fLmzRsuX77M1KlT6dOnD3369GH16tVs3ryZzZs3s3v3bv755x/u3bv3QWONKqOEhATmzp1LzZo16datW7G3CjMzM7l+/To6OjpIpVK8vb1LtNrrgwcPOHDgADo6OsjJydG8eXMUFRVZvXo1165d49mzZzx79ozs7Gyio6O5ffs2bm5u/PPPP++M3cjOzpatdCuVSnFwcHjnakd0dDSbN2/mzz//lF2heh8ROkogNjaW/fv3069fPyQSCfXq1cPCwoIpU6awf/9+Tpw4wa1bt0hISCAxMZHAwEACAwM/22ySrKws2TlOnz7NuHHj+Oabb5BIJLRr1+6TStQKlduLFy84dOgQs2fPZsWKFTx79uy9+yQmJsrCxujRo+nQoQMdOnRgzJgx9O/fn27duvH7778zatQounXrxogRI2Rjje7fv1/seKL4+HgcHR3R0NCge/fu1KxZk5YtW2Jqalri8HDs2DFmzZpFly5dkJeX58CBAyX+fQgfJ39g4enTpzlx4gTLly9HTU2NGTNmYGpqyvr163FwcODQoUP4+fkVO84gNTUVf39/2fiBhw8fyt6/vuT1dGJiYnjx4gVJSUlcu3aN7du30759e6pWrcq8efOKXbE1LS0NZ2dnNDU1kUqlJa67tGPHDoYOHcrXX39NixYtmDlzJhcuXPiohT5zc3MJDg7G0tKSKVOmMHfu3HeKhqWnpxMYGMjjx485duwYt2/ffu+4DhE6ihEVFYWPjw+bN29GUVGRDh060Lt3b0xNTbl//z5+fn4VYhrf2bNnGT9+PA0bNkQikdC2bVsWL17MpUuXyrtrQhmKjIzk0KFDmJmZYWpq+t6rHC9fvpS9GWpqajJy5EjZFYnffvuN7du3c+DAAQ4cOICXlxfe3t7s2LGDGTNm0K1bN3r37s3q1as5duwYfn5+RX4Ty8jI4N69exw8eJC+fftSu3ZtBgwYgIODQ5G3ad727NkzNm/eTJcuXWjTpg3r1q37qN+P8PHyx+usXLlStkhft27d6Nu3L2vWrMHPz++Lr6tRmMzMTFmAym/nz59n7969LFq0CDMzM3bu3MmECRNkg6IlEglWVlbF3kZKTk7GwsICNTU1Fi9eXKIrg0+ePGHs2LGyMuiqqqqyae6fIn+mjVQq5fTp04Vuk5uby/Hjx9m0adN7v+iI0FGEmJgYbG1tGTduHJ07d2bIkCGYmpri5ORU3l0r1OnTpxk2bJjsRd28eXOmTZvG4cOHef78eaFT1YQvy7Vr11i2bBmrVq3Cw8PjvVcSfH19WbRokWygWY8ePWjfvj1aWlpcuHCh0CmLz58/Z+3atbRo0YKaNWsyceJEWfGhkrwxrlu3jl9++QUFBQUWL17M1atXS/Tc7O3t6dKlC02aNBHjOsrRnTt32L59OwsWLKBFixZ89dVXSKVS1q9fj5+fX6VfxTo9PZ1nz54RGhoqq9YZHBwsuy1x//592c/Pnj3Lvn37ZLeK8puBgYHsb6p3794oKCjQqlUrWrVqhZycHFWrVi02dGRmZuLn5ycbjH3q1KkS3bYwMTHh22+/RSKR0LhxY2xtbUvld3L//n3Wr1+Prq4uTk5O71QIzs7OJjQ0FCsrKxQUFDh16lSxt4JE6ChEUFAQ1tbWdOnSBYlEQocOHVixYsVHzY8uS7a2tsjLy9OsWTN+/PFHevToQb169VixYgVhYWFf9BS0/7rExETOnz/PunXrsLGxKdGti8uXLzN27FgkEgk1a9akc+fObN26tdh9goKCsLCwQElJiVatWmFmZoaxsTEaGhocO3aMZ8+eFfuGc/PmTVatWoWWlhajRo1iw4YNJRoAbW9vT9++fWnQoAGjR49+7/bCx8vJySEmJqZA+3eYePToEZqamsjJyck+HDds2FCmwSMrK+udfhY2EyQjI+Od7bKzs0lMTCQmJoYnT57g7++Pv78/ly5dwtLSkuXLl8ue1/r162XjnBYuXCj7+W+//Ua7du2YPXs2s2fPZtWqVaxevZrVq1ejra3N1KlTWb16NSYmJhgYGCCVSpk4cSLfffcdzs7ORd5aSkxMxMHBQXbcwopzvS03N5eXL18WGH/166+/cvbs2VL5PQOcP3+e+fPns27dundu9WRkZHD+/Hm0tLRo0KABxsbGBAcHF3ksETr+JTk5malTpyInJ0eNGjWQSCR069aNv/76q7y7ViLnzp1jzpw5BQbvValSBTMzM0JDQ0Xw+EKdP3+effv2cfDgwRLd/01NTcXKyor27dsjkUj44YcfMDc3f+9+Pj4+jB8/HiUlJebOnUtOTg4XL16UXX41MzPjxo0bxX7wnDt3jnnz5tG5c2c6derE5s2b31sI6tChQ2hra9OrVy8ROorw+vVr2XT74tqLFy8IDw8nPDycoKAggoODCQ8P5+nTpzx48IDbt2+zZcsW9uzZw969e9m7dy83b94kNjaW2NhYwsPDuXXrFqtWreK3334r0JYvX46Pj4/s+MW1+Ph4oqOjC30sIiKiQJ+joqJkj8XExJCUlERoaKisf/nt/v37su1evnxJUlISgYGB72wXEBCAq6srjo6OWFhYFKhhMXnyZNq2bcvUqVNlPzM2NmbBggXvtBUrVnDmzBnOnDlT5K32/Fkgb6/iXFyQSExMlE1KOHz48HuvcqSnp+Pi4iK7vS6RSDA0NOTx48ef9Hp6W3GhA/7/bKf8LwXFzXQSoeP/5OXlkZ6ezsGDB/nuu+9QUFDg559/llUKrUyrXYaHh2NhYUHdunULzDwwMzMjODhYFBL7Avn4+LBw4cIi3xQK215JSYk6depQv359Bg4cyIULF4rdJycnB29vbwYNGkTbtm1lhe8AVqxYweTJk5FKpaxcuZJbt24VeZzLly+zYMECxo8fT4cOHRg6dCheXl7FntvX1xdzc/MvOnTk5uaSkZFRZEtNTSU1NZWMjIwCf8OZmZmkpKTg5ubGX3/99d6mrq7O2LFjGTt2LG3atOGnn35i7Nix9OnTR/ZekT8l/+0PyrVr17J27VomT54sG1RfWOvRowdjx45l/PjxBfZ/u2loaLBz505WrFiBlpYW6urqTJ48WVZYbsqUKRw6dEi2FPuiRYtkBedWr17NiRMnsLe3R19fH319fdl+b7c1a9Zw4sQJdu3aVejjenp67Nixo0CRrKLav2dtfIioqCjs7OyYNGmS7HdaXOiIj49nz549qKio8Ndff713sG1+6GjWrBlVqlRBIpFgYGBQ7BpcmZmZZGRklHga/ftCR3Z2NgYGBnz77beYmpoSFhZW5LFE6Pg/+aOFv/76ayQSCStWrMDZ2RlnZ2fu379f6QrVREVFsWHDhgJvBlWrVmXYsGFigOkXKC8vjz///LPEocPKygqpVIqJiQnOzs5cvHjxva/x4OBg2Zoo8+fPL7D92bNnMTY2RiqVoqqqWuzaEHl5eWzatIm2bdtSpUoVqlSpwvjx44s9938hdMTExHDkyJEi28qVKzE1NeXIkSNcvHgR+N+Hx7Fjx9DT05PV73lfy/+d539A5V8NffvfRYUOFxcXDA0NC2z775Z/rJ9++qnI0LFr164CZfPXrl3L/PnzC5TVzw8cb5fbf/DgAbm5ubLS3bm5uWRlZeHq6lpg38OHD+Pv709eXh6RkZHvPHb48GGio6NLVB68NN77AwMDGT16NNWrV0dFRaXY0PH06VPGjBlDtWrVUFFReW9dm/zQoaWlJZvF2KdPH44fP17kPqdOneLIkSNERkaWqP/vCx25ubm4ubmhr6+PVCotdlkOETr+T0JCAlpaWtSqVYtVq1bx9OlT2cJVlfHKQH5xl40bNyKRSBg5ciQNGjSgVq1aKCgoFLognVC5XbhwgQcPHpTo9bpt2zaOHDlCcnJyiRdnCwoKwtjYmE6dOnHixIkCj2VkZHD27FkWLlxI165dWbBgwXv7OmLECNkHVb9+/Yp9o/L19UVbW5uaNWuWaei4cuUKMTEx+Pv74+7ujru7e4EZATk5OXh6esoei4qK4sGDB7i7u2NjY8OMGTP4448/irySExAQINvXzs4OHR0dWWvRogUqKirY2NiwfPly1NXVUVdXZ+nSpRw9ehR3d3f++ecfXFxc0NXVZezYse/UVWnRogXKysqyhdTebj179mTp0qUsXLgQZWVlWcsPBfv27eP58+ckJCSQkJAgW3jSw8MDZWVlBg8eXOB4Q4YMkR1j8eLFnD9/Xrbvv9ubN28KLBCYX7G5sIUE325FvbbT09OL3DYnJ6fQY31osbxPERsbK5uYYGdnV+wtkydPnqCsrEy1atWwsbF5Z+Dmv+WHDm1tbVnoqFmzJo0aNeL7778v0Fq3bs306dP54YcfaNSoEatXry526m4+CwsL2rdvz4wZM4oMHcePH2fq1KkidJREcnIyzs7ONGrUiGHDhn1UffuKKD94bNiwAQ0NDX7//XcaN25M3bp1mTNnzhdTZMnKyopDhw6VOLV/aa5evYqXlxdubm5FLs70tjt37uDo6PhBA6ODg4OxsbFhxIgRDBkypNA3TR8fH8aMGUPnzp1ZsmRJscd//fo1//zzj2yabu/evYtdo8XX1xd1dXXZtzgvLy9OnjzJkiVLWLJkCUOHDqVnz56FtqFDh2JqasrZs2dZuXKlbJ8lS5YwceJE2XYKCgoFHluyZAn29vZ4eHiwYcMGDAwMMDAwwMjISDYzICcnBzc3N+bNm4eBgQH29vacOHECFxcXNm7ciFQqLXI59wcPHvDnn39iYGDAqlWrsLa2Rk9Pj927d8uWDt+4cSOOjo7Y29uze/duPD09iYiI4OnTpwWuBOzdu5fdu3ezZcsWNmzYwIYNG2T/x3fv3mXnzp2yn+e3y5cvEx0dTVRUFE+fPpW1sLAw2QrX/571FhYWJnsdfP/99ygpKcmOd+/ePdkxoqKiKkQ5gYoif+FFNTU1HB0di6xlERcXh5OTkyx0/PXXX8UGlNevX+Pu7o6BgQEtWrSgWrVqRV6Byr8K1bBhQ6pWrUqfPn3YvHlziWadmZqa8sMPPzB16lQROkpDeHg4+vr6VKtWjXXr1hW6uE1pCQgIwMfHp0Dz8/P7bOfLzc0lKiqK3bt3Iy8vT61atZBIJAwcOBA3N7fPdt6ydOjQIcaMGYOBgQHXrl0r7+6UudWrV2NsbMzOnTvfGzru3r2LhYVFiSsc5jtx4gSjRo2iffv2zJ07t9BtEhISWLVqFYqKikyZMoVNmzYV+9pOSkpi+/bttGvXTlbKvyhvh44GDRrQo0cP5OXladGiBS1atKB69ervvME2bdqUQYMGoaSkhLW1NS4uLrIKj2+vDTNo0CAGDRrE+PHjsbKyYsuWLUyePJlNmzbx4MEDoqKiePz4MW5ublhZWWFlZYWLiwvw/0OHjY0NVlZWHDhwgLt37xIVFcWTJ0/w8vLi0KFDhT6nV69eERgYyN27d3n06BFhYWH4+/sTFRVFVFQU9+/f5/nz57J/R0VFyT6AMjMzC/y8sPa+bT90lsnTp09ZtWoVHTt2pG3btqipqXH//n3Z8SrjFeGyUtLQERUVxZYtW2jatGmRoePGjRusX7+e9evXs2TJErp3706LFi2oWrVqsYHj7da7d2/c3NwICwt77yDu27dvM2zYML766isROkrDq1evcHZ2pm3btvTr1w9/f/9S/ePJycnhzp07stLlSkpKDB8+vEDT09P77NNxnz9/zqRJk2SLKzVq1Ig1a9Z81nOWFS8vL0xNTdHW1mbJkiXFvuC/RHPmzEEqlbJ169b3ho4///wTbW3tD/4dOTg4IC8vzy+//FLkMtwAO3fuZMCAAfTt2xcLC4v3Tvc7cuQIPXv2pE6dOsWO63g7dBTVOnToQK9evWRt4sSJ7Nq1iytXrhAaGkpoaCjbt29n48aNBdq+ffs4f/48165dIzQ0lCdPnnDhwgWCg4MLFLx69eqV7Dj5zysvL09W1yG/vf0hkZqa+kVcgdu1axfjxo2jbdu2dOjQAXNz82IHCwsFlTR0pKam4u3tjby8fJGh4+bNm2zcuBETExPGjRtH9+7dC/17+OGHHwr8PQwePJjZs2djZ2fH2bNnS1T7A/5XHKxDhw60bduWnTt3kpiY+M422dnZrFq1inXr1r134O1/PnQEBQUxbdo0GjRowJo1a0r1kmBGRgZ3797FzMyMHj16ULt27UJfHHJycmzbtq3UzluU/KmKbdq0QSKRoKOj81HlcSua0NBQPD09sbKywtDQkM2bN38Rz6ukShI68vLyCAgIQEFBgdGjR39Q6Lh+/TrLly9HXl6eQYMGyQYxFmbnzp38/PPPtGvXji1btrz32PmhI39cR1EKCx01atSga9eushkzDg4OuLq6ytq5c+feuV8dEhLCo0ePCrRPmZnwpQsODubEiRNMnjyZxo0b06lTJzZs2PCf+vsqDfmhY/LkycUumJiSksKZM2dQVlamatWqLFq0iJcvX75zrEePHnH79m2cnJxYvnw5Xbt2LXC1r1+/fqxbt67A38PJkycJCgr64IGx27ZtQ05Ojv79+xdakTQ1NZWDBw+ioaGBnZ3dO/39t/906EhOTsbd3R0lJSX69u2Lr69vqY3liI+Px9XVlbVr17J8+XLGjRuHgYEBxsbGsqlhxsbGqKqq0r17d6ZOncqZM2c+e+XQJ0+eMHXqVBo2bMjAgQPfGRBYWT19+hRfX18OHDjAqlWrsLW1xcPDA29vb54+fVrpZh8VJikpCV9fXzw8PAq0qVOn0r9/f/bu3VtklcP8y5/ff/89Q4cO/aDQYW1tjVQqRV5eHnl5ebZv346HhwdnzpwhODi4QNu4cSM///wzTZo0QVtbm+vXrxd77I8JHXXr1qVLly5MmDABe3t7bt++LcYPfCa7d+9GT0+POXPmsHDhQvbu3VuigYdCQfmh4311OpKTk2VfDtu3b8/48eOLDXhpaWmyLwX16tWThQ5zc/NPDtO5ubk8efKEUaNGUbdu3UJDR3p6Ordv35Y9Ly8vL7H2SnFCQ0PZsGEDQ4YMYebMmaV23NTUVDw9PenXrx/Dhg3j0KFD+Pj4yP4znj59KpsGdePGDdl/mLa2dplU87O2tqZDhw60aNGCVatWffbzlaXnz5/j6uqKiYkJWlpaLF++nKNHj3L16lWOHTvGxYsXP+uYnU+Vm5tLREQE4eHhZGZmEhcXJxt7ERISwtq1a+nXrx/9+vVjwIABTJo0CalUyrfffsvRo0eLPG5OTg42NjY0a9bso0PHoEGD+OWXX9DS0mLBggUsXbqUq1evcv36dVmztrZm5MiRyMnJIS8vz8qVK4s9dklDx4ULFxg9ejR169Zl8ODB7N69u1LVzqlscnNzuXXrFjNmzMDMzEw2M0f4OCkpKXh6epa4ONj+/ftl277vqlJWVhbXr1+na9eu1KhRgyZNmsjGHH2KrKwsrK2tZaXVx4wZ8877RnR0NOvXr0dVVZV58+aVKOj8p0PHo0ePmDVrFg0bNizV0PHy5Uu2bt1KtWrVaN26NV5eXkWGifzQoampyZo1a0o0dfFT7du3j19++QWJB7b3lAAAIABJREFURMLEiRO/yJUeHzx4wNatW7lw4QKnT59GTU2NunXr0qNHD5ydnQu9L/k5ZGdnyyo5FteSkpLIyckhOjqaixcvcuHCBZKTk2UDC+F/oWP58uWyaXHVqlVj8ODBTJgw4b2hIzs7mylTptCqVStGjhz5UaFDR0eH+fPnY2lpyYULF/Dx8XnnClJgYCDbt29HTU2NYcOGYWxsXOyxjxw5wsCBA2nSpAmjRo0qcjsXFxf69u0rFnwrA/mDz3V1dTEwMPhiZrmVt7i4OAwNDTE0NCQwMLDIsYMpKSm4u7vLQoefn1+JxhkaGBjwzTffMHjw4PcW+nufzMxMfH19+f3336lduzbffPMN69evL7BkQWZmJrdv32by5MnMnj2bM2fOvHdQKlSC0JFfje9zOHfuHIMGDSr10AH/q7rYtGlTJk6cSGJiYpFzwu/cuYO+vj5Lly4t1fMX5+bNm7I1N953j74kUlNTefnyJZGRkYSFhREYGMiTJ0+IjIwssoWGhhIYGMjTp0+JjIwkJiaGlJQUUlJSiIqKIjg4mMDAQNkgvfxtw8PDCQ4OLvSY+bUE3n695ObmEhMTg4aGhqxCq4KCAqdPn5adL//SfG5uruxnKSkpsvn9b/8sf72Gt39WXAsPD8fOzo5t27ZhZ2f3TnVIBwcHHB0d8fDw4PXr13h7exf5Wnn+/Dn79u1DR0eH9u3b06JFCxo0aMCwYcNo2LBhiULH6NGjGTVqFJ6eniUOuAcPHkRPTw9zc/MSzbTKLyJWv359fv/992K3PXLkCFKpFHV19WIHNt+4cYMJEybQvn17LC0tS9Rv4eOkp6dz6tQpFi1axJEjRyr0lcHK5M2bNwWmORe3ymx8fDxSqRRFRUUsLS158uTJe4OHgYEB3333HcOHD/+k0JEfOEaOHEm1atWoW7eubKZSvqysLB4+fMiaNWuYMmUKZ86cKfEEjAodOnJycrh9+zZXr179LMHDy8uLfv360ahRI2bPnl2qx3706BHjx4/n66+/xs7Ojri4ODIzM8nKyirwoRIZGYmbm1upLs7zPm+HjoEDB75THyE7O5usrCzy8vLIyckhNzdXVvkvMzNTVo45v7m7uzNr1ixUVFTo2LEjVatWpWXLlkyaNAkVFZVCW9u2balatSrt2rVDKpViYGAgqzyopaVF48aNqVGjBv369ePnn3+mRo0a/Pjjjwwd+v/au/O4mvP////ZZ8YYM9YxZhgzxtYMn7dthpk3hhiSLDmEZCkpFMpWxpJIMoQSspVUnLQoyhYKlSgmSbSqlJKxtGu5/f6YX6+v3kzKtMnzerk8LxfL65zzPKdzzuve8/V8Pp6DadGixWvv09TUFHt7e65cuSL1LS0tDXt7e9TV1WnevDn16tXD0NAQJycnHB0dsbe35+zZs+Tk5PDkyZNXvhRCQkI4duwYcrmcI0eOYGVlxfz583F3d0cul+Ph4YGHhweurq7S7Y4dO4abm5tUP0FNTY2PPvqICRMmoKmpyYwZM6S2bt06rK2tsbCwqNDPMCsrC1dXVzQ1Nfnss89o1KgR7u7u/3h8QUEBc+bMkVYvLVy4sMxNmV5WWFjI4cOHcXR0LHf/fH19UVNTw9jYuMx5Uq6urqipqbFgwYIy63SU7DL766+/cunSpXL3QxBqi5LQ4eTkxNGjR8sMHY8fP5ZGZ4cNG4aVlVWZpcUB5s2bx6RJkxg/fjxnzpypcPGzkjL8YWFhUv2cRo0aoaqqWmq0q6ioiKioKJYsWULbtm3R19ev0OPU6tBx/fp1Jk2ahKKiItbW1pV+//v376d+/fp88803lT6hsqioiLi4OMaMGcMHH3zA+PHj2bdvH25ubqXePCUn9urcev7l0NGxY8dXfsP08fHBzc2N1NRUQkNDpZELNzc39uzZw7Rp00q1kjoJDRo0oH79+nTq1Ak1NTWGDRtGgwYNXtvq1atH165dpa3R/zd0qKmpMWHCBCZOnCj9WU1NjYkTJ6KkpPTa+2zUqJG0W+rL/VNXV0cmkzFhwgRatGjBf//7X9TV1enVqxeNGzemU6dOGBgYSEHh5dBRVFREaGgocrkcS0tLFi5cyKlTp8jMzOTYsWPk5ORQWFjIhQsXpNvdvHmTuLg46fm4uLhw+PBhXFxcSE9PJz8/X2ovXrygoKDgrSYw5+XlScFjwoQJZU7aLCoqws3Njfbt21c4dFy7dg25XE5YWFi5++br68vAgQNRVFQss/qtq6srffv25ccffxShQ6jTsrKycHFxQUNDgwMHDpQZOrKzs3FyckJdXZ1PP/2UoUOHvvGSqKenJ9ra2nzxxRdvVfwxNjaWHTt2MGLECBo0aEDDhg1RVVV9ZYL6nTt32Lx5M5MmTUJbW7vC585aHTquXbvG+PHjadSoEd9//z2rVq3615cCXrZ3715pg6LyXIuqqIKCAuLj41FVVaVFixaoqqoyc+ZM5s6dy/z587G0tKyRyXAvh46GDRvSuXNnli9fzsmTJzl58iR6enrMnDkTXV1dtLW1+eOPP9i+fTszZ85k+vTpr+yjMGbMGJSVlVm2bBk2Njb4+PiQlpZGampqqfoF/9uSkpJIS0sjLS1NmjCZlZVFenq69O+va6+736NHj2JjY4ONjQ3GxsYYGBhw8ODBUk1TU5OWLVvy888/S6MnHTp0QFVVFV1dXU6cOCH1oaRMM/w93JiVlcXTp0/JyMggJyeH4uJisrKypDkNubm50u3y8/MpKCgodV8lrTJLLxcUFODu7s6sWbOQyWTY2tqSkJDwj8dnZ2czZ84clJWVUVdXL3cp/KtXrxIeHl6h+Ua+vr4MGDCA7t274+vr+9pjbt26xYYNGxg/fjxr1qz5xxUoYWFhyGQyGjduLEKH8M4qLi7m2bNnHD58mCNHjuDl5fWPE0qLi4t5/vw5Tk5O0oozLS2tMoO5l5cXc+bM4fPPP6/wLrN3795l+/btKCkp8cEHH0h1cxITE8nMzJS+CyMiIti8eTODBg3ip59+4vjx4xU+d9bq0JGVlYWPjw+jR4+mcePGdOvWjaVLl+Lv718pX94loaNLly5VVlCqqKiI6OhorKysCA4O5t69e3h5ebF06VKmT5+OgYEBlpaW1VpJMzMzk5MnTzJ37lwUFRWlUOfh4cGjR49wcHCQNu6RyWSYmppy/vz5V5ZH/m978OABGRkZFap0WVmeP39ORkYGGRkZJCcnk5CQIP29pB06dIhOnTrRrFkzmjRpQqdOnTA1NeXevXvExcW9cY+D2qa4uJjHjx/j6OiItrY2s2fPfmMoP3LkCDo6OshkMk6ePFnmsVevXsXPz4/o6OgKL0ktCR3t2rV77QqW8PBwLC0t0dTUZNGiRa9d/19i7969/PDDD3z99deYmZnx/PnzCvVFEGqLkgq2crmc5cuXY29vX+aGbn/99Re2trbMnj2bHj16oKKiwp49e7h9+/Zrj3VxcZHOJ2V9Zi9fvoyfnx9+fn7Y2NiwePFilJSUaNasGR07dmT79u3ExMS8cp4NCwtj7dq16Orqcvjw4bdahFCrQwf8vW557969dO3alSZNmtCxY0d+/PFHxo4di5mZGadOnXrriU4loaNt27ZVvnT04cOH0m+KT5484c6dO4SEhODr64uFhQVGRkZs27atWkoJ37t3Dx8fHw4cOICGhgbNmzdnzJgxeHp6UlRURGpqKjdu3CAkJISQkBCioqLe6RUuBQUFBAYGYmJiwueff46CggIjRozA3t6+zJGBd8XDhw9ZtmwZMpmszJM3/L2yytjYGJlMho2NTZnP/8yZM8jl8rd6jXx9faWNxl63guXKlSvY2dlhZWWFl5dXmZ9hKysrvvvuO7p37y7teSII76Li4mJSUlLw8vJCT0+PuXPnEhAQUOZt0tLScHZ2Rl1dne7du9O1a1cGDx7MuHHjmDp1KlZWVly+fJkrV65Igebs2bM4OztjaWn52mZkZMSiRYtYtGgRM2bMQCaTMXv2bCwsLDh37txrl75GRUVhbW3NmjVrOH78+Fufd2t96ID/V3th8+bNTJ8+nV69elG/fn2UlZUZNWoUa9euJTIyssL3WxI6qmL1SnllZWXh5+eHhoYGFhYW7Nmzp9zlad/W1atXWbJkCRoaGsyYMYNJkyZx8eJF4uPj60QRrZfl5uZKxXOmTJlCy5YtGTFiBMeOHau2ZbNVLSIiAmVlZb799ttyTfZ0dnZm7ty56OrqcvDgwX+coFay4uZtQsf169dZvnw5+vr6pUYRb926hZOTE+vWrWPnzp1cunSJ9PT0f7yfu3fvsnr1an799VeMjIyIiIiocF8Eoba5f/8++/btQ0dHBzs7uzeWyk9JSSEwMJDNmzejqqpK79696dy5M40bN6ZLly4MHz6c4cOHY2BggJqaGsOHD6dPnz58++239O3bVxq1VldXx9zcnI0bN0oLGEpacHDwa8NGREQEoaGhWFtbo6Wlxa5du8r8zL7JOxE6SmRnZxMWFiZNsDExMeHLL7/kq6++Yvny5VLCi4iIIC4ujvz8fCIiIoiIiMDT0xO5XM7WrVvZvXs3crkcXV3dGg8d8Pf67cOHD7N69WomT57MpUuXqmSOSYmSOR1dunRBW1sbBweHKnusmvLs2TMiIiIICwvDxcUFU1NT1q5di6amJm5ubnUmcMDfI1cTJkzgt99+e+NIB/y9U+j+/fvR1dVFT0+PgwcPvjZY7Nq1Cz8/v7e67PT48WMCAwM5f/58qX/ftm0bmpqaGBoa4uXl9cYvr4MHD/Lbb78xbdo0zp07V+F+CEJtdf78ebZu3cratWuxsbHh7Nmzb6z2mpqair+/P3Z2dujq6tKjRw969uwphYoVK1Ywa9YsBg4cSI8ePfjvf/+LkZGRNMndzc2NW7duERERUebll/z8fG7dusWxY8fYsGED9vb2bNmyhd27d792w7eKqNTQ8eTJEwICAti1axcHDhzA399f+r+kpCRiYmJe2yIjI/Hz83vt/4WEhEhJLCAggJiYGKKjowkNDcXd3Z0hQ4bQtGlT+vTpg0wmY968eaxatYoVK1bg7e0t7cY3ePBgevfuzWeffcZXX33FsGHD6Nu3b5WFjsePH3PmzBkuXLhQrvknqampTJ48mWXLluHo6FjmzOZ/y9vbm/HjxzNgwADWrFlT7lUM74LHjx8TGhrK0aNH2bZtGx4eHoSGhpZq79rcjfLYtWsXdnZ2eHt7ExMT88bj4+Li2L9/vzTicfTo0VeOiYyMrPRRN0tLS3bs2IGfn98bA0diYiIaGhp069YNMzOzOrFxmiCUuHv3LidPnpQud+rp6eHq6lqu22ZkZHDhwgXs7Ow4ePAg169fL/Ud5+bmhp2dHZ6ensTFxVWoX0+ePMHd3R0tLS369evHuHHjsLW1xd/f/1+NcJSo1NARGRmJkZERLVu25LPPPmPu3LnA30NDFhYWWFhYYGVlxdq1a1myZAmrV6/GysqKDRs2MHXqVLZu3YqVlRXGxsZs3LgRe3t7/vjjD7S1tZHJZGhpaWFlZYWNjQ3379/n6tWr6Ovr0759e7799ltGjhyJsrIy3bp1o1mzZgwaNEhKgAMHDqR///5SK6mTUNLXygodmZmZREdH4+TkxLBhwzA2Ni7XctjU1FTU1dX5448/cHZ2rtLQsW7dOkaNGsWsWbMqVHuhtvvrr784deoUy5YtQ1NTkw0bNlRomee7LDw8HAcHBzQ1NdmyZUu5glXJsl5TU1N2797NixcvpM9VYmLiv55flJOT88r7ODQ0tNwTQX19fenRowfKysqlfoERhLoiKioKGxsbaX7Fjh07SE5OJjU1tVr78ezZM5KTk4mOjubIkSP07t1b2sdl1KhRuLq6/uMmdRVVqaEjISGBw4cPM3v2bHr16sWcOXN49OgRBw4cYODAgWhra7Ny5UomT57MgAEDGD9+PCtXrnyljRgxQpod6+fnh729fan/X7NmjVRafNOmTQwcOJAuXbrw22+/MXz4cNq1a0ePHj0YOnSodBtvb29ptq6fnx+xsbFSRdJmzZoxefLkSnkN7t69i7m5Of3790dRUVGanFmWgoIC7ty5w8SJExk2bFiZG3f9W0lJSYwbN46ePXtiZmZWp66RX7hwgSVLljBnzhy2b9/+3u3N8ccff9C5c2eUlZUrtLQ8JSWFkJAQEhISOHToEDKZTHr97t69K61KKmlvGv3Izs4mOTkZPz8/du/eTUxMDI8fPy7XfKGioiLpcQ4fPkyfPn0wMzMTu5oKddbdu3fx8/PD3d2dXbt2sWvXLuzt7cnIyKjyOXbPnz/n/v37+Pr6smvXLtatW8evv/5KgwYNaN26NT/++COGhoaVuslflczpSE9Px9nZGSMjI06cOMHixYs5cuRIpZ9Is7Oz8fLywt3dXaoxUfLClWcJqr+/P8OGDUNBQYEvv/yyUvoUFxeHiYkJ7du3R11dHScnpzJDR0FBAQkJCVhbW/Pbb7/RoEED9u3bV2VzDszMzOjSpQsDBgzAxcWlSh6jJuTm5rJnzx50dHTKPURZ19jY2NCzZ0969erFnj17KnTb9PR0Tp48ibu7O/Pnz2f+/PlMmTIFmUzG+vXrpVone/fuxc3NrVStkqysLB49eiTVUbl06RJr165lyJAhdOvWDX19/XLvoJyZmcnBgwc5evQo8+fPR1dX970Lj8L76cqVK+jq6ko1klxdXUlOTpY+V0+fPq201Y3Z2dk8evQId3d35s6di7KyMmPHjmXKlCmMHz8eRUVFDA0Nq6QS+Ds1kfRl+fn5eHh4oKOjQ3Bw8Fslwri4OFasWFGpoQP+fvMMHTqUTz/9lOnTp5Odnf3a/hUXF0uBY8SIESgoKPDhhx+W65r82ygqKsLMzEw6kYSHh1fJ49SEkl1ko6KiarorNSY4OJjff/+dyZMnY2tr+1ZVTl9mbGzMtGnTmDJlCurq6qirqzNw4EB69erFqVOnpM+gXC5HT09POkZdXZ0pU6awbNky3NzcShUhK6m++7+fh5LKvCWXGQ8dOsSxY8eq9DKjINQ2qampuLm54ebmJlUbVldXZ9KkSVhaWhIZGVmhGlUvV7x+uZ04cQI9PT2++uorGjVqxAcffICioiLLli2r1AKcr/NOho7s7Gy0tLRo1aoVSkpKWFtbv7Eu/etUVehISEhg27ZtKCkp0bRpUzQ0NF57PSw2NlYKHA0bNqRp06akpKRUatXKl/n5+WFgYIBMJsPd3b1aS69XtcLCwlf2tXnfFBYWcvXqVVavXs2UKVP+9cZoubm55OTkcOnSJZycnHBycmLjxo3o6upKq2RevHiBt7c3zs7O0jFOTk4EBweTm5srlXkvcfr0aTw8PF6pxJiSkoKHhweOjo7SBnCJiYl1bgm3IJSluLiYFy9eSPtcHTt2DCcnJ+bNm4e6ujqbNm2q0CXxmJgYaX+ol5urqyvOzs7MmzcPU1NTQkJCyMzMJDc391//svIm71zoyMrK4vjx46irq6OsrMzmzZvL3Ca4LC+HjlatWnHq1KlKGb4qKCggNjZWCh6ffPIJjo6O+Pr6sn79egwMDDAwMGD06NEoKSlhZ2fH9u3bsbW1rdLiYGvWrJH2IansvWaE2qGkYuBPP/3EkCFDKqXSbW5ubqlddtPS0kot6c7Kynpld91/GpY9efIkhoaGDBgwgJUrVxIdHU1iYiIbNmygXbt2dOrUialTpxIbG1vlX36CUNtlZmbi4+ND//79adasGa1atWLIkCFs2rSJa9eu8fz5czw9PVm4cCE//PADXbp0kZqKigp6enqMHDmS77//ntmzZ6Ojo8ORI0eQy+UkJSWRnp7O48ePK7TFwb/1zoSOtLQ0PDw8WLlyJQsWLMDGxoawsDBSUlLe+gXLzc3l1KlTDBkyhOHDh6Ovr19pJbxfvHhBamoqN2/exMzMDCcnJ+RyOfv27cPAwIC+ffvStWtXtLS0OH36NOnp6Tx69KjKfrO7fPkyurq6yGQyVq9e/d6s6njfZGZm4u/vz5YtW9iyZUutq23x+PFjjhw5Qq9evRg0aBA2NjasW7eOL7/8kk8++QQ1NTXu3LnzXo9YCQL8Pepx6dIlVqxYwZdffomCgoI0UXz48OH8+uuvmJiYMHv2bFq3bk39+vVRUFCgZ8+eDBkyBAMDA3bu3MnWrVuxtbUlMjKSO3fukJ6eTnp6eo2F+ncmdNy4cYP58+ejqamJtbU1CQkJlfKihYaGStUc1dXVK31fh6KiIpKSkkhMTJTan3/+ia+vLydPnuTGjRukpaVV6mO+LD8/n8DAQIyNjZk6dSqrV6/m0qVLdW7/ijt37hAUFMTRo0fZunWrVHRHU1NT+ntVV3qtLZ49eya9zzw9PQkKCiI4OLjWjBz4+fnRv39/PvvsMxQVFfnmm29o0aIFkydPFpNGBYG/v7evXLnCihUrUFRU5D//+Q/r1q3j9OnTBAYGcvbsWY4fP05gYCCXLl3i6NGjUjt//jyBgYHcvn1bOudURn2NyvJOhI709HScnJyYNWsW1tbWxMbGVtqIQHp6Onv37qVfv35MmjSJ3bt315niUTk5Ofj7+zNy5Ei6du3KkiVLuHz5cp0KHLdu3cLFxYVZs2YxcuRI+vXrR+fOnencuTPt27encePG0t+3bt1aqz58VS0yMhJjY2OMjY0xMTFh7969BAYGkpmZWaP9KgkdJXUAFBQUGDBgQLVueigItdnTp09ZsWIFPXr0oHHjxmhpadWZ8gbvROi4d+8ee/fuxdraukqqZ8bExJTaqr0u1ATIysqSRji6d++OqqoqZ8+erfETTmXT09OjX79+NGvWrNRJ7HWta9eubN++nZCQkDoTLMsSFRXF0qVLGTduHD/88AMTJkxg3759XLt2rUZHffbv30/37t2ln0unTp2wsLCosf4IQm2Sm5tLcHAwampqNG7cGCUlJY4fP15nvrPeidBx/fp1bGxsuHDhQpXcf1JSEgsXLqRfv36oqakRFBRU4a28a4unT58SHh6Oh4eHNHF02bJlVb6fS3UrLCwkPj6etm3bvjFsvNy6d+/OwoULuXnzZk0/hSr35MkTLl68yJYtWxg2bBiGhoYcOnQIuVyOr68vN2/erPY9aBITE9myZQu//PILnTp1olOnTsyZM4fo6Ohq7Ycg1FapqamsXbuWvn378s033+Du7l6nLg3X+tDx4MED9uzZg4mJSZXVlcjMzMTT05MvvviCAQMGYGBggK+v71tv3VtTnj17xvnz51m8eDG//PILI0aMkAJHVa6KqQk5OTns2LGD5s2bvxIsmjZtSrt27aTWtm1b6tWrh4KCAi1btmTo0KGcPXu2pp9CtcnLy+PSpUul2ubNm9m2bRuBgYGkpKSQkpLyjzUxnjx5QkpKirTnUUm7ceOGdNvw8HDi4+O5c+cOoaGhREVFERcXR2hoKH/++ad0nJeXF35+ftjZ2Un7Ivn6+pKbmysdk5qaKpbKCu+lvLw8Ll++TP/+/alfvz46OjrVXhK9qtX60OHs7IyGhgZ2dnZV+jhPnz5l6dKlfPjhhygoKNC7d2+8vLzIzc2t0setDM+fPycpKQlfX18WL17Mf/7zH9q0acPgwYMJCAio6e5ViadPnzJixAiaNGnCJ598Qvfu3enTpw99+vRh3LhxLF++XGpGRkbSXA9lZWVkMhmenp7vxM+2qty6dYvjx49z6NAh9uzZw549e3B2dn5lt9nMzExOnTrFoUOHWL9+PTKZjPHjx6OkpISysjK7du3C0tKSCRMmsGTJEmbMmMGYMWMwNjbG2toaHR0dFi1ahKurK2fOnOHs2bM8ffr0lf7Ex8dL/di3bx9paWl1qo6MIJTH/fv3MTExoX79+rRq1Qp3d/dKW1FZW9T60OHq6oqZmVm1zGovKCjghx9+4OOPP6Z+/fro6upy+/btKn/cfyM3NxcfHx/09PQYP348/fv3p3fv3qxatapOBo7CwkKysrK4e/cuDRo0QEFBARUVFf7888833vbkyZPSsuF169a9F5dYyhIREcG2bdvQ1dVFV1cXHR0dDAwMSh3j7++PiYkJGzdulEKHkpISLVu2pF27dujo6PDll1/StGlTPv30U1q2bMngwYOxsLDA29tbar6+vmWGiNDQUKZOnYqKigqqqqpYW1vXmWvYglAeBQUFBAYGSkUl58+fX+cCB7wDoePWrVvVfnJYsmQJ7dq146effsLb27vWDfUWFxdLrSRwdOzYkd69e7NmzRquXbtW012sMikpKezZs4cxY8ZQr1496tWrh6WlZbmGIL29vZk7d640Yfh93aPlnzx58gRvb+9S/xYQEICrqyuurq6Ym5ujrq6OgYEBrq6ueHl5UVRUJJVU3rFjB66urty5c6fCj/3gwQPMzc2pX7++dCmsoiWfBeFdVVxcTExMDFZWVgwbNoyvvvqqprtUZWp96CgsLKz2+gJZWVl4e3tjYGCAhYVFrRrt+Ouvvzh+/LjU9PT0+PLLL9HT0yM0NJTs7OxaU4+hsiUlJbFhwwY+/vhjGjdujIKCAiNGjCh3MalFixYxadIkETr+QXFx8SuF9l68eEFeXh55eXlkZ2fz/PlzMjMzycvLk47Nz88nMzOTnJwc8vLy3uqySFFREcnJyVhbW6OiokKjRo1QU1Nj//79JCcnV8rzE4Ta6u7du1hZWTF06FBat27N7Nmza7pLVabWh46akpWVxenTp5HJZHTu3JmZM2dy/fr1mu4WcXFxLFiwALlcjlwuR0tLizVr1hAWFlatpWxrQlBQEKNGjSo1afTatWvlft7z5s2Tfp7NmzcXyzRrmcLCQmkka/To0bRt25axY8cSEhJS010ThCp14sQJhg4dykcffUTPnj158OBBTXepyojQUYZnz55haWnJ4MGDGTt2LIsXL2bLli3VUsToxo0b2NraYmpqiqmpKXZ2dri5ubFixQpmzJiBq6srDx5N9PORAAAT4UlEQVQ8IDIykqSkpDo/KTIpKQkzMzM+/fRTFBQU+Oijj/j999/LVeisoKCAgIAAFBUVadOmDU2aNEFBQYG1a9dWQ8+Fing5eKioqPD1118zffp0nJyciIuLq+nuCUKli46OxsDAgE8++YSWLVuio6NT012qUiJ0vEFsbCxHjx5lxYoVyGQypk2bxrJly9i+fTvbt2/n/PnzBAcH/6tKl8+fPyc4OJjAwEBsbGyYPXs2w4YNo1u3bnTo0IEOHTowZMgQ5s2bx6xZs7C1teX+/fvv1fXuixcvoqysLAWO4cOHEx8fX66h/JycHFasWMEnn3xSqiDVvn37qqHnQkUVFxeTlJREUFAQ69atY/r06fz222+sWbOG2NjYmu5ehTx58oTg4GCCg4O5evVqnb30Kbyde/fusWLFCjp27Ejr1q2ZOXMmN27cqOluVSkROsrh8ePHXLt2DWdnZ1auXCnNCVBUVGT48OEYGBhgbW2Ng4MDDg4OeHl5ERMTU+o+IiMjcXV1lY5xcHBg69atGBkZMW/ePFRUVBg9ejTdunWjUaNGdO7cmV69eqGsrMySJUvYt28f3t7enD179p374q0MQUFBTJw4EQUFBZo0aULfvn0JCwt7Y/2RvLw8AgMDUVRUpFGjRlLoaNu2LdbW1tXUe+FtJSYm4uDgwMSJE/nvf/+Lvr5+rdvE7n8lJydz5swZrKysWLp0KStXrmTlypX8/vvvHDx4EAcHBy5fvixW5wi4uLjQt29fFBQU6NOnD0eOHKnpLlU5EToqoGREwtHREUdHRyZNmoSqqipqamqlyqirq6tjaGhYasLnpk2bGDJkCD179pRa+/btUVBQ4MMPP6Rr1650794dFRUVFi5cyO7du3F0dOT8+fN1rjjM20hPT8fc3LxUAbB169aVeXklOzuba9eusXLlSho2bPhKETF9fX2ioqJKTVQsKiri3r17REVFERUVVaf2qXlX3b9/HwcHB9TU1OjRowejRo3Czs7ulWBfGzx48AAXFxemTp2KoqIiQ4YMYf369djZ2TFp0iSMjY35/fffMTU15cyZM9VeEVaoPS5fvszUqVNp1aoVXbp0wdTUlPj4+JruVpUToeNfCAsL4+rVqzg6OmJtbY21tTXm5ubMnj0bFRUVjI2N2b59O0uXLmXKlCm0aNGCNm3a0Lt3b1RVVdHU1ERTU5N58+ZhbW2Nra0tQUFBdX5+xtvy8PCQyp43bNiQfv36YWtry5kzZ/D395daWFgYt2/fxtvbm9WrV9O7d29p2+fPP/+cjh070qxZM/r378+CBQswNzfH39+fK1euSMvWNm/ejKOjI0lJSTX9tAX+X/CYOHEiHTt2pGfPnixduhR/f39iY2NrRcXd1NRUzp07h7GxMcrKyqipqbFlyxYiIiKk4oObNm1i8+bNqKioYGpqyt27d2u620INSE5ORlNTkxYtWtCiRQsMDQ3fmzlLInRUsuTkZOnkd+3aNQoKCqSy02pqaixevJijR49y//79mu7qO+fWrVvo6+vTo0cPWrduLY1YKCkpoaSkxKBBg1BWVmbRokWsXr0amUyGiooKbdu2pW3btnz//fcsXrwYMzMzxo8fz7fffssnn3xCq1atGDRoEKNGjWLbtm2oq6ujp6eHm5vbe7UrbW2XmJiIXC5n1apVaGho0KFDByZNmsTWrVsJDAzkzz//JD4+vkYKKj169AgXFxesra2xtLTEwcEBf39/aWfQvLw8Lly4wPTp05HJZHTt2pW5c+fW+ev3wuv5+PgwcOBA2rZti0wmq7J9xWojETqEd0pGRgZubm7o6+vz9ddf07FjRyZPnky3bt1o3rw5ffv2LXWpa/LkycyZMwcjIyOOHz8uleC+ffs2tra2TJ48me7du/PNN9/w448/smTJEpYsWYKHh4cY+q6lHj16xLFjxzA0NERbW1uqvaKsrIyhoSFnzpwhISHhH/eSqUzFxcUkJiaye/duZs+ejZ6eHpcvX37tsYWFhaxevZq5c+cyZcoUqVaMGNl8fxQXF/Ps2TOpoF5Z75e6SoQO4Z2Un5+Pl5eXNGfGxMQEbW3tV9rChQvx8fEpc6VPSkoKly5dqsbeC5UhNzcXT09P5s2bh7a2Nt99951U50BVVRULCwueP39eZfVrSk4gmpqatGzZkpEjR3L16tU33u78+fMYGRmhpqaGqalpuUr4C++2oqIi8vLyyMrKwsXFBUdHR/T19cv1fqlrROgQ3lkvl4N/UyvPfQnvnpd/xhcuXMDIyIiuXbtSr149OnbsiL6+PqdPn66Sxy45gUydOpWJEyeyc+fOcs0BKi4u5uLFi/zyyy/MmDFDhI73QEZGBq6urtL7ZdKkSeV+v9Q1InQIglAn5Ofn8+zZMy5evMjy5csZN24ckydPZsaMGSxYsIDjx4/j5eX12l1u38bLoUMmk3Hz5s1yl4C/ePEiBgYGrF27VoSOOiwhIQE7Ozu0tbWZPn26NKcnKiqK7Ozs93InZRE6BEGoU3JyckhNTSUwMJCNGzcik8mYNGkSc+bMoVu3buzbt69S5nv8b+iIjIws1+0CAwP5/fffmTZtGuvXrxeho46KiYlh5cqVtG/fnk8//ZRvv/2Wffv2ER0dXStWW9UUEToEQaiTcnJySEhI4MaNG4SEhLBjxw6GDx+OtrY2q1evZsOGDTg5Ob11sb23DR2nTp1i/vz5yGQyETrqqOjoaIyNjfnqq69o2bIlo0ePxsLCgocPH773l3JF6BAEoc4rLCwkPj6egIAAbGxs0NbWlla8qKqqYmRkxKFDhwgPDy/3fRYUFBAXF8fFixfZvn37G6/PFxcXExYWhpmZGdOnT6dPnz6MHTuWkydP/tunJ9QSkZGRODs7o6Wlxddff02bNm2YOXMmgYGB7+X8jdcRoUMQhPdKfHw8Z8+excPDAzMzM3777Td+/vlnZsyYgaWlJeHh4YSHh1do1YuPj0+pSzZpaWnS/YSHhxMaGipVMe7VqxejRo3i559/ZtiwYZiYmFTLJpJC1SgsLOTWrVvI5XLMzc0ZOnQoioqKKCkpsWrVqvdyhUpZROgQBOG9lZKSwpkzZ7C2tsbExARTU1OOHDmCubk5Hh4ehIeHl6vYmI+PD2FhYdy7d48nT54QGRmJXC6XWkk11e7du6OkpMSmTZs4ePAgmzdvRl1dnVmzZnHy5EkCAgKq4VkLlSU/P5/w8HC0tLTo378/Y8aMQVVVlVWrVuHr6ytGN15DhA5BEN57GRkZBAUFERQUREBAgLR1gampKd7e3kRGRvLs2bN/vP2NGzc4fvw4crmckJAQgoKCkMvleHt7ExQUhL+/P1ZWVlhZWXH+/HlpBU1CQgLm5uaMHTsWQ0ND/vjjj+p6ysK/kJ2dTXR0NKdOnUJPT48GDRrwxRdfsGzZMnx8fEhLS6vpLtZaInQIgiC8pKCgAH9/f5YuXSpNEl25ciUXL14scwPAsLAwLly4UKqVZ45IYmKidPy1a9cq86kIlej58+fEx8cTERHBhQsX2LBhA6NHj6Zt27b06NGDpUuXipGNchChQxAE4TUuXrzImjVr0NHRYfbs2ZibmxMQEEBaWhrZ2dk13T2hmmRlZfHw4UOp+u3IkSNRUVFBQ0ODRYsWsWTJEk6ePElOTk5Nd/WdIEKHIAhCGYKDg/H09MTT05MtW7ZgaGjIqVOn3utaC++D/Px8srKyOHHiBLq6unTo0IEGDRrwwQcf0K1bNzZu3FjTXXwnidAhCIJQhqKiIqndu3ePrVu3Mn/+fHx9fWu6a0IVycvLw83NjdmzZ6Ourk779u2pV68eioqKLF++nICAAAoKCmq6m+8kEToEQRDKKSYmBhcXF7y9vWt0OD0jI4MjR44wb948qTk5OfHw4cMa69O7Ljk5GXt7ezQ0NOjQoQOtW7emadOmjBgxAlVVVYyNjQkICODJkyfk5eXVdHffWSJ0CIIglFNeXh6PHz+WVrIUFhZy8eJFzp07J7XqmEwYFRXF1KlTadu2LWpqashkMrS0tDh06BAPHjyo8sevC8LCwtixYwcmJiaYmJhgZGTEuHHjaN68OY0aNWLo0KGsWbOGkJAQ7t27R0pKipi3UQlE6BAEQXhLxcXFpKam4u3tjVwux8zMDHt7ey5fvszly5e5fft2pT1WQkICly9fxsPDA319fdq0aUPjxo2l0NGlSxdkMpkoNPYamZmZXL58mUuXLrF161bU1dXR0dHhp59+4osvvqBfv37MmzePTZs2Scukr127RmJiopi7U8lE6BAEQfiXEhMTiY2NJSgoiBs3bhAbG0tsbCxRUVFcv379lVbW0tvXiY+P5+DBgyxfvpz58+ejoqKCkpISu3fvZtOmTVhYWKCvr4+DgwPJyclV9CzfLampqVy/fh0/Pz8sLCxQUlJi2LBhfPfddzRu3JhBgwYxePBgxo4dy5YtWwgKCiI2NlYse61iInQIgiBUkczMTK5fv16qOqm5uTkHDhzgypUrREREvDIPIzc3l6NHj0otODiYgwcPoqenh66uLlZWVri6unL69GkKCwuJjIzk9u3b3L59u8Jhpi65d+8e3t7e0uu2c+dO1qxZg5GREWPGjOH//u//mDx5MqtXr8bU1BR7e3tcXV0JCAgQc2GqkQgdgiAIVSg7O5vQ0FBCQ0Nxc3NDS0sLmUzGH3/8gVwu5/jx45w+fVpqnp6eyGQy+vXrh6qqKjt27GDz5s1s3ryZ48ePEx8fX9NPqcZlZWURExPDnTt3pNdt69atzJo1i0GDBjFixAh0dHQwNzdn79697N27FwcHB8LCwsSqkxomQocgCEI1KC4uJiQkhJ07d7J8+XLWr1/PgQMHsLKyQkdHB1VVVQYOHCi1xo0bM3z4cHbs2MHZs2fr/GWTnJwc0tPTgb9fqwcPHkgBISMjg4iICM6ePYubmxuHDx9m586dODo6smjRIqlt2LCBOXPmYGhoiIuLC9HR0TX5lITXEKFDEAShmt24cQMTExOMjY2ljd8GDRqEgoJCqdavXz8WLVrEqVOniIqKIiEhgefPn/PixQuePHlS00/jrfz111/ExMQQEhLCzZs3iYqKIioqinPnzrFr1y6ioqKIiIhgz549JCQk8OjRIy5cuMCKFSvo168f7du3Z+jQoVhaWnL+/PlS7V19Td4nInQIgiDUAHt7e3R0dFi3bh1WVlaMGjWKDz/8kHr16vHxxx/Tpk0b2rZtS/PmzRkwYAAymYylS5dy7tw54uLikMvlpKWlUVxcDPw9UlDVlw5evHhBXl4ehYWFZGZmlmrp6ek8fPjwtS09PV067siRI2hra9OuXTt++OEHxo4dy9SpUxk5ciTdu3dn1qxZUpPL5fj4+ODj44OlpSULFizA0tKS0NDQKn2eQtURoUMQBKGGhIeH4+7ujru7O7a2towcOZImTZowfvx4HBwccHNzw8jICA0NDakZGxuze/dupkyZgpaWFnl5eRQUFHDq1Cni4+PJy8sr1fLz8ykoKKCwsFB63MLCQvLz86X/Lyoqori4mIKCglK3LSgooKCgQDo2PDycK1eucP/+fZydnXF0dJTazJkzGT9+vNTU1NSYOHEiEyZMQEtLC7lcjru7O3PmzGHKlCl07NiRjz76iH79+rFmzRrpdXi5ZWVl1eBPR6gKInQIgiDUkKKiIunEnpSUxMaNG1FQUKBhw4bY2dmRkZFBXl4eOTk5UsvLy+PBgwc4Ozvj7OwsnaDnz5+PhoYGmpqapdrixYtxd3fHy8tLGgnx9/dnxYoVaGpqsmHDBsLCwkhJSWH//v2lbuvg4IC7uzsmJiZoamqioaHBtGnT0NDQQFlZmQ8//FBqjRo1omHDhlLr1q0bP/30E+3atUNLSwtPT0/y8/PJzc3Fx8cHR0dHbt26RVZWVqmA83IrGcUR6g4ROgRBEGqBwsJCIiIiGDp0KAoKCrRp04bdu3dLkyv/99jXXd5ITU3FysoKmUwmNXV1debPn4+7u7sUOs6fP8+hQ4c4cOAAhw8f5vr16zx48AAXFxd27twp3Xbfvn3I5XLp2AMHDmBmZoZMJmPWrFns2bOH6Ojo17aEhASSkpKIi4sjLS2t1KhFdnY2mZmZovDWe0iEDkEQhFoiLy+Pmzdvsm7dOtatW4ejoyOpqakVuo/U1FTu3LlTqt27d4+MjAxp5ODp06c8evRIapmZmeTn5/Po0SPS0tKk2z18+LDUcY8ePSI5OZk7d+4QHR3N48ePq+JlEOowEToEQRBqkcLCQpKSkqSWm5tb010ShEojQocgCEItFhMTQ1hYGCdOnCA4OLimuyMI/4oIHYIgCLVYQEAA27ZtQ09Pj61bt9b5ImFC3SZChyAIQi127949bG1tmTNnDgsWLMDZ2ZmUlJSa7pYgvJU6Fzqys7N58OABDx48IC0traa7IwiC8K+VBA8tLS3mzZuHm5tbTXdJEN5KnQsdt2/fZvfu3ezevRtnZ+ea7o4gCEKliI6O5sCBAyxYsIDff/+dp0+f1nSXBKHC6lzo8PPzY8aMGcyYMYMlS5bUdHcEQRAq1bVr11i5ciUXL16s6a4IQoXVudARGxvLsWPHOHbsGL6+vjXdHUEQBEEQ/n91LnQUFRWRn59Pfn6+qHYnCIIgCLVInQsdgiAIgiDUTiJ0CIIgCIJQLUToEARBEAShWojQIQiCIAhCtRChQxAEQRCEaiFChyAIgiAI1UKEDkEQBEEQqoUIHYIgCIIgVAsROgRBEARBqBYidAiCIAiCUC1E6BAEQRAEoVqI0CEIgiAIQrUQoUMQBEEQhGrx/wFKIrmjM/P+6AAAAABJRU5ErkJggg==)
- Construct the
finite automation equivalent to the regular expression
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAR0AAABGCAYAAADxVED7AAASuklEQVR4nO2dbUxT1x/HXZa9W/ZuyZJlZpmLzrglRrdkj3Eby3QZLkxT0KEyFUWtwjTD4UABQRRBQJzIrAERGFJQLJRHeSpQgYI8lGfl0VIQKbQU2lKg/f5fkHZib9tbkEvZ/3ySvrnncO5puffTc37nd09XgEAgEBhkxVJ3gEAg/H9BpEMgEBiFSIdAIDAKkQ6BQGAUIh0CgcAoRDoEAoFRiHQIBAKjEOkQCARGIdIhEAiMQqRDIBAYhUiHQCAwCpEOgUBgFCIdAoHAKEQ6BAKBUYh0CAQCoxDp2BHV1dUYHBxc6m4QCIsKkY6dUF1dDX9/f9TV1eHx48fo7u5e6i4RCIsCkY6dkJOTg8OHD2PHjh24cOECmpqaaP/twMAAOjs7F7F3hP8iCoUCYrGY8fMS6TCERCKhnDrpdDqIxWJkZGTg0qVLcHR0xOXLlyGTyWi1K5VKUVxcjOrq6pfd5WXNzMwMGhsbodVql7ordsfQ0BAaGhogFApRUFDA+PmXhXS0Wi3a2trQ1taGqamppe7OvKitrYVAIMDTp0/nHJ+ZmUFGRga4XC7Cw8Ph7u6O3Nxc2u0WFBQgJSUFT548edldXtbodDo0NTWBz+djZGRkqbtjNwwNDSEuLg6HDx9GbGwsHj16xHgfloV0lEoluFwuuFwuJiYmlro786KnpwdcLhd37tzB0NCQ8bhOp0NtbS1EIhGOHz8Of39/NDY20mpzeHgYSUlJ4PP5i9XtZc/Ro0chEAigUqmWuit2QUNDA44cOYJNmzYhOjoaUqmU8T7YvXS0Wi26u7uRlpYGgUAAjUZjUketVmNwcND4jabX6zE0NITp6WnG+imXy9HQ0IC2tjazdbKzs+Hn54fs7GzK8oSEBLS2ttI+Z1VVFXJzcxct6KxSqSCXyxelbab466+/cOvWLfT39y91V+yCrq4uJCcng8PhoKysDA8fPmS8D3YvneHhYXC5XGRkZGBmZoayTltbG+Lj41FUVATg3ylLe3s7paQWg5qaGuzduxdeXl5m6zQ3N+P8+fMICwtb8PnGx8dRVlaGjo4Os3XGxsbmfGYajQZyudzst/7AwACGh4eNcZDHjx+jtLQU4+PjC+4vXSYmJjAwMICxsTFa9VUqldX/MY/HQ3Nzs8X4jkKhgE6nM1s+MzMDuVxufJm7FplCqVQy+qX6MrF76QwNDSExMdGsdDQaDXg8Hk6cOIHy8nIAs1OW3Nxc7Nq1Cw8fPmTkAnny5AmuXr1qUTrt7e2IjIxERETEggOcpaWl4HK5lNLR6/XQaDTgcrkYHR01Hm9tbUVmZiZEIpHJ+ScnJ/HHH38gJiYGfX19AGanhBkZGSgsLMTk5OSC+ksXgUCA33//Henp6bRuqpqaGojFYouxvsDAQERHR1Ou8On1ekxMTCAlJcWs6HQ6HQYGBpCUlITMzExkZmZibGwMWq0WSqWSsc/GgEajQXZ2NoaHhxk978vC7qXT2tqKffv2mZVOWloaWCwWLl68aFK2Zs0aBAQEMBJkpSMdAOjs7ASXyzWOyuaLJekYhLN792709PSYlPf19aG0tHTOMT6fDw8PD9TU1Mw5LpFIwOVykZOTs6D+0sUgnaCgIDQ0NFitX1NTAy6Xi7q6OrN1ioqKwOVyKaVjEM4vv/xiNr4xMDCAv//+Gx4eHpR9zczMtNrPl8XzCw9EOouAVCpFaGgo3n33XUrpiMViBAcHm0jHMNJ5++238f3336Oqqor2Oevq6pCZmYmWlhab+mqLdKKjo3H27Fmb2n8RrVYLjUZDORowSCcxMXHOSMdAZWUlQkJCAABTU1Pg8/lIS0tDUlISJBLJnLoSiQQhISHYsGHDgvpLl8WQjlarRVlZ2aJJ58KFCzZfL/PFIB2ZTGZxOqjRaIyjMqVSyUjf6GLX0pFIJAgMDMSqVaugUCig1+vnlCclJeGLL77Ahx9+aDLSUSgUcHNzwzvvvIO7d+/SPueNGzcQFhZGewXJQE1NDZycnPDxxx9brNfZ2YnIyEj4+fnZ1D5dlEol8vPzjat9LwaC+/r6kJGRgVu3bkEoFEKr1SI9PR3Hjh0Dh8MxufEkEgmuXLkCFouFoqKiRZ+qCgQC/PDDD9i/fz9t6YSEhCAlJcViPaFQiKysLBPxyGQyuLu7w9nZmVI6UqkUCQkJ8PLyQnJy8pyy8fFx5OfnIzEx0ebrZb7o9Xqr8SdgdnHFcA3QjY8xhV1Lp66uDtu3b8fq1aspyzkcDtatW4f33nuPcnrl5eWFN998E7dv36Z9zujoaAQFBdl8EQmFQnz99ddYs2aNxXoG6Xh6ekIkEtl0DgO1tbUoKyubs/RuQC6XIz4+HuvXr4eHh4fJqo1KpYJYLMb169cRHBxslI6bmxuqq6tN4hMajQbNzc2IiYnB3bt3Fz14KRAIcODAAfj4+NCWTlxcHAQCgcV6QqEQISEhJiuHz549A4vFAovFopSOWq1GfX09EhMT8ezZM5NyhUKBBw8eMCYdAyKRCAqFwmz5zMwMBgcHMTg4aHcBZ7uWTmVlJbZu3Yrt27dTlhuk8+mnnyIjI8Ok3CCdc+fOmSTlmWO+0mlra8OhQ4doS+fQoUNml86tER4eDm9vb8ophVwuB4fDwSuvvIKtW7dSxnTq6+vh5uYGBwcHqNVq+Pj4YOfOnXj8+LFJ3dHRUeTk5MDb2xu+vr60AuBarRYikQgikQhqtdqm92br9Eomk6GiosLi9AqYlY6Pjw9SU1PnHLcmndbWVoSFhSEqKoqy3a6uLnA4HHA4HHR1dVntLwA8ffoUIpHIYnqFOQx5XRkZGSSmsxhUVlaCxWLB09OTstwgne+++w5CodCk3CCdiIgIytjG1NQUxGIxxGIxNBoNuru7ceDAATg7OyMvLw/A7BBaLBajpaXFZHr3PE+ePEFAQIBV6cjlchQVFSEmJob2Rfoi165dw969e42rdc8zODiI48ePY8WKFTh58iSlbCsqKrBp0yasXbsWExMT2LlzJ1gsFqV0JBIJwsPD8cEHH2DDhg20kuxUKhXS0tKsLlNTYat0JBIJioqK5i2d/v5+rF27Ftu2baOUTnFxMbZs2YJt27ZRtltdXQ0/Pz94eHggLS3Nan+BWZFXVVWhpKSEVv3nmZqaQnBwME6fPo3e3l6b/94esHvpODo64qeffqIstyadyMhIfP7555QjisnJSTQ2NiI4OBjBwcEYGhqCQCDAV199BQcHB+Tm5kKpVKK8vBxhYWHg8XhWpRMaGorNmzdbfE8KhQIlJSWIjY2dd1JfW1sbLl++THlT9vb2YuvWrVixYgV8fHwopZObm4uPPvoIW7ZsgVqtxpkzZ+Dr62sSRAZmb+qgoCC89tprWL9+PaV0RkZG0NHRgY6ODojFYty9exchISHg8Xjg8/loaGigHczs6urC2bNnX2ogGZiVTkREBAoLC43HNBoNiouL8eqrr8LJycmsdDZv3gwnJyfKdg3SYbFYiI6OttpfA3K5nFLy1picnMSePXvAYrEsJpJOT0+jo6PDeB3bE3YvnW+++cZqTOezzz7DvXv3TMrj4uKwf/9+SiFNTEygrKwMUVFRiIqKgkwmQ2trK1xdXeHr64u+vj4MDw8jPz8f169fR21trUXptLe3w8fHB87Ozhbf09OnT5GYmLig6RUAcLlcyuG5VCoFm83GypUr4eTkRDm94vF42LhxI0JDQ40xnaioKMoHUg3Sef3117F7927KRLz+/n7jN3dcXBy8vLyMUxZPT0/cuHHDmPtDh3/++QdRUVG0pcPhcKymIAiFQnC5XDQ3NxuPyWQyXL161ap0HB0dsWfPHsp2bZHOyMgI+vr6jK9Hjx6hqqoKEokEer0eUqkUfX19FqekdKWjVqtx+/ZtuLq6QiQSMZYkS4dlLZ3s7Gw4Ojpi9erV8PX1NSnftWsXnJycKKVjjujo6HnlXdANJAOzF+pCpRMYGIjs7GyTkcf4+Djy8vLAZrPBZrNNRi8qlQo5OTlgs9nIy8ubE0gWiUQmgWQ60jEgk8lQWlpqbJ/NZiMzMxOlpaWUQW9z3L9/Hzdv3qQtnRMnTuDy5csW6+Xk5OD8+fMoLi42HhsbG0NaWhreeust/Pzzz2al4+DgAAcHB8p2DdJxc3PDzZs3Lfahvb3d+PkkJiYiMjISFy9eREVFBXQ6HaqqqlBaWmpxh4H5SOfGjRs2ff6LjV1Lp6amBj/++CPef/99KJVKypFGWloaNm7cSDn83bhxI3bu3In6+nra5+RwOMZ4ji3QlY5Wq0VpaSnYbLbVFRdLhIeH4/r165QjGa1Wi7y8POTl5ZkMrTs6OhAeHg5PT0+Ul5djamoKBQUFOHXqFOLi4kxuvJ6eHvj4+OCNN97AkSNHaGXfqlSqeS/XqlQqREREwNfXl1Z+VXl5ObZt2wZvb2+L9cLCwrBq1Sr4+PjMEachkLxv3z7KkV55eTlcXV3BZrMp2zVI5+zZs7QXH3p7e8HhcBAaGkqr/vNotVqw2Wy4uLhYlI5GozHu0RQXF0ekQxfDt+zKlSvNZiTzeDx8+eWXcHJymjMsnZiYwLFjx2xO2qqurkZLS4vN+ShCoRDffvst1q1bZzF4+ujRI4SFhS04T0coFFLGYKzR0dGByMhInDt3zqRMIBDMufF0Oh0qKirg4OCAlStXgs/n01p+XYh0DIFkFouFhIQEq/U5HA5cXV2t1jVIx8XFZc4I6tmzZ3BxcUF8fDxlX/v6+uDv749PPvmE8lELoVAIPz8/kxwea/T391MuBFhjZmbGmD3e3t5utp7hUZh79+4hIyODcrl/qbB76Vy9ehW//vqrWekYso9ZLBZOnz4NYDbCv3//fjg7O89LOmlpaTbvqCYUCsFisbB3717weDyz0iooKICzs/OCpaPX6y3GmMzR0dGB1NTUOdMMAzqdbk6bnZ2diIqKAovFApvNtpqQZoBJ6YhEIty+fdvq09IG6Zw5c2bOezSMdFxcXCinV3q9HrW1tXB3d6ecDl+5cgVBQUE2jaYN7dL9PF9Ep9OBz+dbFIlarUZ6eroxQXQ+18piYffSiYmJsfjsFfBvAltycjL4fD54PB5cXV3R0tJi86Zf1dXVaGpqsunvuru7jVm7zs7OcHd3B4/HowwItre34+bNm4w8y3T//n2Ti3N6ehoqlYrWNKmwsBC7du3CwYMHbcrq1uv1UKlUUKlUNt9YFy9exNq1a7FhwwbjntHmEIlECAgIgJubG4KCgiyKx8XFBevXr0dSUtKc49bydIDZKU1PTw+ysrLmHK+qqkJKSgrq6+sZ31wuJyfHYp6OWq1Gamoq3N3d7W5bD7uWjlarRXV1tVXpGOqOjIwYX11dXfO6ECYmJmyO9Gs0GgwODqKzsxOdnZ3o6urCyMgI5Q33sh74BICmpiaLq0JyuRwjIyPzviEUCgU6OzvR29trMfv1ZcLn83Hp0iUcPXrUalynvLwc8fHx8Pb2xqlTp/DgwQOzdf39/XHy5EmTB1qVSiViY2MRGxtrce8gw9YWL/7tyMgIYytDarUahYWFKCwsxJ07d5Cbm2s2VjM6OoqDBw/C2dnZ7naVtGvpALNLwGFhYTh58uR/Yr/biooKBAYGLlg6TU1NyMrKsrifznJEJpNBKpWivb0dbW1tFkUwMjIypy5VAigANDY2wsfHB+fPn5+zZA7MykQqlUIqldrd4wIv8nxfDS9zwpPJZMYRHJGOjWg0GjQ2NiI8PJzy2aDlRn5+PgICAha8TaSlrS0IcykqKsJvv/2G5ORkSjHpdDrU19ejtrbW7hLp5oNKpUJJSQmcnZ1x7tw5u3tcwu6lA8xOnZqampCenr5s90g2UFNTY5KKPx/6+vrQ2tqK5uZm8gN9VuBwOAgICDCZWhl4fo8ae1rlmS+jo6NISEjAjh07UFtba3df1MtCOsDsitSdO3fQ0tJiV9mVtjI8PDzvZ66oaGhooPyVCcK/XLt2DVlZWWa/8XU6HRobG+1uaXm+jI6OIjU1FfHx8XYnHGAZSWdmZgZVVVWIiYlZkh3s7ZWenh7k5+eT370yQ319PR48eEDrZ2jq6+tRWVlJ+zfH7JXx8XHU1tYudTfMsmykYyAiIsLuAmNLjWGqRfgXvV4PmUyGP//806YHayMiIlBSUmLzlhwE+iw76RAIdDBMx/l8vk0/o1NVVYWcnBzKx0sILwciHcJ/kunpafB4vGW/8PBfhEiH8J/F3vNu/l8h0iEQCIxCpEMgEBiFSIdAIDAKkQ6BQGAUIh0CgcAoRDoEAoFRiHQIBAKjEOkQCARGIdIhEAiMQqRDIBAYhUiHQCAwCpEOgUBgFCIdAoHAKEQ6BAKBUYh0CAQCoxDpEAgERiHSIRAIjEKkQyAQGIVIh0AgMAqRDoFAYBQiHQKBwChEOgQCgVH+B27mpfv0dw/HAAAAAElFTkSuQmCC)
- Define regular
expression let
- Construct a transition
system M accepting L(G) also metion the rules for such construct.
- Describe the
following set by regular expression {0,00,000,………..}.
- Convert the
regular expression 1+(0+11)0*1 into its equivalent NDFA.
- Describe pumping
lemnca for regular sets.
- Construct a
regular grammar equivalent to the DFA.
![](data:image/png;base64,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)
-
- Write the
name of regular expression properties.
- Construct transition
system for the following regular grammar-
![](data:image/png;base64,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)
- Prove that
the set is not regular
-
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGYAAAAqCAYAAABBRS51AAAJXElEQVR4nO2ZaXMTRxqA87O2ams/pHYru1uEXJukUjmoQC0QIFkcsA3YGBvb2CCf8olvDMYGbDC+ZEm+jW/5ki3fkiVZ50hz9D949oNDAkY2CiFBu6irnk8z0/N2P93vdPe8Q7zEZHnnTQcQL5HLz2KEEHFigLiYGCUuJkaJi4lR4mJilLiYGCUuJkaJi4lR4mJilP8NMZqM2H5Cx8AU5rl13G4b84YWbtdUUl5RTUObif5FJ0Eh0N50rG+VGDWMWO+i5oGZu8ZBZidaKc3O4PLFZM4nnuNcajbX6x4z4lIIqTEQ71sjRmgI2Y/bG8C5aGa4q4oztRZs3jCKtMJoUw65iae5YvbiltQYiPdtEaNIiMV60kpbKHxkwRUO4pUUVE0gNJXNgSoeFJ8iucONM/C2iFE2sXTc525eLT3rgqDyW14oY594wF39ZVIyC6gY8eENRdGRioSYqyQxr5Gc1lk8e+KbbK2h+moOd5Zk/LK253kVIdboryykqa4N01akdwQJ+S08vJxCU8cEU+5XbZ+P9dF7GO7oebAiCMi7da+PttJ8I5mzqeW0WVw4gntj3BOLzxKFGHWHhc4abqYn8+MjO9sB5dWC1hREcJ5ufR661Ezybj/GsCQRfKEjoxWjIYSPtZFW2hoaqH8wgi0okLW9zysIMcf9pFPkXimhaTnSO8LIoXXG7zYxNLXCqv/Xtk9DKDusjLRQe/U4ief/Q5FF4Anv1u1aesJQs56SnMv8UDnKoM1HeN+6wsjSenSpzLfYQUdNGocvGrA4goRfaHwUqCHEZit5P1wnR9fJZOCXa5rkxmGbYby/l66ubjq7ejD0jzO5ZMcpaS+K0WRUaZvliUF6Gutp7exn2LHfgIlGjIwSdmI1m5hbtrPt9+N3bzI3v4HTF0ZW9h88mhxEci4yYbxHffEFzh75iCNHnxXz030eK9vGaxw+dZs7I+vPz/oIsUT3jXFOMtZczL/+mcm9OSeOp6NclVElNxsb66yurkVky+XBJz8z6k/pSCkys/R0pGkSO/NGOqoyST55hM8+/YxPPv2cT4+cJVnfRofVj/qcmGmcAQd2Sy/1GcU0GyzMew6axdGI8RHcGaTs48PkVhsw2dZYme6htKQV4+g8i2sOnN4gUoTZrfg22RqqIuPkUc4X6rh47kcyIogRvmV2BnQc/rCIql4rWwekw4B7IDoxytYg/fWJvPvXQ5y7v8D0trx7zb+KdySPLz7/iHf/9l5EjmdV0GLbR4wmI/wjNKemkp1exa0pJ36/D79/GXPZeRLPpnC6fByXIqE+FXPPzNSUieLkMowL2zgkdXcR8DrFbKmEvXbWRx9Qfulb/n3uMhkNRsbWgxHEuHBPmxhZtLPpmcdUkUXuQWIO6agyLLwOMQrOsSaa0z7g3b+/z3upj+icde3mSEVC8a4wNTnB6OiTiFiW13FIz4g5U0CKvv+XGaN4cViXsC1v4Qg+XQiE2eot4npODsf1wzifEZOaX0ST/iTv/+Njvvj2BEdPnuL4yVMkpOsoG/ZGWEy8ihiBpsqEfU42rDOMDxvpaKqiIu8aF3S1tI6vsuELoQqBpsjIfg++kIKs2hisuhZZjH8Nz3AF37yfT/1rESOvMd5cSsF335Ksy+Krr3Ko65pjTfo13xgVNexmo/0KyVeqyX8wh2tPXg367WxYpxk3mehpu03ttTOcSEjjuH4Ip6aguqYwPZnDPDTE9GAL9Q23nqPpYTcmmxQh3byamGevywE39sVxhjvv0nAzj4ysLBoHZln07q1nZX8xsovASgc5XydSfn+EqX3Tb5Ri5E0DLaUFJJ0rwTg/ROmJE+gaDZg2QwjZj7w9jaGni0ft7RHpm5xn0W7HPtFEQ/4Vbtw20r2wg/J0xqge1mf6MT5upvFOI7erGqgtL+TGhWMcOZ2yK0YI1KgHwetIZXvSleTFtTrHdF87rQ0FpKVepLp3ilnPrxAjQsjBJYZKrlKqr6Spb4aViKu/qMQobJtLKS4u5GzdFF7JxWz1UVLLblEzYkcObOCfrOD0d8f47IsvI5JUdIuW4Ukmbn7DmfQqGoeWWAsqu2damozmHaMpJ4mEH86TWHyHdtMk08vbWA0l3MjTvTExmqqgSD7c9jWsM0P0Npejz0zhVHopd4aXWfOGfhpc0YpR0WQvO9NtVKcncL2skY71VxKjIYSDwZIkyoqKqZsNoSkSoQk9yRfKuFo7xprQEKpCOBwmFApFJCwrKGqYsH+FsfLvuVR0l9rBLWQhELJEeKycxKx6Mpun2ZQVVFVF0zTsgwXcyMt6Y2KUgBPHRBsVF7/h6NlLXK7pZtjm+ak92j6HpQeIUX1IzhFqv/8OXX03xtXAPouWl4lRw4iNTvTJuVwvesQTn4bQFLTAGC2ZFynIr6d9I9rO0dBkH4GRAhIvV5F9Z2r346dIaJYKkn/M51JpPxZJoKlhgiu91KWf5MuvznMst481ISKMzt9RjG2D9VkzNZWtdJufMDa7zIrDg/+lpxQHiAls4Bmv5tgnmVR0zLAc3m9v9BIxmhxk25hJWm41+ofzuNWns8jLbPNVCouLyDI4ou8wRULMVZN8tpi0skFsQuyeBrgnaa8qJjstnZQcHTl5JZTfbKC6OJPzZzI5ndTGlCII/ZFi1rx4tm2MjS+ztRMidMAGM2oxPhs7A/l8eEhH9W9ZlWlyCMdoDc19o/TZfM897LV20Wnson7IHr0YNYSwNZN1pojcnzeYux3nXjDRfVvPtaxsMq4VUdrYx+j4ID1tPTTWDbOkiN3U90qoCLHJWFMd7fcNjGxHukciHLTSW5hPe98s8y981KPFidX8iPabt+je2HOuGPU+RiIcWIxug/la0MIIl4HKhDLKC00sxuh/E1mWcTgczM3PH4jVuoTb7Y66Xs27xLY5l8OfFFFjtGJ/yf1/oBgZ4TJTmVBMoa6bicDv9J7fiN3h4EZePn/6818O5NAHH1Hf0Bh1veHtOaytlziUcJemsc0Dzsr+aDFCQyhuLK2l5Ced5ERSNgUDHnZi7MeWLMtsbW0xY7EcyPzCAk6XK4o6A6wMNlGXeoyvjyWQcX+BGUekpfYbEyMQQiWwZWFqoJP2bjNDq6GIB4P/X4TxrM0w2fuQ+4/7md4M4Nt3RfbGxMSJlriYGCUuJkaJi4lR4mJilLiYGCUuJkaJi4lRXhATL7FV4mJitPwXriT7apyIpVsAAAAASUVORK5CYII=)
- Obtain a
DFA for the below regular expression-
![](data:image/png;base64,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)
- A regular
expression corresponding to following subset of {a,b}. “the set of all strings
containing at most 2 a’s”
![](data:image/png;base64,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)
- Construct a
DFA with reduced states equivalent to the regular expression 10+(0+11)0*1
- Show that L={oi1i | i>=1} in not.
- Construcst a
regular grammar are gernerating the regular set represented by a*b(a+b)*