Level Difficulty in Candy Crush Saga.ipynb

{"nbformat":4,"cells":[{"cell_type":"markdown","source":"## 1. Candy Crush Saga\n<p><a href=\"https://king.com/game/candycrush\">Candy Crush Saga</a> is a hit mobile game developed by King (part of Activision|Blizzard) that is played by millions of people all around the world. The game is structured as a series of levels where players need to match similar candy together to (hopefully) clear the level and keep progressing on the level map. If you are one of the few that haven't played Candy Crush, here's a short demo:</p>\n<p><a href=\"https://youtu.be/HGLGxnfs_t8\"><img src=\"https://assets.datacamp.com/production/project_139/img/candy_crush_video.jpeg\" alt=\"\"></a></p>\n<p>Candy Crush has more than 3000 levels, and new ones are added every week. That is a lot of levels! And with that many levels, it's important to get <em>level difficulty</em> just right. Too easy and the game gets boring, too hard and players become frustrated and quit playing.</p>\n<p>In this project, we will see how we can use data collected from players to estimate level difficulty. Let's start by loading in the packages we're going to need.</p>","metadata":{"deletable":false,"dc":{"key":"3"},"tags":["context"],"run_control":{"frozen":true},"editable":false}},{"outputs":[],"execution_count":174,"cell_type":"code","source":"# This sets the size of plots to a good default.\noptions(repr.plot.width = 5, repr.plot.height = 4)\n\n# Loading in packages\nlibrary(readr)\nlibrary(dplyr)\nlibrary(ggplot2)","metadata":{"trusted":true,"dc":{"key":"3"},"tags":["sample_code"]}},{"cell_type":"markdown","source":"## 2. The data set\n<p>The dataset we will use contains one week of data from a sample of players who played Candy Crush back in 2014. The data is also from a single <em>episode</em>, that is, a set of 15 levels. It has the following columns:</p>\n<ul>\n<li><strong>player_id</strong>: a unique player id</li>\n<li><strong>dt</strong>: the date</li>\n<li><strong>level</strong>: the level number within the episode, from 1 to 15.</li>\n<li><strong>num_attempts</strong>: number of level attempts for the player on that level and date.</li>\n<li><strong>num_success</strong>: number of level attempts that resulted in a success/win for the player on that level and date.</li>\n</ul>\n<p>The granularity of the dataset is player, date, and level. That is, there is a row for every player, day, and level recording the total number of attempts and how many of those resulted in a win.</p>\n<p>Now, let's load in the dataset and take a look at the first couple of rows. </p>","metadata":{"deletable":false,"dc":{"key":"10"},"tags":["context"],"run_control":{"frozen":true},"editable":false}},{"outputs":[{"name":"stderr","text":"Parsed with column specification:\ncols(\n  player_id = col_character(),\n  dt = col_date(format = \"\"),\n  level = col_double(),\n  num_attempts = col_double(),\n  num_success = col_double()\n)\n","output_type":"stream"},{"data":{"text/html":"<table>\n<thead><tr><th scope=col>player_id</th><th scope=col>dt</th><th scope=col>level</th><th scope=col>num_attempts</th><th scope=col>num_success</th></tr></thead>\n<tbody>\n\t<tr><td>6dd5af4c7228fa353d505767143f5815</td><td>2014-01-04                      </td><td> 4                              </td><td>3                               </td><td>1                               </td></tr>\n\t<tr><td>c7ec97c39349ab7e4d39b4f74062ec13</td><td>2014-01-01                      </td><td> 8                              </td><td>4                               </td><td>1                               </td></tr>\n\t<tr><td>c7ec97c39349ab7e4d39b4f74062ec13</td><td>2014-01-05                      </td><td>12                              </td><td>6                               </td><td>0                               </td></tr>\n\t<tr><td>a32c5e9700ed356dc8dd5bb3230c5227</td><td>2014-01-03                      </td><td>11                              </td><td>1                               </td><td>1                               </td></tr>\n\t<tr><td>a32c5e9700ed356dc8dd5bb3230c5227</td><td>2014-01-07                      </td><td>15                              </td><td>6                               </td><td>0                               </td></tr>\n\t<tr><td>b94d403ac4edf639442f93eeffdc7d92</td><td>2014-01-01                      </td><td> 8                              </td><td>8                               </td><td>1                               </td></tr>\n</tbody>\n</table>\n","text/markdown":"\nplayer_id | dt | level | num_attempts | num_success | \n|---|---|---|---|---|---|\n| 6dd5af4c7228fa353d505767143f5815 | 2014-01-04                       |  4                               | 3                                | 1                                | \n| c7ec97c39349ab7e4d39b4f74062ec13 | 2014-01-01                       |  8                               | 4                                | 1                                | \n| c7ec97c39349ab7e4d39b4f74062ec13 | 2014-01-05                       | 12                               | 6                                | 0                                | \n| a32c5e9700ed356dc8dd5bb3230c5227 | 2014-01-03                       | 11                               | 1                                | 1                                | \n| a32c5e9700ed356dc8dd5bb3230c5227 | 2014-01-07                       | 15                               | 6                                | 0                                | \n| b94d403ac4edf639442f93eeffdc7d92 | 2014-01-01                       |  8                               | 8                                | 1                                | \n\n\n","text/latex":"\\begin{tabular}{r|lllll}\n player\\_id & dt & level & num\\_attempts & num\\_success\\\\\n\\hline\n\t 6dd5af4c7228fa353d505767143f5815 & 2014-01-04                       &  4                               & 3                                & 1                               \\\\\n\t c7ec97c39349ab7e4d39b4f74062ec13 & 2014-01-01                       &  8                               & 4                                & 1                               \\\\\n\t c7ec97c39349ab7e4d39b4f74062ec13 & 2014-01-05                       & 12                               & 6                                & 0                               \\\\\n\t a32c5e9700ed356dc8dd5bb3230c5227 & 2014-01-03                       & 11                               & 1                                & 1                               \\\\\n\t a32c5e9700ed356dc8dd5bb3230c5227 & 2014-01-07                       & 15                               & 6                                & 0                               \\\\\n\t b94d403ac4edf639442f93eeffdc7d92 & 2014-01-01                       &  8                               & 8                                & 1                               \\\\\n\\end{tabular}\n","text/plain":"  player_id                        dt         level num_attempts num_success\n1 6dd5af4c7228fa353d505767143f5815 2014-01-04  4    3            1          \n2 c7ec97c39349ab7e4d39b4f74062ec13 2014-01-01  8    4            1          \n3 c7ec97c39349ab7e4d39b4f74062ec13 2014-01-05 12    6            0          \n4 a32c5e9700ed356dc8dd5bb3230c5227 2014-01-03 11    1            1          \n5 a32c5e9700ed356dc8dd5bb3230c5227 2014-01-07 15    6            0          \n6 b94d403ac4edf639442f93eeffdc7d92 2014-01-01  8    8            1          "},"metadata":{},"output_type":"display_data"}],"execution_count":176,"cell_type":"code","source":"# Reading in the data\ndata <- read_csv(\"datasets/candy_crush.csv\")\n\n# Printing out the first couple of rows\nhead(data)","metadata":{"trusted":true,"dc":{"key":"10"},"tags":["sample_code"]}},{"cell_type":"markdown","source":"## 3. Checking the data set\n<p>Now that we have loaded the dataset let's count how many players we have in the sample and how many days worth of data we have.</p>","metadata":{"deletable":false,"dc":{"key":"17"},"tags":["context"],"run_control":{"frozen":true},"editable":false}},{"outputs":[{"name":"stdout","text":"[1] \"Number of players:\"\n","output_type":"stream"},{"data":{"text/html":"6814","text/markdown":"6814","text/latex":"6814","text/plain":"[1] 6814"},"metadata":{},"output_type":"display_data"},{"name":"stdout","text":"[1] \"Period for which we have data:\"\n","output_type":"stream"},{"data":{"text/html":"<ol class=list-inline>\n\t<li><time datetime=\"2014-01-01\">2014-01-01</time></li>\n\t<li><time datetime=\"2014-01-07\">2014-01-07</time></li>\n</ol>\n","text/markdown":"1. 2014-01-01\n2. 2014-01-07\n\n\n","text/latex":"\\begin{enumerate*}\n\\item 2014-01-01\n\\item 2014-01-07\n\\end{enumerate*}\n","text/plain":"[1] \"2014-01-01\" \"2014-01-07\""},"metadata":{},"output_type":"display_data"}],"execution_count":178,"cell_type":"code","source":"print(\"Number of players:\")\nn_distinct(data$player_id)\n\nprint(\"Period for which we have data:\")\nrange(data$dt)","metadata":{"trusted":true,"dc":{"key":"17"},"tags":["sample_code"]}},{"cell_type":"markdown","source":"## 4. Computing level difficulty\n<p>Within each Candy Crush episode, there is a mix of easier and tougher levels. Luck and individual skill make the number of attempts required to pass a level different from player to player. The assumption is that difficult levels require more attempts on average than easier ones. That is, <em>the harder</em> a level is, <em>the lower</em> the probability to pass that level in a single attempt is.</p>\n<p>A simple approach to model this probability is as a <a href=\"https://en.wikipedia.org/wiki/Bernoulli_process\">Bernoulli process</a>; as a binary outcome (you either win or lose) characterized by a single parameter <em>p<sub>win</sub></em>: the probability of winning the level in a single attempt. This probability can be estimated for each level as:</p>\n<p><img src=\"https://assets.datacamp.com/production/project_139/img/latex1.png\" style=\"width:150px\"></p>\n<!-- $$p_{win} = \\frac{\\sum wins}{\\sum attempts}$$ -->\n<p>For example, let's say a level has been played 10 times and 2 of those attempts ended up in a victory. Then the probability of winning in a single attempt would be <em>p<sub>win</sub></em> = 2 / 10 = 20%.</p>\n<p>Now, let's compute the difficulty <em>p<sub>win</sub></em> separately for each of the 15 levels.</p>","metadata":{"deletable":false,"dc":{"key":"24"},"tags":["context"],"run_control":{"frozen":true},"editable":false}},{"outputs":[{"data":{"text/html":"<table>\n<thead><tr><th scope=col>level</th><th scope=col>attempts</th><th scope=col>wins</th><th scope=col>p_win</th></tr></thead>\n<tbody>\n\t<tr><td> 1        </td><td> 1322     </td><td> 818      </td><td>0.61875946</td></tr>\n\t<tr><td> 2        </td><td> 1285     </td><td> 666      </td><td>0.51828794</td></tr>\n\t<tr><td> 3        </td><td> 1546     </td><td> 662      </td><td>0.42820181</td></tr>\n\t<tr><td> 4        </td><td> 1893     </td><td> 705      </td><td>0.37242472</td></tr>\n\t<tr><td> 5        </td><td> 6937     </td><td> 634      </td><td>0.09139397</td></tr>\n\t<tr><td> 6        </td><td> 1591     </td><td> 668      </td><td>0.41986172</td></tr>\n\t<tr><td> 7        </td><td> 4526     </td><td> 614      </td><td>0.13566063</td></tr>\n\t<tr><td> 8        </td><td>15816     </td><td> 641      </td><td>0.04052858</td></tr>\n\t<tr><td> 9        </td><td> 8241     </td><td> 670      </td><td>0.08130081</td></tr>\n\t<tr><td>10        </td><td> 3282     </td><td> 617      </td><td>0.18799512</td></tr>\n\t<tr><td>11        </td><td> 5575     </td><td> 603      </td><td>0.10816143</td></tr>\n\t<tr><td>12        </td><td> 6868     </td><td> 659      </td><td>0.09595224</td></tr>\n\t<tr><td>13        </td><td> 1327     </td><td> 686      </td><td>0.51695554</td></tr>\n\t<tr><td>14        </td><td> 2772     </td><td> 777      </td><td>0.28030303</td></tr>\n\t<tr><td>15        </td><td>30374     </td><td>1157      </td><td>0.03809179</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nlevel | attempts | wins | p_win | \n|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n|  1         |  1322      |  818       | 0.61875946 | \n|  2         |  1285      |  666       | 0.51828794 | \n|  3         |  1546      |  662       | 0.42820181 | \n|  4         |  1893      |  705       | 0.37242472 | \n|  5         |  6937      |  634       | 0.09139397 | \n|  6         |  1591      |  668       | 0.41986172 | \n|  7         |  4526      |  614       | 0.13566063 | \n|  8         | 15816      |  641       | 0.04052858 | \n|  9         |  8241      |  670       | 0.08130081 | \n| 10         |  3282      |  617       | 0.18799512 | \n| 11         |  5575      |  603       | 0.10816143 | \n| 12         |  6868      |  659       | 0.09595224 | \n| 13         |  1327      |  686       | 0.51695554 | \n| 14         |  2772      |  777       | 0.28030303 | \n| 15         | 30374      | 1157       | 0.03809179 | \n\n\n","text/latex":"\\begin{tabular}{r|llll}\n level & attempts & wins & p\\_win\\\\\n\\hline\n\t  1         &  1322      &  818       & 0.61875946\\\\\n\t  2         &  1285      &  666       & 0.51828794\\\\\n\t  3         &  1546      &  662       & 0.42820181\\\\\n\t  4         &  1893      &  705       & 0.37242472\\\\\n\t  5         &  6937      &  634       & 0.09139397\\\\\n\t  6         &  1591      &  668       & 0.41986172\\\\\n\t  7         &  4526      &  614       & 0.13566063\\\\\n\t  8         & 15816      &  641       & 0.04052858\\\\\n\t  9         &  8241      &  670       & 0.08130081\\\\\n\t 10         &  3282      &  617       & 0.18799512\\\\\n\t 11         &  5575      &  603       & 0.10816143\\\\\n\t 12         &  6868      &  659       & 0.09595224\\\\\n\t 13         &  1327      &  686       & 0.51695554\\\\\n\t 14         &  2772      &  777       & 0.28030303\\\\\n\t 15         & 30374      & 1157       & 0.03809179\\\\\n\\end{tabular}\n","text/plain":"   level attempts wins p_win     \n1   1     1322     818 0.61875946\n2   2     1285     666 0.51828794\n3   3     1546     662 0.42820181\n4   4     1893     705 0.37242472\n5   5     6937     634 0.09139397\n6   6     1591     668 0.41986172\n7   7     4526     614 0.13566063\n8   8    15816     641 0.04052858\n9   9     8241     670 0.08130081\n10 10     3282     617 0.18799512\n11 11     5575     603 0.10816143\n12 12     6868     659 0.09595224\n13 13     1327     686 0.51695554\n14 14     2772     777 0.28030303\n15 15    30374    1157 0.03809179"},"metadata":{},"output_type":"display_data"}],"execution_count":180,"cell_type":"code","source":"# Calculating level difficulty\ndifficulty <- data %>% \n                group_by(level) %>%                 \n                summarize(attempts = sum(num_attempts), wins = sum(num_success)) %>% \n                mutate(p_win = wins/attempts)\n\n# Printing out the level difficulty\ndifficulty","metadata":{"trusted":true,"dc":{"key":"24"},"tags":["sample_code"]}},{"cell_type":"markdown","source":"## 5. Plotting difficulty profile\n<p><img src=\"https://assets.datacamp.com/production/project_139/img/tiffi.jpeg\" style=\"height:150px; float:left\"> </p>\n<p>Great! We now have the difficulty for all the 15 levels in the episode. Keep in mind that, as we measure difficulty as the probability to pass a level in a single attempt, a <em>lower</em> value (a smaller probability of winning the level) implies a <em>higher</em> level difficulty.</p>\n<p>Now that we have the difficulty of the episode we should plot it. Let's plot a line graph with the levels on the X-axis and the difficulty (<em>p<sub>win</sub></em>) on the Y-axis. We call this plot the <em>difficulty profile</em> of the episode.</p>","metadata":{"deletable":false,"dc":{"key":"31"},"tags":["context"],"run_control":{"frozen":true},"editable":false}},{"outputs":[{"data":{},"metadata":{},"output_type":"display_data"},{"data":{"text/plain":"plot without title","image/png":"iVBORw0KGgoAAAANSUhEUgAAAlgAAAHgCAMAAABOyeNrAAADAFBMVEUAAAABAQECAgIDAwME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\nsDCCEv8HE+I6O31SYysAAAAASUVORK5CYII="},"metadata":{},"output_type":"display_data"}],"execution_count":182,"cell_type":"code","source":"# Plotting the level difficulty profile\nggplot(difficulty, aes(x = level, y = p_win)) +\n     geom_line() +\n     scale_x_continuous(breaks = 1:15) +\n     scale_y_continuous(label = scales::percent)","metadata":{"trusted":true,"dc":{"key":"31"},"tags":["sample_code"]}},{"cell_type":"markdown","source":"## 6. Spotting hard levels\n<p>What constitutes a <em>hard</em> level is subjective. However, to keep things simple, we could define a threshold of difficulty, say 10%, and label levels with <em>p<sub>win</sub></em> &lt; 10% as <em>hard</em>. It's relatively easy to spot these hard levels on the plot, but we can make the plot more friendly by explicitly highlighting the hard levels.</p>","metadata":{"deletable":false,"dc":{"key":"38"},"tags":["context"],"run_control":{"frozen":true},"editable":false}},{"outputs":[{"data":{},"metadata":{},"output_type":"display_data"},{"data":{"text/plain":"plot without title","image/png":"iVBORw0KGgoAAAANSUhEUgAAAlgAAAHgCAMAAABOyeNrAAADAFBMVEUAAAABAQECAgIDAwME\nBAQFBQUGBgYHBwcICAgJCQkKCgoLCwsMDAwNDQ0ODg4PDw8QEBARERESEhITExMUFBQVFRUW\nFhYXFxcYGBgZGRkaGhobGxscHBwdHR0eHh4fHx8gICAhISEiIiIjIyMkJCQlJSUmJiYnJyco\nKCgpKSkqKiorKyssLCwtLS0uLi4vLy8wMDAxMTEyMjIzMzM0NDQ1NTU2NjY3Nzc4ODg5OTk6\nOjo7Ozs8PDw9PT0+Pj4/Pz9AQEBBQUFCQkJDQ0NERERFRUVGRkZHR0dISEhJSUlKSkpLS0tM\nTExNTU1OTk5PT09QUFBRUVFSUlJTU1NUVFRVVVVWVlZXV1dYWFhZWVlaWlpbW1tcXFxdXV1e\nXl5fX19gYGBhYWFiYmJjY2NkZGRlZWVmZmZnZ2doaGhpaWlqampra2tsbGxtbW1ubm5vb29w\ncHBxcXFycnJzc3N0dHR1dXV2dnZ3d3d4eHh5eXl6enp7e3t8fHx9fX1+fn5/f3+AgICBgYGC\ngoKDg4OEhISFhYWGhoaHh4eIiIiJiYmKioqLi4uMjIyNjY2Ojo6Pj4+QkJCRkZGSkpKTk5OU\nlJSVlZWWlpaXl5eYmJiZmZmampqbm5ucnJydnZ2enp6fn5+goKChoaGioqKjo6OkpKSlpaWm\npqanp6eoqKipqamqqqqrq6usrKytra2urq6vr6+wsLCxsbGysrKzs7O0tLS1tbW2tra3t7e4\nuLi5ubm6urq7u7u8vLy9vb2+vr6/v7/AwMDBwcHCwsLDw8PExMTFxcXGxsbHx8fIyMjJycnK\nysrLy8vMzMzNzc3Ozs7Pz8/Q0NDR0dHS0tLT09PU1NTV1dXW1tbX19fY2NjZ2dna2trb29vc\n3Nzd3d3e3t7f39/g4ODh4eHi4uLj4+Pk5OTl5eXm5ubn5+fo6Ojp6enq6urr6+vs7Ozt7e3u\n7u7v7+/w8PDx8fHy8vLz8/P09PT19fX29vb39/f4+Pj5+fn6+vr7+/v8/Pz9/f3+/v7////i\nsF19AAAACXBIWXMAABJ0AAASdAHeZh94AAAgAElEQVR4nO3dB3zU5PsA8KctlA1SRXGg4kIQ\nXAXH31lFXByrLBlFRhURKIiIMkUZ4k9wMByIiAwRRBAQAUGmDBmCDJm2BQptX2QUSikd+V/y\nZrxvLsmN5Erv+ryfD5c+T3LvvZf3Sy6XS96AgAVLEApc7gZgCc+CsLAEpSAsLEEpCAtLUArC\nwhKUgrCwBKUgLCxBKQgLS1BK8GCdkkreKa6cKcjhE+ez+fhCwVk+cek0H+df4uOzF3UVFpzn\nEzlZugoL+Pi0roln9U3M1jUxR9/EPF0TC3RNzNK/Z30TL+rfc76uifr3XHBB10T9ey44o2si\nH54qyPXWxHOBNbEIYBGpFBCunBJy+MS5bD6+IJzmE3kn+bgwj4/PXNRVKJzjExfP6CoU+Phk\nPh+f1jfx/Hk+ztE3MV/XRMF2Ewt1TdRVeFq4oGuirsIc4RSf0HXDSeESnzirf89CFp/I1b9n\nXRP/k5uIsNSCsAjCIgiLNhFhISyEhbCkgrAIwiIIizYRYSEshIWwaEFYBGEhLLmJCAthISyE\nJRWERRAWQVhSQVgIiyAshEULwrrssFY1ufPhEcfZDMIyaiLC8g/W4mhwl8ZsCmEZNRFh+Qer\nFkhlJpNCWEZNRFh+wTpAXUEvJoewjJqIsPyCdViG1YfJISyjJiIsv2CR+ymsBUwKYRk1EWH5\nB2ttBdFVOzaFsIyaiLD8g0V2vhZ3F7zJZhCWURMRlp+wyCkho2qlA0wCYRk1EWH5DyvnHW6T\nhbCMmlgyYBUufK1F50niX6kD4xNmFqgz1PBQUusPst3TDT3yvcNKiWE3WQjLqIklA9YXLaas\nWvCx+4+zHftvnt9iupJXw8Lus88N/EYQ8hK3+rDFItwmC2EZNbFEwNrr2iD/NTv+jCBMj8/W\nhydd2cKqJEGYN4x9nuE7EmFxmyyEZdTEEgHr0x7ubZL0V//h7ocU12Z5hhqKsFYnCWfaHfEJ\nlnuT1U9NICyjJpYIWD0+/rJVs8HH3H+9NMX9kNdknjxDDQu7/3h+8BRhwhfc8wzfkQQr5Upt\nk4WwjJpYImC1a9V747rExDxBaDJbjFtNk2dooXvnfVR2Svss5SkTO3To8FqeVIQ8ruQLBe7H\n92CQkigo4BcoEPL5RCEf5gm6RL4uLhB0NRbqK9Q1Sf8K+foKwqGJ+go9muj1PfrWxFw/YL3U\nNEMQDrpWKZJa8rDUcPBCYUZC4lrxz0GxsbENLao8V63yf15fF0sIFu2ogHdYia+Ij62+M/8o\nlMqm7vmbEzJ2x2cqzzPcBstnkA5U97Lwo9CoiSXio3B4ogRrhry3nszvvCth/qtbhMkTBCFp\njS+wtL0shGXUxBIBa0mT44Lwj2u9fHxhGn+4QQnnDxWEyePdsFb7AkvbZCEsoyaWCFi5r7y2\n6rfOvQsE4WyHfhvmNRcPkP7W9Bgbuv9ulyoIGxNO7GqR4RMsdZOFsIyaWCJgCZkjWrX+4KT4\nV8rA+IQZ4m84y1xH2VAQJn0uPn7brvPv6tMM35F6lc4geEOaIiyjJpYMWAEWw3ekwlI2WQjL\nqIkIK2BYyiYLYRk1EWEFDivlygr7CcIybiLCChyWvMlCWEZNRFg2YNFNFsIyaiLCsgHLvcnq\ni7CMm4iw7MByb7L2ISzDJiIsO7CkTRbCMmoiwrIFK9W9yUJYRk1EWLZgiZsshGXURIRlD5Z7\nk5WMsBCW47Dcm6z+CAthOQ/LvclK5RdAWARh2YdFBkN/fgGERRCWA7BSq1XcxyUQFkFYDsAi\nw7lh2BAWbSLCsg0ro1oFbpOFsAjCcgLWuff4TRbCIgjLEViZV3GbLIRFEJYjsLIHc5sshEUQ\nljOwUq8qz2yyEBZBWM7AIkPYTRbCIgjLIVjcJgthEYTlECxuk4WwCMJyCha7yUJYBGE5BYvd\nZCEsgrAcg+XeZP0jxwiLICzHYJGhkCTHCIsgLOdgaZsshEUQlnOwtE0WwiIIy0FY6iYLYRGE\n5SAsdZOFsAjCchKWsslCWARhOQmLDIPe4gRhEYTlKCx5k4WwCMJyFJa8yUJYBGE5C4tushAW\nQVjOwqKbLIRFEJbDsKRNFsIiCMthWO5NVi+EJTURYTkKK7Va+X8QFkFYTsMi70IvhEUQluOw\njlQrn4qwEJbjsNybrDuffmU7twDCQlj2YfUAdym7nE0hLOdhbWpx6z1JyWwmzGGtAKncwS6A\nsByHtbGCuJbvSWNSYQ5rKIUFfzE5hOU4rKfoWh7BpMIc1iAZ1jYmh7Ach1WJruUmTCrMYf1M\n3/H1GUwOYTkOK4au5ngmFeawSFvpHf/AphCW47DiKayJTCrcYaWPefi2qjCHTSEsx2H9c53o\n6vlMJhXusMSzG1ZE1ElnEgjL+cMNh58EeIbd3ygRsE43h0+ZBMIKwgHSrgCPcokSAWt7merM\nXQUQVhBgPQtVK5a8LRbpBW9pCYQVBFh3lW0N69hEyYCVXK3sDjWBsIIAq/IdH3H7GyUEFhkN\n7dQEwnIe1r/QcC10YjMlBNaJWpErlQTCch7WWuiaFV2PzYQSrAtSKbzAlRwhn09cusTHecJF\n9+NceEJJFOTwCwgFfHxRV2GuoKsx/yIfFwh8rG/iRSHPlyaaV+C1iZeEXP+amKOv0FsT8wXd\nWuObOA+GF9xXijCZXH2F3ppYqO9Y2sTzRQArSyoFWVw5L1ziEzkX+ThXyBYncfCjnCg4xy8g\n6GrMztNVKOTwiUvZfJwv8PE5b028qGviJeE8n/BoYr6uifr3rG9inp9NzBZydU3Uv2ePJnLR\nWPg2PxGWM5kL+vfsrYkFhbom0vd8tghgGW2DffwoJGRV5O0naAI/Cp3/KOwFv18aD+8xmVD6\nKDR6Rz7DIm3gfzSBsJyH1RwOX/oDmjGZkgPr7/JXHpb+QFjOw2oQmXsps8qNTKbkwCJvyCMp\nIyznYV1bXbhEHoe9WqYEwUq5pox0VQXCchxWWmQDN6w+MFNLlSBYZBy0EicIy3FYW6G5G9Y0\neFNLlSRY6bUjxMt1EJbjsBZALzes3RCnpUoSLPIDNMhEWFITnYU1HsaI1xVeX1U71a9EwSJx\nMA1hSU10FtYAmCXCagyb1VTJgrW+1M1pCIs4Dqs9rBFhDYVJaqpkwSIdYBTCIo7DehL+FWEt\ngEQ1VcJg/VPpigMIy3FYt1aSxm5ILRWrpkoYLPI29EBYTsPKLFuHDgpSO1q9yr6kwTp6Q/Q+\nhOUwrL3QiMJqD+rwKyUNlvubcUuE5TCs5dCVwhoLo5VciYOVcQ8s5hdAWHZhfQNDKaxV0EbJ\nlThY7q8usZlcAmHZhfUefEVhpZe/TcmVPFikMUzmYoRlF9YrsEQe0e+hiINyrgTC2lO6BjtC\nGMIidmG9ALtkWD1grpwrgbDyusC7bIyw7MKqF50hw/oa3pFzJRHW/spV9jMxwrILK+YmZXDb\n7fCcnCuJsE4OgW5MjLBswkqFR9VRk6tdJSdLJKy0m0ut12KEZRPWemirwnoW5LHPSyQs8iU8\nr8UIyyasH+BNFdY7MIUmSyaszAYwT40Rlk1YH8EnKqw58DpNlkxYZElEXXU0J4RlE1Yf+FGF\ndSjiYZosobBIY20kVoRlE1ZL2KTd8uTWcvSC85IKa2v0tUfkGGHZhPVQxFENVmtYLU1LKizS\nHQbKMcKyCeuGasxNmkbDOGlaYmEdjKmwm8YIyx6s9FL3MbCWQQdpWmJhkRHKCHQIyx6sv8DF\nwEqLriNNSy6s47dErZX+QFj2YC2CHuz9Cu+Pkm4vV3JhkanwtDRFWPZgTYJRLKxu8LM4KcGw\nyEP0VigIyx6sQeJVwBqsSTBMnJRkWMsiaonHXBCWPVid4HcW1iZxl6tkwyIt4BOCsGgTA4f1\nFOxnYWXG3CBOSjSsneWqJSMs2sTAYdWqQLibjcfBLlLCYZHe4ohOCMserIq1CAerH3xHSjos\n6VYoCMsWrP3Sl2sG1kxpSM6SDYuMgbYIi9iCtVI60MzA2gdPkBIPK/3OyBUIyxasaTCIcLBI\njcoZJR6We7td/4ef/uHmIyziD6yR8DnhYTWDPxAWuREAKoxlMwiL+APrNWnIAhbWcBiPsD6h\n919nh3NAWMQfWI3hL8LDWgxdENbdFFYrJoWwiD+w7i8l/nzBwjpS6l6EdQ2Fxd4oG2ERf2BV\nkw60s7BI3ehjJR5WAwqrPZNCWMQPWEcjHpIqZGElwJISD2ua5CpiLpNyGtas+hVrJqWymXCC\ntYnuRnCwPoGRJR4WGV0JoCLUPqhlHIY1VaL7NDsmVzjBmktvfcXBWgvxCIukbPzzWHv4v2Nq\nwllYGfJe3HdMLpxgfQLSsRoOVkalmghL+hH6RCNool7A6iysndQVvMHkwgnWm/CDVCELizwS\nsR9hSb8VHn0QXlZiZ2Htl2ENYnLhBKuteJhdD6s3zEZY9Efo/XeoXe/wPtYDFNYaJhVOsB6B\nFKlCDtZUeAthyWc3/H1DxCc0dhjWpitFV0PZVDjBuimGVsjB2gkNEZZy2sy6K6K+lf5w+nDD\nwZsAxnCZMIKVEX03rZCDRarHnEFYymkzv5Yr+4s4dfwA6dWgjasvlTCC9Te8SCvkYb0AOxGW\nej7Wt1Ex4o6o07AOwVXQkcuEEawl8AqtkIc1CL5BWNqJfmPhur+ch7UUukTFcpkwgvUVvEcr\n5GHNg9cvD6yzL7mOi9PUgfEJMwvUtBoeSmr9QbZ7uqFHfhHCIv3hzoOOw5oAn91RPoPNhBGs\nITCVVsjDSo588PLAmtBRgnW2Y//N81tMV7kpYWH32ecGfiMIeYlbi3KLJV4fXv+I07D6wLIW\nsIXNhBGsLvL9vnSwSK2yOkdFA+tg64USrNnxZwRheny2nFbDk65sYVWSIMwbxj6Le0dKcRZW\nemN49qTDsBpDylDxKnSthBGsRkDP69bDagsbdRUWBazC/rPXS7D6D3c/pLg2y3k1FGGtThLO\ntDtSxLDI0YfgZYdh3Vm2YA68zWbCCFbtsvTXdT2sD+FTXYVFAWtl11wK66Up7oe8JvPkvBoW\ndv/x/OApwoQvlGek7d27d/9pqRSc5kqWkMsnsnP4+KJwjk/kn+Hjwnw2Sq0LQ3UVChf4RK6u\nwjyBj89wTfyvTD1hLzRjUxd0FV4UsvhEga6JQj4fn9O/ZyHbuon5+ibqKswSLvKJC/oKPZpI\nJ5VvV5qYx81eBZ10FeqbeElXYX4hH5+lTTzlB6wLCesECqvJbDFuNU2eoYXunfdR2Snts5Sn\nDIqNjW3oXawTJe0mGO9kfYehtVBYqZaTVRafchqeMZ5xqVwdZ15B+/LmHdaUtwUOVkselhoO\nXijMSEhcK/65YOTIkR/nSKUwhysXhXw+cSmPj/OEXD5RwIc5gi6xIybqe65C4RK/QL6+QkFX\nI9fEBTBQyG8QdYptkq6J+fom6t6jRxNz9e/Z7ybqK9SvxTx9hcJFoyb+CZ1NmvhwZIZ1Ewv0\n71nXxIu0wmyVjVdYJ5rvPH9+petwjvlHoVQ2dc/fnJCxOz5TeSL34a4Uh/ex3OXMuvJlFrEV\n2tvHeh++EnI6wAomFT77WDOUnUf9PhbpAT/xFQZ/H2uHi5bh8t56Mr/zroT5r24RJk8QhKQ1\nRQ3r4qxSlVczFdqD1Ql+F3JGiZfaqSV8YH2gvC8PWFO4E4WKBNa5v91llmtVinx8YRp/uEEJ\n5w8VhMnuvZ2k1UUOi0yMuHa7VqE9WI/AEcH9efgakwofWD1hgVyhHtYO+UdEtcIi+kmH7mOd\n7dBvw7zm4gHS35oeY0P33+1SBWFjwoldLTKKHhZ5B2odUCu0B+ua6qeFnAPwJJMKH1jNYJtc\noR7W2WrX8BUWKSwhZWB8wgzxN5xlrqNsKAiTPhcfv23X+Xf1Oew7UktwYJFXIFa5sMYerOSI\nR8XLv6pfzeTCB1b9SPkuyJ6wnoOdXIUl+UdoWqRey2gCjU7IFdqCtRxeFmHFATPySPjAqn6t\nUqEHrMHyr4hKhQiL9lraE9CaHlS2B2sSjBBhvc5+SQobWGmRDZQKPWAtgN5chQhL7rV/60I/\nWqEtWG/AbBHWBBih5cIG1hZorlToAet4BDtuAcLSem1XDXFkfLuwmsA2Edbv0E7LhQ2s+epW\nyRNWTs2K6WyFCEvttT+vihTvQ2sPVp3odBFWmngnI6WEDazx6sn8BrDiYS1bIcLSem15hegf\nbcLKKFebDgpyRzntXL+wgfUWzFIq9IQ1kjvBAWGxvfZ96Uqr7MHaDo0prGawWU2GDax26kbJ\nANYS5fZqtEKExfba5xHVtydv+pdfwB9Yc6AvhTWQ+fYdNrCegMNKhZ6wjkXXZStEWFyvDYYK\nAODazy7gD6xRMJHCmg5vqcmwgXVLFbVCT1jk3ihm8CaEpeu1mz1HIfIHVhdYRmFtc38mKiVc\nYGWWraNWaACrCzu0K8Lie22tPKYHe9aLP7Aeh0MUVmalW9RkuMDaA8+qFRrAGi9fGkYrRFhc\nr02XYX3N5PyBdV01ZajIBpFHlGS4wFoGXdUKDWD9Ac2YChEW12tLZVjsmX9+wEqJeFiB1Um+\nUIqED6xvtLFOjGBlVL6RqRBhcb2WTsfrrnOCyfkBayUkKLBGa4d1wgXWcJisVmgAy/2lca9W\nIcLie21zbberWtxFcn7A+lLczaCwFsKrSjZcYCXCr2qFRrD6wEytQoSl67UTi+7lr2P2B1Z/\n8dA0hXUQHley4QLreditVmgE6zv5Z3ypQodhrWsTe/NNYglZWOTcUOY/nlj8gNUM/lTHeb8u\nRsmGC6y60erPVIaw9kCcVqGzsKZApQZPSyWEYc3VXRfgB6y60SdUWE+rexzhAqvqzVqFRrDI\n9VXU438Ow7rNleXhI+Rg7VPPOqLFd1iZFcTb2sqwesGPcjpMYKXAY1qFhrBcsEmt0FlYpdc7\n5+qywcovfyeX8B0WvVRFhjVJPV4YJrDWQVutQkNYQ2GSWqGzsGqsDANYQmypY2zCd1hzIYmo\nsNao/RAmsGZDf61CQ1g/Qze1QmdhDWoTDrAS4Hc24Tus0dL1nDKstOh75HSYwPofc8KVMazU\nUupQhg7DWlzz6W+W/yaWUIY1hruO2Q9Y3WAJ0e7+dWdZ+VzdMIHVB+ZpFRrCIrWj05QKnYUF\nagllWIuhB5vwHdaTIF72qsBqoQxGFiaw4plzF01gdYBlSoXOwpqullCGlcpdx+wHrBuuFB8V\nWIPgG5oOE1gPRmi7niawxqoDkeORd6Ne465j9h3WkcgHxYkCaya8SfNhAut6Zq2YwFoNrZUK\nEZZBrz3FXsfsO6xV9M6tCqzt8ALNhwesE6XuZyo0hpVe/jalQudgzZ9f4P6nlJCG1VM9tikW\nn2FNhmHiRIGVWUU+Uh0esLZDE6ZCY1jkoYiDcoXOwQLICZOd93MT2XMhfYc1AGaIE/We0A9E\nSnfKChNYC+F1pkITWK/DHLlC52AtWlTg/qeUkIa1mjnG7AesePqLhgqrMyyVpuEBayJ7hyAz\nWF/DO3KFuI9l0GvasU2x+AzrntLHxYkK60P4WJqGB6yB7O2IzWBtV06LR1iGvVY7mjmF1FdY\nmRXpnqsKazEkStPwgJUAq5gKTWCRalfJFToLq/br8/4LB1gt6Q1qafEV1t/wnDRVYR2WB2AJ\nD1hxcEALTWE9C3TQTYdhPRAFkff1++VcqMMaop3d7Tusn6CXNFVhkRuqSpPwgHVHBbZCM1jv\nyBc4Of1ReHZh33sioNTDg0Ib1vfQV0v4Cku57YcG6xl6Lm94wOJOJjKFNUf+7hiMfayT0+uE\n+OEGslP+VJOKr7BeAemOrQysJPrlOyxg7YeGbIVmsA5FPkQrdBpW3oYRcWWgervQhkViamgJ\nX2E9BXTIBw3WF/CuOAkLWCvgZbZCM1jktnLS9x6HYY1rXAmqNhu/xwFWlxfWIxGH1ISvsGrQ\nPSoG1lpoI07CAta33JUA5rBag3QzBqdPm4nssKXAQ0gIwurGDHDhI6xjUfLIrxqs49H1xElY\nwBoBX7AVmsIaDWOlCp2F1ag8XN3my0OhD2ucOiiiz7DWwks01mCROtLxsLCA1V3eg5QrNIW1\nHDpIFTq8j5W7Zthj0XDjy9+FOKylzB6Fj7C+gSE0ZmDR42FhAasx7GArNIWVFl1bqjAI3wqz\nZ9cO9W+FJDXyATXhI6x3lPv1MrCGSEd1wgLWvaXY8SzMYZHYyGQSBFjnl74VGwmR94c4LHJL\nRfXaSx9htVKO1jOwvoc3SJjAurIGG1rA6gY/E8dhDX20NECdnj+d8lASarAaK7cj8hnWfaXk\nCwkYWPR4WDjAOi8O0MRUaA5rkjTYkdPfCm/pNivdCVSXHVZ/7bd8H2FVUYbwY2CRquKQUeEA\na6960jGt0BzWZmmQTIdhpTB/F+66EMKwpionFvkKaw80kmMW1kMR/4YHrKXsj1yWsDJjridB\nPW0mBzaGMKw/oamS8A3WAvWaMRZWV/FKw3CA9RWM4yo0h0XiYBfCIma9llHhdiXhG6yP1DXP\nwvpIPFwYDrAGKeccyxVawOon7kUgLLNeqx+lDE7rG6zusFCOWVhLxNEMwgFWR9jAVWgBayb0\nQVjEtNc6wm9ywjdYDdVLxlhYyRH/Fx6wnoBUNrSCtU8cyxBhmfWaNjitb7BurqLELCxS44rw\ngFUzhgutYJEbK2cgLNNe+1kdnNYnWGnaQCscrGfh73CAlV76Hi62hNUM/kBYpr12KEIZnNYn\nWOvoGTJi4WD1hdnhAGunNKQcU6EVrPdgPMIy77XrlY2/T7CmaqcrcbAmw9BwgPWLNrg4rdAK\n1mLogrDMe62hMvi0T7AGabeR42Cth1bhAOtLeJ+v0ArWUffnpuOwcpZ/8cXyHPGv0D7yrp6w\n7iOstrBOiTlYJ6LvCgdYg5nbL0oVWsEi9UofdRrWt1eKAzdc6cTwWJcblnzCuo+w6keqg0dx\nsEjd6LQwgNVZPfgiV2gJqxMscRjWLGgw6dcFI2vAD6EPa62yO+4TrKo3qTEPqzWsCwNYz8A+\nvkJLWJ/CSIdh1W1TKE7O3VPPAViFUpEnahH0CW/zvVZgEl8qc6/vFaTDCyYLjIGZQWuijQr8\nXIt1yxX48Qp/Q7tAm5hnDCt6E51OjHYAFhV82bZY7g8xaYwPn7ZYi6C7GvNbrB+gTxhssSrx\nQ9972WJlVLrZ4S3WtfIXwQk3hgGs1vI9232B9TF8pMY8rF3QKPRhHYRndBVawiKPRqQ6C6tn\nC+mj8GzdYWEAaxh8KU19gfU6LFBjHhaJqRH6sFZrdwaQK7SG1Rt+chbW/GvvHrfgh6HV7/vV\ngbHe6QtdPlhzxF/piW+wGml3XNPDeiQiLeRhTeeGOCReYU2FgcEa592B4SLpC10+WLvl7b8v\nsG6ppN33XgerG6wIeVij4VtdhdawdsKzwRrn3YGx3ukLXT5Y5KrrpYkPsI6Xvk+LdbDGwSch\nD6snfxMYr7DItTGFOKKfaa89Rkf58AHWBmilxTpYv0JiyMNqCod1FXqB9SIcQlimvfaqdIWc\nL7CmaZdeeMBKjXw45GHFRula4A3WIJiFsEx77VM6TrAPsIbAFC3WwSI3VfbotVCDdc11um7w\nBus7ePBz7pRThMX02m+QIE58gPUSrNFiPaznuftckBCElRb5gH+wFlZ1f3e7bi2bQlharx2N\nqi9OfIDVIPKoFuth9ePuc0FCENaf0MIvWCnXSkcFaqUzOYTF9Npt5cXbtvsAix0A0APWFBjO\nPyHkYP0ESX7Bmikfb1rO5BAW02tN4E/iC6z9EMfEelgb+KvTQxDWZ/ChX7AmyrDYSxERFtNr\nb0vHBb3D+kW+UwAteljp5e7inxBysPrD937BWkFdRe5kcgiL6bXv4C3iC6xPmfH/PGGRe0un\ncXHIwXoJ1vq3895EgsX9voiwmF7bJg2c4h1WL/iJiT1gtQfu+1HowXoc/vUPVnK3cgA9uf9O\nCIvptcxK4tBE3mE9D38zsQesUfA5F4ccrJpX6LvB23EscrYzLOISCIvttQbiHQe9w7q9fCYT\ne8D6GXpzcajByixzl9+wzk/TnRCBsNhee1m8K7tXWBej72ZjD1iHuZs6hB6sPfCc/7D2QnMu\ngbDYXhsj3nHQK6y9EM/GHrDOy6dJKCXUYC1174b7Daug0s1cAmGxvSbdcdArrAUwgI09YT3B\n3pEt9GB9De/6D0t4LGI/m0BYbK8djnjEB1hj2JvQGcHqwe/Ihhqsd+HrAGAl8UO1ISyu18T7\n43iF1ZW996gRrIncca6Qg9UNlgYAizuVCGHpeu1Z2Okd1iMRKWzsCWs1d+eskIP1HOwJANYe\n9tZ8CEvXa+IoRF5hVbuBiz1hZUY2YONQg3VXdGYAsLKuuppNICyu1ybDEK+wDsGTXOwJ63zN\niuyBrlCDdUVNj27wBVZD7rAxwuJ67Q9o6RXWUt1FdwawXpRvwU1LiMFKFscUDQBWf+XmQlJB\nWFyvpZet7RXWeHoGs1oMYPWHGUwcYrCk++UFAGuWfF0mLQiL77W7S6d5g5UEc7nYANZU7vak\nIQbre+gfEKx93C4CwuJ7rS2s8QbrRfiLiw1gbeJ+3wgxWB/CZwHBIjUqM3uWCIvvtfdgkjdY\ntaQTmLViACujfC0mDjFYSeJJQYHAcsFmLYGw+F77EXp5gZUezY9UbQSL3FuKOTkpxGC1EE/Q\nDgTWUPY20giL77V98JQXWH/qT2k3gvUSvbc7LSEG64GIY4HBms8OtYywdL1WrboXWLOUe0Er\nxQjW+zBRi0MM1nXXkMBgJTP3P0ZY+l57Eo5Zw3oPpvPzjWDNg55aHFqwjkfFksBgkdvLafeR\nRli6XusBy6xhJUjXiDHFCJb7E1WLQwvWdunOjQHBasPsACAsXa+Nh4+sYf1fhO4FjWCRatdq\ncWjB+hleJwHCGi2eJykXhKXrtd/hZWtYV1+bz883hPUEaKe9hRasCdIPCwHBWkoHv5AKwtL1\nWlqp+pawDsNjvsDqTodEkjdKMSwAACAASURBVEpowXpH2ocMCNax6HpqAmHpe61Wuf90FXKw\nlkFnX2B9xvygGFqwOko7SgHBIneXVgdLQVj6XmsOW3UVcrAmwkhfYP0GHdU4tGDFwUESKKxO\n8KuSQFj6XhvEnf1B9LD6whxfYMlDIkkltGDdXlF8DAzWJzBKSSAsfa/N5K/B0cNywXZfYJFb\nK6i/yIYWrPK1xcfAYK3VxmZFWPpe+0t3c1EdrNplMnyC5dI+UUMK1j46KHlgsNLL36YkEJZH\nr13BX3nJw8ooU/ukT7AGwHdKHFKwfoPO4iQwWOTBiENyAmF59NojEf/yFbKwtkET32B9q10N\nFVKwpsJgcRIgrO7qODwIy6PXusMSvkIW1g/whm+w/pR+GZFKSMF6n95RKEBYX6q/0CMsj16b\nwNzZS6qQhTUSJvkGK6PC7UocUrBehV/ESYCw/pRGGBMLwvLotTXQla+QhdUZlvsGi9wfpRws\nDClYL4I04GOAsDJjlPFQEJZHr52MeIivkIX1KBzyEVZ7WCnHIQXrntLSoNoBwiJxym3REJZn\nr93MXhSgg1X9GuIjrJEwXo5DClbMjdIkUFh9YSZNICzPXtNdhsPCSo54xFdY86GHHIcSrCPw\nf9I0UFjfwZs0gbA8e22A8r9OrpCBtQI6+QpLGww+lGBtgDbSNFBYu+FpmkBYnr02jbvclIP1\nObzvKyxyzTVyHEqw5sAb0jRQWKR6DJ0iLM9e28oPp8nC6gff+wwrDvbROJRgjZNPAg0Y1guw\nTZoiLM9eO8VdbsrBagpbfIbVA+bTOJRg9ZXH5QsY1iD4WpoiLINeu6/UMbZCBtZd0ek+wxoP\nI2kcSrBaw0ZpGjCsudIp8wjLsNfac7dEZmBllruT+Azrd2hP41CC9TAckaYBwzoYQb9WBgHW\nplGdW/VZLf2ZOjA+YWaBOkcNDyW1/iDbPd3QI784wtIOQUkVarC2i79Y+AorrdT9NA4lWDWu\npNOAYZGaFaQjrEGA1XPowpXvuxa7/zrbsf/m+S3Uu9urYWH32ecGfiMIeYlbi+UWSzsEJVWo\nwZojDgHlKyxyuzx6SAjBSi99L00EDqsFrBcnQYCVLj4MSHQ/zI4/IwjT47PlGWp40pUtrEoS\nhHnD2OcZvqPLAusAN9ITA2u0uCnzGVZT+dLWEIK1Q/kROXBY79PNfbD2saa2dD/0H+5+SHFt\nlnNqKMJanSScaXekeMIi1auxFWqwusJSP2C9I93+MKRg/QLdaSJwWL9AF3ESLFgD+7ofXpri\nfshrMk/OqWFh9x/PD54iTPiCe4rhO7o8sJ5i7xfOwJJuOeEzLHr7w5CC9QWMoInAYR0pdZ84\nCRKs9a717scms8W/W02Tk1ro3nkflZ3SPktZfNlnn302+YJUCi9wJUfI5xO5l/g4T7jIJwr4\n8IKgS1zUVyjoasy/eOENWMxUKKh/3lDNoIkXhTw+cUmucA80M26irgKvTbwk5Ho0kStME+WE\ntybqKxRypOlwmO1jE/UVak2sG33aoImF+o6lFZ73D1Zym081SS15WGo4eKEwIyFxrfjnoNjY\n2IY+iS2aMh3GGqXPRzzmTy2Fle9wpjlFV7rDVu8LeSldYYvvC2tHBXyBldFpmPQEs49CqWzq\nnr85IWN3fKb777S9e/fuPy2VgtNcyRJy+UR2Dh9fFM7xifwzfFyYz8fn9BUKF/hE7rnT66Gd\nFucJyl9roJP78YxHEy/yiQtKhfWjjtMmZvELFOiaKHhtYrZHE7mSL/DxGV2Fnk3UVyg38Rk4\nJDeRn39ayOPj87omXtCaOA7Guh8v6d5zfiEfn6VNPOUPrDOv9s2R/pD21pP5nXclzH91izB5\ngiAkrVGeZvjhfnn2sdLYOxJq+1hfwXDixz4WSYDfxEkI7WPdWU5OBL6PRVaKw3kHYx/rQp9X\nz9C/pOML0/jDDUo4f6ggTB7vhrW6GMIitaO1IcQ0WG9J59P4Dmu0OP5wSMGqeIecsAHreNk7\nSVBgDW8yb727FAjC2Q79NsxrLh4g/a3pMTZ0/90uVRA2JpzY1SKjOMJqCX9oFaqwWkjDAvsO\n62f65T3YsDLGd2g9irvTd6CwDqjnkNmARepHJgcFVkeXVMRPw5SB8QkzxN9wlrmOsqEgTPpc\nfPy2Xeff1ecZvqPLBGsIc0tCDVa90seJP7AOwBPiJMiwMp4Cd6nN3pEsUFir1AGu7MDqBgvx\nR2iTXpsNfbUKFViZFaQPCt9hkWulX96CDOtDkEoikwoU1ncwUE7YgTVR3BVFWIa9thOe1SpU\nYO2E58WJH7Cegr0k6LAaUVjswACBwhqtDvZsB9YGaIawzHqtag2tQgXWPOglTvyA1Qt+JEGH\n9SSFdR2TChTW6+o4hHZgZVS+CWGZ9dojEYfVChVYY+BTceIHrInwPgk6rDcoLBeTChRWU/V2\neHZgEfG+4wjLuNcSYbFaoQKrGx3UwQ9Yq6VDOkGGlXyj6Kr0NiYVKKz7o47LCVuwesMPCMuk\n1z7W7heuwoqjIyH7AStNOr0p2IcbXoeYG6pw97oLFNbVygXy9mBNhbcRlkmvLdPuF67CqkGv\nbPIDFrmzbHrQYR2JqUQKl0XVPKqlAoSVFvGgkrAF6y/3Vx+EZdxrqdr9whVYR+VbxfgDqzls\nCjqsEdAnr5B0Ze9vGiCszRCvJGzBIldfjbDMeu0W9X7hCqzV0E6a+gNrEEwNNqzjN5TZ7Yb1\n73WlVqm5AGHN03Dag/UM7ERYJr3WGJS9YQXW1zBUmvoDa4Z4G9zgwvoUuki/FU6F+9UbdAYI\n61P4n5KwB+stmIqwTHrtLXUMUQXW23LGH1jbxZFygworo1bUFvoj9AvwoZIMEFZ/mK0k7MH6\nHpIQlkmvfev+ZiNXKLespXwtpz+wMqvUDDKsqeII2BKsXZUr/S0nA4TVFtYpCXuw9sPjCMuk\n1/6EJkqFcsvuLUUP8vgDizSITAkurPoRa5XTZkap4zQGCOsxSFYS9mCRGpVzEJZxr2VUUIYs\nV2BVupVO/YL1MiwLKqy50o+aFFZGA+XjO0BYN1dVEzZhNYHdCMuk1+pHHZErpC3bpfwu7Res\nMfBJUGE9Jo1FK5/ot7b09XSTExiszOi6asImrGHwLcIy6TX5vGIV1nzlbrx+wVoErwQT1nJ4\nWGqi3Gs95dt9BwZrNz17Qyo2YS2AngjLpNdG05+cVVj/c297pOIXrEMRjwUT1ovwg9REudeO\n3BT5q9TEgGD9ypzTZRNWctRDCMuk136W//crsF5Vfpb2Cxa5PiaIsDZE3iUdxlXPeZ8DdaST\nXAOCNVm6VoQWm7BIrbKZ/AIIS+k1cVtDK6Qte1oZoM8/WA1hT/BgtZXPoNYupmhBLyQKCNYw\nmKIm7MJqC2v5BRCW2mvXy6NpyrBuvEKe7x+sJJgTNFg7o2+iFxNpsPbHlNsaKKxu7m+wSrEL\n6wNlx0EpCEuF9Yw8Fj6FlRal/CrtH6wvYHjQYCXCWBozl399DE8FCutZ2KMm7MJaBp34BRCW\nCquPPBwnhbUW2srz/YPlfl6wYO2vcLU8pCUDK/Mx98djYLDqRGv7RXZhpZWpxy+AsFRYX8Iw\nWqHUMvl2a8RfWMej7w4WrH7wrhyzF6xuKlPtYGCwqtyiJezCIveXSuVihKXCWgutaYVSywbK\ng135C4vUjj4XHFipMZWV8/K5K6H7Q8eAYP1Lr4KkxTasV3U350NYKqwT0XfRCqWWtaYjIBK/\nYcXDjuDAelce65/oYKXVilgQCKy18vlmUrEN6ytlzGi5ICzt6GPdaOm6dQrr/ijlInY/YQ2G\nmUGBlVa93D4l5sduWBRx23l+eZ9gzZLHiZOKbVjboSUXIywNVht6LIbCEs9/ocVPWLPgnaDA\nGsccJ9cNCtJe3jtkmugDrDHsWNG2YeVUvJWLEZYG6134QqpQbNleenN3sfgJawe4ggEr/ZbS\n29VYB+tAtTJ/cAmfYPVW7qQhFtuwch9W7zsuFYSlwZoDSVKFYssWwmvKfD9hubd1wYA1WT38\nQTyHMfoSHuZ+UfEJVnPYoiXsw3pdugpcLQhLg7UbGkoVii0bqxyL9B/WQxFngwDrnoh1Wuwx\nPtaLdGQurYk+wGoQyQyFZB/WFP4eagiLOdnpKun6TQnWa+qoBn7D6gIbnYf1g3gyvVo8YB0q\nX5UZ99k3WNdWZxL2Yf3FtRBhsbAely59lmA9o/3c4S+s/8FXzsP6P+4wkeeIfkO5L2W+wDoe\nVZ9J2Id1KoYdpgRhsbC6S5spCVbNyup8P2FlDoBru2zlFrAPawU8xsaesE7Ug1lsE73D2iYO\nPqQW+7BOq/cdlwrCYmB9BqMJhaXecIn4DauLOGRH2RVsyj6s57ihGozGIF0eVUP7TcUXWAuU\nM2Sl4gCsN2AGEyMsBtZv0JFQWOvln3fE4h+sRXSQodrsArZh7Yisy33rMxrcthv0ZproHdYE\n+IBJOABrOvRjYoTFwDoaFUsorGnqGIr+wnqLwpKG9lOKbVjt4BsuNoKVfH3pNVoTvcN6m9vA\nOABrt3gCj1oQFnvR3u0VMiiswUxP+gfrTRnWHiZnF9b2UrdncAnD4bi/g1hlKV9gdYDVTMIB\nWOS6GGazirBYWNKN4URY7Jm2/sH6kbrift+wC6srTOAXMB7n/UVpF5E20TusJ4E9Uu4ErBeB\n+c6CsFhY74iDxYiwGkRqd4n2c+e9legqahGbsgnrn7LX665UMIa1u0rFnUoTvcO6rRKbcALW\nIGZMc4TFwfpOHCxGhBVzozbfT1jp/3uydqVI7rc7m7D6wIe+3ZlitHKM0gdY/5Xjvl84AetH\n9ka1CIuFtU0cDcENax+7H+rvAVJ3r02BpmzCHqx/q1Q96RusjAYwTW6iV1j7oRGbcALW4YiH\ntRhhsbAyK90iwVqsXGMolgBgnaoXsZJJ2IM1BN7y9V46a0tfc5g20SuslfTGqEpxAha5pbx2\nRyKExY1q9kBkigjrE21EsoBgnf6e/+ptB1baNeX3+3yTpiToRpvoFdY0GMImHIHVkvnKg7A4\nWC/DUhFWT/ZUpUBgkUfYGmzB+hC6+373r6M3Ry4hPsEaAV+xCUdgjWTOsUBYXK+NgXEirOdg\nl5YLCNYvcL/2Tc4OrPSapf/y47Zy8yNqH/cJVnf+4gdHYC2BzmqMsLheW+z+KHHDurUi8/0+\nIFikEUxXE3ZgfQHt/bpfYUtx5FQfYDWGv9mEI7COSsPc04KwuF77N+IRN6zjzAoKFNbayNrq\n0XI7sOpFrvcL1v4ry27xBdY9pdPZhCOwyF3R6rmDCIvvtRpV3bA2cic3BQaLxKt31rIDa5Z0\nzxx/7rD6GcT5AivmJi7hDKwOsFyJERbfa8/BzjxhujrQrVgChLUtuoby39cGrAel4eD8gZX5\nOHzhHVY2PMIlnIE1VjtjAmHxvdYXvs8ThsLXTCpAWKSzupYDh7UInvRoIrGGRTaXiTnkFdZe\n9toM4hSsVVqtCIvvtckwJE9ox/3wHyis3eWvkgclDhxWQ3rUwr+bjQ+Aqyrf1v8om/KA9St3\n8pRTsE6UraXECIvvtT+gZZ7wQOQRJhUoLJKkXLcSMKw1Efd5NpF4gzVJOr/iBa6Jelhf6saz\ncgYWaRD5rxwjLL7X0svWzhNiarDzA4Z1qGrlA9IfAcNqIf/25xesE1fSM3fmsE3UwxrIn+vs\nFKxE9eImhKXrtXtKZ//n/l7FlIBhkUHy2cKBwtoSdUeGQRO9wNoin2r4GpPzgNVBvu2GUhyC\nNUkdaQlh6XqtLWzbQH9wU0rgsFKvKScdwQ8U1svK6Ap+wdolw4LrWn6knL3jAevxCG4fzClY\nG9XTOhCWrtfeg6nfcJcZ2IBFxtDbawYIa2/Z69OMmuhtH+seiVWpuBj341WNhqzIMIB1UzU+\n4RCszCrKXgTC0vXaj9BvAD8KgQ1Yx28u/ScJGFYv9VRj/2CtqyrCeo+QrWNbX+/+q8IT/Rfp\nWnC+1H18wiFY5HGQr8hGWLpe2wfPNoOdbMYGLPI5tCCBwjpcOUa5UtA/WGT/oJd6KgMib52Q\nIN6cvPwDvX9kPvwOSAf0meIUrCTlTnWXD9aZOKk8fTJLKu1ouEG4JEbv0ejrrKyci1lZc2n0\npjgnV9hDo8b0eVmNabiHRm/ENXzaHc2j0VfSK8SNpNE6acGnOudIUSZ9XtzxS9li2JlGK7Ou\nua52+bNjaDRJnHOu4Gca9aLVHJReIe4Z+fWbxT31lDv8i0Zviy/YMG4Wjb59siLUj4sbcU6K\nNtFqWmcJ+e7orPz6yVlZ2e73/CqNfhUXzBE+c/9ZE2p+TKtZKr1g3Cs0SpFeIS7uDA1b0/e4\nkUbDaDWzc6Xoexq9Pq1r7QiAqEo31nssLq5p1qF25aHqN43ozH3SkgW9afQzreZz+h4/oNEq\n91pzxy/T6IS0Fhs+lUHDjvSJm7NpN0JNMfoyq6DQHf1E5/UV12J+1l73n22DDytT3sU8nSOV\n22i0VMgXow40GpaTcykvJ2c8jZ4T5+QJ22hUhT4vpxINt9PoGRpNotFgGnWi0WIa3XlJik7K\nr388P1cM76bRvJynodQ9OYk0GiAtWfg1jZ6g1eylURn59avRcAONXDQaS6ORNHqJRitpdGOO\nUOCOsuXXP5yTk+t+zw/QaKa44CWhD4160SfOolEDGv0rP/E8DW+i0QoataHRB9JazBlHI1dO\n3qXk6d1vpVHlI7HStDQNd9H3+CSNJtNq3qZRNxrNp1FdGp2QXz+ThnfSaKm0FnNa0WhQTqHg\njj6nUUP3nxcLcv5y/1kz+LAKD0rlpHyCymEaZtLPmVQaHaMfhWk0ShHnXBBO0ki9eOmQFMq/\n1acc/C/THck7vcfEZ504KB/uPC4tePQs/SjMPCi/Iv2c+ZdGx0kPgObkCI2kD4+T+fLry8fR\n/zt1QgrVlz92jH39gwdPnErWXv8+mH3wLP0opE87eFj+KJRfP4N+FCbTSHriOcHduKHQ7aD8\n4ZV2IoV5/Qx3m//TXl9ccYcyD8onBdMVl5xDf9JRV5y0856+5fPO9aIAImh3X31AeX13KWBf\n393wUxlipK24VHfj5WOf0oo7duqI3HHyijtPPwqPVLuKrjjpo5DpOPdHYbr45oMPq5juY625\nHeDK79mMnX0scQS3BwPaxzpeI1o72dDPfSyrsxuSZ/epLm9y2IGPnNrHIs/CX9IUd975Xttz\nlfQx9wuTsgeLPA2zAoE1ERJMmkhswSLib4lSiWJ/t3IM1tvipZkEYRFdr71OVzpzHZNdWGsi\na1/yH1Zm7ajNJk0kdmGtKSO9x+fYBRyD9YPyawPC4nqtIYUVw6RswiLNYbr/sL7jRq9yFhYZ\nFe1+i7ewo0s4B2u/PJIXwuJ7LZ7Cqsmk7MLaXOq2E/wCPsCqH7HKrInENiyy9t3e49O4jGOw\nyI2Vpa8DCIvvtZkU1ptMyi4skgAf8Qt4h7UEnjZtIrEPS77ZOFOcg9WU/ryNsHS91lt09fRx\nJmMb1q7y1xzhEl5g7R/brxYsNG9i8Yb1Lj3XH2Hpe23lqHfncAnbsMib/FXHXmAtEn/qK7XU\noonFGtZCem4IwvLsNYGP7cMiV1Q5wIaWsI5cR4/Ps/tAoQQrhY7GjLCKAFb+O9CHjS1hzZUP\nX7KfhaEEi9xZRtyRQFhFASu1Wnn2y70lrG9kWNOZXEjBagu/E4RFigTWydHQlYktYf0hw9pm\n1cTiDGuMdLcYhFUksNJuKr1Fi61gHWtLXbEQQwvWcuhAEBYpGlhkArTSYgtYf98Hd3WpAlX7\nc8cvQwpWWnQdgrBIEcHKuCtSO5RuDuuXq6HFEXLulLcmFmdY5L6oVIRFiggWmQbPqrEprLHR\nUUN8amKxhtUFfkFYpKhgkQbaSGcmsE4kQtW5vjWxWMMaDyMQFikyWAvhISU2hrX/Ubhtg49N\nLNaw1kE8wiJFBovEwQ9ybAhrVQ145rCvTSzWsDIq3oKwSNHBWhFRRx7jzwjWV+UieitDAIY4\nLPJ/EfsRVtHBIk2UW4J4wkrvHVFhqh9NLN6wXoe5CKsIYW0qdQs9HccDVuazcLM2RHrIw/oa\nBiGsIoRF2sM4aaqHtbUWPLzPryYWb1jb4AWEVZSw/i5bXTrjTwfr+8qQwJ5ZGPKwyJXXIqyi\nhEVeo8NHcbAyh0SW+YpfPuRhPQW7EFZRwtpf6QrxAmYWVooLqq/wu4nFHFY/+A5hFSUs8pY0\npiwDa8c90GC3/00s5rBmQF+EVaSwUqqV38vCWngVtDoaQBOLOay9EIewihQWGQGJDKyxpUsN\nCaiJxRwWub6qvokIK7iw0m6M3qrASmsHMfMCa2Jxh9UY9iOsIoVFPoO2Mqxd9aHOtgCbWNxh\nDYaZCKtoYaXXilonwVp5AzRNDbSJxR3WPOiLsIoWFpkKL6S748/LRvRWbooYfrAORz6KsIoY\nFhFHbIxtCxWn2WhicYdFbiuvqwBhBRvWT/QqnBvX22lisYcVB6/O5RIIK9iwGnhe3hV+sDqK\nb/FF9h6uCCvYsKpSWOwwRWEHayJ9j8OYFMIKNqyadKUzlxmGHyx5XMR6TAphBRuWPLQsO1RS\n2MGSB61nbzuNsIIN68Tz7lUePcBeE4s5rATwGD4XYQX9cAP5+YNP1nOJsIP11xWiq7LM2dYI\nqwhg+XMXe5MmFnNYZOVDUZH3cqNdIiyERRw4juXxiggLYREnYOH5WAhLLAgLYRGEhbBoQVgI\niyAsqUKEhbAIwkJYtCAshEUQllQQFsIiCMvgHSEsn5qIsBAWQVhiQVgIiyAssSAshIWwaEFY\nQYVlWFLjPrBeYELcHusFGiVaz18a97P1Aj3irOcfjBtnvcC4uIPWC8S9Zj1/Ydyv1gskNrKe\nvzduvPUCY+JSLefnxvWxrmBe3ErrBTo1tp5f1LCSY9+1XmBs7N/WCzz8kvX8hbE/Wi/wcqz1\n/P2xo6wXGBW733qB+p2s58+L9WK/3cPW83fFfmS9wPDYfy3n58Z6+e85K3ap9QItn7Cej7A8\nCsISEJZBQVhCSYSVMWCO9QILB1jvHQiDPrWev3XAJusFJg6wnp824CfrBX4akGa9wNsTredv\nHrDVeoFPB1nPTx2w0HqBOQMyLOfnDfjSuoL1A3ZYLzB2mPX8ooaFpaQUhIUlKAVhYQlKKVJY\nRz57vck7FvM3jercqs9qiwX+HNgh/pWZuZYvcvYl13HTmStcYlls8fTCha+16DzJdPZbUgWu\nXeYVrOvTqtNYYj5/bY/miSa7SMz6SR0YnzCzwHwB41WpZU1WpbaA8arkqjVak9oCXlZlkcJa\n1fXDRCtYPYcuXPm+Vbcv+GTR7181+9jyRSZ0tILVbL27nLB4+hctpqxaYP4Kf4vPf7uNue1t\nro/+XNapV77Z/O2usZu/bWL8HrX1c7Zj/83zW0w3X8B4VWpZk1WpLWC8KrlqjdaktoCXVVmk\nsAoFYZgVrHTxYYCXb8LC5BamveYuB1svtILVwkvle10bvCwhCAUdPjGf+XFX97tc60oxm9/v\nDffDhPaGb0FbP7PjzwjC9Phs0wWMV6WWNVmVuqd5rEp2vuGa1BbwsiqLeh/LEpZUprb0ssC8\nppfMZxb2n73eElah9Qfppz2klWdZtrm2m8/8qKcgbpaSzdoXP8P9uN6112S+vH76D3c/pLg2\nmy4gmK1KNmu4KtkFjFalMt90TaqwLFdl8YM1sK/V3JysHRZ7QIKwsmuuJawmrVwv/2Qhp8fH\nX7ZqNviYZQs/7uix86OVHU0XZR15822z2flNZ7sf/3QtM5kvr5+Xprgf8prMM11A8AWW4apU\nFzBZlcp80zWpwLJelcUO1nrXeqvZLVyuMRafhBcS1glWsLZM37T+A9dM8wrateq9cV1iYp5F\nE3LbWB5dXBfvcr113nR24gj3w0yXARmpyOunichPaDXNdAHBB1jGq1JdwGRVyvPN16S8gJdV\nWdxgJbexPrL+z465bSzOPpjytmAJSyofxptvw19qmuHeu3Ctsnj6etc/FnN3t5r016rEt03x\nz2/y67kt7VxmR/c5WC1twTJZleoCJqtSnm++JtnXNV+VxQxWRqdhVnvmUllpugMjnGi+8/z5\nla7DOZYV/OE6ZDov8RXxsdV3Fk8f1c2q8jeGuB8OudaZzc8f38TVcrapXOc+Cs1WJfs0o1VJ\n51usSbYC81VZvGCdebWvtQmxpLg2ms3aQY8yuYZbVrDWddh03nDpi1SrGebPzo63Uie0nup+\nyG8y13yJrJSczaYbVXbnPdnOzrvpqmSfZrQq6XyLNclWYL4qixWsC31ePWP5bGmneb7L9Kf7\nc3+7yyzXKtMv+9L/4eGtzD8KlzRxd/k/Vvt5K8wPJYil50D3wz7XGqtl8sx37tnDDdM8DjcI\nPsMyX5XyAqarks63WJNyBV5WZZHCylm/PqnH+vUXzOYPbzJPPOhm/p3rza9+XfpJs/etX8Vq\nH6v/l0sWD3RZnFiT+8prq37r3Nvia9+Qnpavvtj18cZfO3cxfY/bvlr+U1Ib41M4tPVztkO/\nDfOaexwg1RYwXpVa1mRVagsYr0q+WoM1qS3gZVUWKazjdPN61Gx+Rzrf/NNwblLrNkkLLA5j\nicUK1owereL7rLB6duaIVq0/OGk+/3RTi085dyn8tVerhA/Mj+0f6Neq9XsmpwYx6ydlYHzC\nDA/e2gLGq1LLmqxKbQHjVclXa7AmtQW8rEr8ERpLUArCwhKUgrCwBKUgLCxBKQgLS1AKwsIS\nlIKwsASlICwsQSkIC0tQCsKyVxbBfMeWCquCsOwVhGVSEJa9grBMCsKyVxCWSUFY9golc3Fk\nnTJVXtwuCEuAng780DV5TBZhYfG3SGQuPRnVadLoW8ptEfKrS4MkHYC+bBZhYfG3SGTGgXi+\n2+nr4gThTRCHuhwMO7gswsLiZ5HI3F8zRyyvlLoo7IIBglB4890Cl0VYWPwsEplyIJfjbk43\nFAirQRxxj8kiLCx+32dBZwAAAL1JREFUFolM2bs30pIrCJ/Ab0KXKPHUZCaLsLD4WSQy9apo\n16pklu54ofLz4l9MFmFh8bNIZP4Hb0mBdOlBkwqTQbqOmckiLCx+Fnq4oRE8MeaLtxs0FDPz\noHIV6eIYJouwsPhZKJm8T2PLl7+t/XIxkxsD8jX4WhZhYcHiTEFYWIJSEBaWoBSEhSUoBWFh\nCUpBWFiCUhAWlqAUhIUlKAVhYQlKQVhYglIQFpagFISFJSgFYWEJSkFYWIJS/h/uGLNLFTW7\nAQAAAABJRU5ErkJggg=="},"metadata":{},"output_type":"display_data"}],"execution_count":184,"cell_type":"code","source":"# Adding points and a dashed line\nggplot(difficulty, aes(x = level, y = p_win)) +\n     geom_line() +\n     scale_x_continuous(breaks = 1:15) +\n     scale_y_continuous(label = scales::percent) + \n     geom_point() +\n     geom_hline(yintercept = 0.1, linetype = 'dashed')","metadata":{"trusted":true,"dc":{"key":"38"},"tags":["sample_code"]}},{"cell_type":"markdown","source":"## 7. Computing uncertainty\n<p><img src=\"https://assets.datacamp.com/production/project_139/img/mr_toffee.jpeg\" style=\"height:350px; float:right\"> </p>\n<p>As Data Scientists we should always report some measure of the uncertainty of any provided numbers. Maybe tomorrow, another sample will give us slightly different values for the difficulties? Here we will simply use the <a href=\"https://en.wikipedia.org/wiki/Standard_error\"><em>Standard error</em></a> as a measure of uncertainty:</p>\n<p><img src=\"https://assets.datacamp.com/production/project_139/img/latex2.png\" style=\"width:115px\"></p>\n<!-- $$\n\\sigma_{error} \\approx \\frac{\\sigma_{sample}}{\\sqrt{n}}\n$$ -->\n<p>Here <em>n</em> is the number of datapoints and <em>σ<sub>sample</sub></em> is the sample standard deviation. For a Bernoulli process, the sample standard deviation is: </p>\n<p><img src=\"https://assets.datacamp.com/production/project_139/img/latex3.png\" style=\"width:195px\"></p>\n<!-- $$\n\\sigma_{sample} = \\sqrt{p_{win} (1 - p_{win})} \n$$ -->\n<p>Therefore, we can calculate the standard error like this:</p>\n<p><img src=\"https://assets.datacamp.com/production/project_139/img/latex4.png\" style=\"width:195px\"></p>\n<!-- $$\n\\sigma_{error} \\approx \\sqrt{\\frac{p_{win}(1 - p_{win})}{n}}\n$$ -->\n<p>We already have all we need in the <code>difficulty</code> data frame! Every level has been played <em>n</em> number of times and we have their difficulty <em>p<sub>win</sub></em>. Now, let's calculate the standard error for each level.</p>","metadata":{"deletable":false,"dc":{"key":"45"},"tags":["context"],"run_control":{"frozen":true},"editable":false}},{"outputs":[],"execution_count":186,"cell_type":"code","source":"# Computing the standard error of p_win for each level\ndifficulty <- difficulty %>%\n    mutate(error = sqrt(p_win * (1 - p_win) / attempts))","metadata":{"trusted":true,"dc":{"key":"45"},"tags":["sample_code"]}},{"cell_type":"markdown","source":"## 8. Showing uncertainty\n<p>Now that we have a measure of uncertainty for each levels' difficulty estimate let's use <em>error bars</em> to show this uncertainty in the plot. We will set the length of the error bars to one standard error. The upper limit and the lower limit of each error bar should then be <em>p<sub>win</sub></em> + <em>σ<sub>error</sub></em> and <em>p<sub>win</sub></em> - <em>σ<sub>error</sub></em>, respectively.</p>","metadata":{"deletable":false,"dc":{"key":"52"},"tags":["context"],"run_control":{"frozen":true},"editable":false}},{"outputs":[{"data":{},"metadata":{},"output_type":"display_data"},{"data":{"text/plain":"plot without title","image/png":"iVBORw0KGgoAAAANSUhEUgAAAlgAAAHgCAMAAABOyeNrAAADAFBMVEUAAAABAQECAgIDAwME\nBAQFBQUGBgYHBwcICAgJCQkKCgoLCwsMDAwNDQ0ODg4PDw8QEBARERESEhITExMUFBQVFRUW\nFhYXFxcYGBgZGRkaGhobGxscHBwdHR0eHh4fHx8gICAhISEiIiIjIyMkJCQlJSUmJiYnJyco\nKCgpKSkqKiorKyssLCwtLS0uLi4vLy8wMDAxMTEyMjIzMzM0NDQ1NTU2NjY3Nzc4ODg5OTk6\nOjo7Ozs8PDw9PT0+Pj4/Pz9AQEBBQUFCQkJDQ0NERERFRUVGRkZHR0dISEhJSUlKSkpLS0tM\nTExNTU1OTk5PT09QUFBRUVFSUlJTU1NUVFRVVVVWVlZXV1dYWFhZWVlaWlpbW1tcXFxdXV1e\nXl5fX19gYGBhYWFiYmJjY2NkZGRlZWVmZmZnZ2doaGhpaWlqampra2tsbGxtbW1ubm5vb29w\ncHBxcXFycnJzc3N0dHR1dXV2dnZ3d3d4eHh5eXl6enp7e3t8fHx9fX1+fn5/f3+AgICBgYGC\ngoKDg4OEhISFhYWGhoaHh4eIiIiJiYmKioqLi4uMjIyNjY2Ojo6Pj4+QkJCRkZGSkpKTk5OU\nlJSVlZWWlpaXl5eYmJiZmZmampqbm5ucnJydnZ2enp6fn5+goKChoaGioqKjo6OkpKSlpaWm\npqanp6eoqKipqamqqqqrq6usrKytra2urq6vr6+wsLCxsbGysrKzs7O0tLS1tbW2tra3t7e4\nuLi5ubm6urq7u7u8vLy9vb2+vr6/v7/AwMDBwcHCwsLDw8PExMTFxcXGxsbHx8fIyMjJycnK\nysrLy8vMzMzNzc3Ozs7Pz8/Q0NDR0dHS0tLT09PU1NTV1dXW1tbX19fY2NjZ2dna2trb29vc\n3Nzd3d3e3t7f39/g4ODh4eHi4uLj4+Pk5OTl5eXm5ubn5+fo6Ojp6enq6urr6+vs7Ozt7e3u\n7u7v7+/w8PDx8fHy8vLz8/P09PT19fX29vb39/f4+Pj5+fn6+vr7+/v8/Pz9/f3+/v7////i\nsF19AAAACXBIWXMAABJ0AAASdAHeZh94AAAgAElEQVR4nO2dB3wUxRfHXyq9I9hQUCygCJo/\ndkUUOxdKDAhCEDWIgBQRQRAQpIkKKIgUAyLFgFIEBOlVehVFiphQAknWQg8hZf+3M7O7M5fb\nvb2WZJP3+3y4u7fDvrx5+Wb33e7sDMgoVBAEBR0AqmgKwUIFRQgWKihCsFBBEYKFCooQLFRQ\nhGChgiIECxUUBQ+sfxVdvvAvr/NXBPNizkXBzjgvmJk5gvlvlmCdzRGdXbgsmJdyXJydFX25\nOMsU48xxceYSZ46LMzHOnKuiM5c4PXX6PxPfhbfT7DedD2BJii6fl3idvSKYF+QLgp1xVjCv\nyn8Ldo5g/SuLzs5fEsxL8jnR2b+CmS06++eqGKd8WXTmEqfs4kywJDlLdOYSp2unXeI07fQ/\nrp12idO7TrvE6WWnxTjZbxrBQrAQLFUIFoKFYHHOECwES40TwUKwVCFYCJYqBEtCsBAsLk4E\nC8HSnCFYCJaaFgQLwUKwdCFYCJYqBAvBUoVgSQiWFjuChWAhWJwzBAvBUtOCYCFYWuwIFoLl\nI1g/VjTWPAQLwfIVrJ9u5lQVqvDmAgQLwfIVLMGcBOPE2BEsBAvB4pwJFoKFYGlCsIoSWKe7\nQacUIXYEC8HyH6yttwNA7c187AgWguU3WKl3g6I6p7nYESwEy2+wlgPVj1zsCBaC5TdYMxlY\nX3OxI1gIlt9gbWJgreViR7AQLL/Bkl4kXD2TzsWOYCFY/oN1NDYEIGIXHzuChWD5D5YkjYEm\n0J+PHcFCsAIB1iQYVaFyMhc7glWcwMpd/FbLjhOVT8f7x8TNztEaNPPPHq1GXXK+b+mS7SVY\n43rAR1zsCFZxAmtSy4R1i8Y6P5xr32f7wpYz1e2amds58UL/abKcFb/L4xHr9FFOY2DEzlLX\n/KaapxGs4gTWQccW9ikx5qwsz4y55Gr+7bgkr+shy/MH8/vxP06L/coPYKzZCFZxAuvzLs5j\nEvnUZ4jzJdmxnTVopgLW+h7y2bYnPIO1phGnxk0aN3owtMRjzFyOYBUnsLqMnRzb/INTzk9t\nEpwvWdHzWYNm5nb+4eIHCfKEScJ+/I/TYncz5j0OxmuxI1jFCKy2sd23boqPz5Ll6ETFjp3B\nGnTTWbyPuJT8ynl1l0XDhw8fm6Eo62oGr8xswbwqO5sPht96kdnZmUJzjiyYGbmCdUV2cZYl\nmFmyi7Mroi8XZzlinLKLM7Eb2bKLMzFO2cWZm07zzopGp+n/vqRh4xmsNs3SZPmoY51K0ksi\nWJr5wWJ5Vlz8RuXjgKioqCYeHatqB3Mt/19U4ZZ+VcAzWPGdlNfYb41PhUTbOmdvj0v7LSbd\n+fmfU6dOnaaTg4tzhZ8XZxa/KF9yvm4Lvfsfal8RZynPksUpz8Vp38/KLs7EWcozZHGK+Sxx\nlvIc0dl/4qzl5+UMwb58STAz5XOCnS1Y/8ouztx1WtcVlzi967RLnN51Wozb206LcdLf9D9e\ngDUknoA1i1XrSWLxrprZb+6Up06Q5R4b1P34M692Gnf7XGFTmMVO41hjFaMaa1n0aVn+w7GZ\nXV+YIV5uUM2Fg2R56ngnWOu9B2tdyH0sdgSrGIGV2emtdas6ds+R5XPtem+Z30K5QLqq2Sne\ndH5ue1yWt8adOdAyzXuwpCYwn8aOYBUjsOT0YbGtRv2tfEruHxM3S7mHs8JxkjdleeJXyus3\nbTuu1Xbjf5wWu3uwlsOjNHYEqziB5aP4H6fFbjB3w6OwlMSOYCFYAQVrPjQhsSNYCFZAwZLu\nh1USgkXiRLACCdZsaCohWCROBCuQYEn3hGxEsEicCFZAwfoaYhEsEieCFVCw0u4M245gSQhW\noMGSxkN7BEtCsAIO1pmbIvYiWAhWwMGSPoFOCBaCFXiwUq4rkYRgIVgBB0v6CN5FsBCswIN1\nomq5ZKEZwZIQrACAJQ2A98W0IFgIViDA+qtCpSQhLQgWghUIsKR+MFhIC4KFYAUErJQy15zk\n04JgIVgBASujG4zk04JgIViBAetwyRu4id8RLAnBCgxYZzvya1UgWBKCFSCw9kbWPKOnBcFC\nsAIElvQyTNLTgmAhWIECa0fY7WlaWhAsBCtQYEnNYYaWFgQLwQoYWJtC66kzvyNYEoIVMLCk\n52CemhYEC8EKHFgroKGaFgQLwQocWNITsJilBcFCsAII1o/QmKUFwUKwAgiW9AAso2lBsBCs\nQIKVCM/TtCBYCFYgwZIahGwgaUGwEKyAgjUdWpC0IFgIVkDBSq8TtlVCsIgQrACCJX0FbSQE\niwjBCiRYqbdE7EGwiBCsgID1Tn2qGlC1fv37oupzehzBQrB8BivWeNG5ygiWD2C14/82xb/U\n2OIElvZxJHSVGkGK0IxgeQ/Wg8Z/qfWLJVinqpc+hGBJgT0V1qouOiuOYEmDoDeCJSFYAQfr\neOXyjyBYCFbAwZJ6QCQ03843I1h+glWzmuisWIKVcpdSYJbZxjUjWH6Bte7REHhoNe+sWII1\njH51eYprRrD8AWtPBSWfZblzQPEEK5qCVY5rRrD8AasNTWgLzlmxBCtGvSyqC8HyB6wGNKF3\ncM6KJVjjaR5e4poRLH/AepQmtKG+pXiClf4sORP+wTUjWP6ANZqC9RHnrFiCJaWNvwbKldjH\nbUGw/AErvZnC1Qtp+pZiCpYkNYJR0I6zESz/rmO9B/A/wVnxBev47WGbdRvB8g+skQDXCc6K\nL1gpCfCibiNY/oHVHULgAO+sGIH1xy5OD8CWnfVgGrP2IFh+gtUSSsJM3lkxAgsH+gUYrK8G\n6qrhBOsx3RxfnMD6PI7TG52cL9fDk9R6C8HCgX4+gyWmRcnxhtA6qcxGsLwHa2GCpqlht86t\nWFa3f7ApWNmKcnOyeeXkiqYsNrv871zioy1MY7YstGbLLs5EM9fVt8vOLs5cA3Ox3QXGOfMm\nMEudDpRv3kiCGDkajhk1+9lp2o2r+QAWz7H2R+H9EUvaE3kdW64Cj1h+Fe/LoEdOP5jGObPn\nEYv/cVrsPoAlxcNQaiNYfoE1BT7JmQvdOWfFHKzD5SoeJTaC5RdYg2FuzmF4nHNWzMGS+kJP\n8o5g+QXWG7AlR6pRPl3bUOzBSq5Wcr/yjmD5BdbzcDJHigZ9CGmxB0saBR2UNwTLL7Duibia\nIw3kVv5AsE7XCvtFQrAk/8CqcpOz0wugs+6s2IPl/ELjkBAsyS+wToU85Oz0sdAHdWcIVnp9\nZb5bBMsfsLZBrNLpW0upNzIQLKcWwUMIluQXWPOhp9LpGNikOUOwlFUFEhEsv8D6AkYrnf4I\nxmvOECxJWh9aJw3B8gesvjBH6fRSeENzhmA51QImIlj+gNUONiidPhEepTlDsJzaHVlD7DeC\nJXkFVmP4k3S6TonTqjMES9HrMFZoRbAkr8C6vQzt9MuwVnWGYCk6VLbqX3wrgiV5BVbZO2in\nR8FnqjMEi+hd6M2bCJbkDVhHoTHt9AqIU50hWETJ1Uv/zpkIluQNWOuhPe10SmQ91RmCRTUO\nXuMsBEvyBqzZ0I91+p4INiIXwWK6UjOCmzYMwZK8AetjGM86HQc/M2cIFlXOV9BctxAsyRuw\nesAC1ukxMJI5Q7CoctLvCVmuWQiW5A1YL8F21ul18DJzhmBR5Ujz4GHNQrAkb8B6MOQk6/SZ\nkncyZwgWlTMtj8M81UKwJG/AqlFV6/T/QpOoMwSLypmWVSF3qTOHIViSF2ClRdbXOv0GLKHO\nECwqJS3RMJlZCJbkBVgH4AWt0+PZg5oIFpOSlu0RN7F1UBAsyQuwlkO81unNEEOdIVhUJC2v\nql+WESzJC7AS4EOt02llb6HOECwqkpY/ylah96IRLMkLsIbAVL3TD4X8SZwhWFQ0Le9AH/KO\nYElegNVJeRpF7fRbMJ84Q7CoaFqSqpY5qLwjWJIXYDWF/XqnJ8MHxBmCRcXS8hEdtY1gSV6A\n1SA8Ve/0dvKYJoKliqUl5eaIHRKCRZ1ZBeuaGpLe6fRKNYgzBItKzfEEaCkhWNSZRbBSQh6Q\nuE43AmUpGQSLSU1LWr2Q1QgWdWYRrJ3kb1HrdA9IlBAsTVqOv4PGCBZ1ZhGshWQmP63T06Gf\nhGBpyjlTkSkcylR0UW8Ey6TTE2CUxHV6DzwnIViaclLrM90GpevXhUr1OQ1DsEw6/T5ZkkLv\ndNVqEoKlictxU/h6H7QSWhEsk07HwTqJ73QT+BXB0sTleFv4zTsRLOtgPQWHJb7T78K3CJYm\nPsftoT+CZR2sO0uRODVns+AdBEsTn+MDJSKg/DvHuS1+gnW4O6eefXvz5jLbg1XuNhKn5ux3\neBLB0sTneDFZZ+gxbiFaP8HaYbyaEYy0O1jH4AkSp+7sukrpCJYqPsd30l/5V/oWP8FKWc1p\nHLTnzT/sDtZGeIXEqTt7AXYjWKq4HB9nx5I39E2BrLGWwruiM5uDlUiHGnGd7g8JCJYqLscp\noRSsrvomBMu405/BOBKn7mwevI1gqeJz/AQFa6G+JYBgHWoP968XnNkcrF7wPYlTd3Yk5DEE\nSxWf491VFK7CggLW+opO15Gf8s5sDlYr2Eri5JzdVD4NwWIScnz0LajVN7zSVm1DwMBKr0MO\nhiV3cc5sDtYjQC7M8J1uBlsRLCYxx8otnU+g5iHVDhhYO9kXg9GcM5uDVbMSjZNzNhi+QrCY\n8oIldYOGbLKnwIG1kYE1hHNmb7DSI++mcXLOFsKbCBZTjnSU00ZofvToEQc8eZiYJwMG1qly\nFKwfOWf2But3MkpG7PRfoQ8gWEw5Z0yujncNXPE+ljhsxjuzN1gr2PU+odO1S6UhWFQ5qY14\nNXlSeX24FNRW3j8L4OWGr0sBdDnJbbA5WNNhEI2TdxYLmxAsKjHH6tDkXVXDvlXeA3mBtDLo\n0yURZ/YGaxibSUXo9DAYj2BRuQdL+qlE6dVSQMFKDhFKd9uD1YXNWyR0+id4HcGiMgBLSgit\nviegYK11llhtBGf2BssBe2mcvLMT4fcVOFjn2jhOK+/H+8fEzc7RNmvmnz1ajbrkfN/SJbsg\nwJIGwh1H/QVrN/dgRmnloj5nj7U5WFFhdPkcsdN1SogZKwCwJrQnYJ1r32f7wpYzNdxUM7dz\n4oX+02Q5K35XgRyxlHV2Hk7xE6w9N+uqCNUjQjj7S5uDVf16FqfgrC3sEOPMd7COtlpMwEqM\nOSvLM2Musc2a+bfjkryuhyzPH8zvxf84LfYggZX6HLQ8F7hTYSs42AJ2885sDVZKaEMWp+Ds\nY5goxpnfYOX2SdxMwOozxPmS7NjOtmumAtb6HvLZticKCiwpuR68HziwosKuDIBZvDNbg7Vb\nnR5f7PRKYaGPAgBrzeuZFKw2Cc6XrOj5bLtm5nb+4eIHCfKESeoeKQcPHjz8n6Irl/7jdSFT\nMC/JlwU784JgZsmC+V+OYJ2TeWeHbgyZKjRnyBdFZ+dEXy7OsnirUk15DgzmnYndyJTPmwT2\nn5wtmJ467RKnfNbE9zn5qujsimC67/RS6M585fKNaSXqi3HKLs48dFqMk/6m//UCrMtxm2QK\nVnSiYsfOYA266SzeR1xKfuW8usuAqKioJp6JDah+qxixKkCuJHhOPgjtAuSt4DUTvnC7PSr8\ncqB/lP7lzTNYCf1kAayXRLA084PF8qy4+I3Kx0XDhw8fm6Eo62oGr8xswbwqi83ZmYKZIwtm\nRq5gXZFFZ6siy+/kzCzZxdkV0ZeLsxzOWAdd5YwS9/DOXOKUXZyJcco5ghnMTl/NEkz3nR4C\n85gv0Vk8bBDilF2cedVp+r8vadh4BOtMi/0XL65xHMswPhUSbeucvT0u7beYdHVH/syrncaD\nVWM5df4rqMEtO+dHjTUeRsuX60ae4ZzZusZ6FdawOEVn49R5glmc+Vtj7XNQDWHVepJYvKtm\n9ps75akTZLnHhgID61IvqK8/aOgHWL1ggXw5BvQxhDYH62lgg9ZcOr0BWgtx5i9YF351ao5j\nXTK7vjBDvNygmgsHyfLU8U6w1hccWOmt4GntMOMHWNGwX748AKbrW+wNVt0S6SxO0Vl66TuE\nOAvglg6tsc61671lfgvlAumqZqd40/m57XFZ3hp35kDLtIIDSzr9uLYsrT9g3RX5j3x5JvTV\nt9gbrAq3qHG6OHuQLarD4iwwsOTk/jFxs5R7OCscJ3lTlid+pbx+07bjWm0f/sdpsQcXLOlY\nHfhITYvvY95L3+nM8U5+QJatwUqGx9U4XZx1g8V8nHgTmsjtjH67rwllZzDfwdoPLzhznMaf\nJ2wN1mZ1fcI8nZ4mjOFAsKjcTxW5qnTJZTQtPoO1AN5WctwgPEXbZGuw5mpP37p2+gC04ONE\nsIgM5iCdHVaZLBztO1ifwFglxy/DRm2TrcEaA2PVOF2cZZarxceJYBHlBSuRjFi+FUo97Hxr\n3OQJfhzzHutgvQWLlRx/CFO0TbYGq7c2Gta101kPhxzh4kSwiPKCNdbkWYuN1sF6Fn5Xcpyo\nzE3GZGuwXoZf1DhdweoCP3BxIlhEhtNxp70IzdKl/nQhIt2ZZbBql01XcrxPWTqSydZgPQbq\nRYU8YE2BAVycCBaR8TzvJ/8HvXwH60xkfZpj7fKPzcG6paIWpytYO6EpFyeCRWSygMChWtDr\nQXj5oODMKlg7oCXNccNQ7QaRncFKL1lXi9MVrPTKN3JxIlhEZitT/KKMWofyq3hnVsH6zvnt\nnOS4vXrv1t5g/QHPaHG6giU9QRbVYXEiWERmYO0tQSr22twUpZbBGgYTaY6HwwR1m53BWg0d\ntTjzgNUTvtPjRLCIzMAax74LbuacWQXrNVhBc7wAuqnb7AzWDL1AzwvWdO6OaDDB2tQ6qiZ5\nLsXmYI1kYK3mnFkF6wk4SnN8EJqo2+wM1kj9mYm8YO3Vz5PBBCsByjV8isjmYC2jXJU+wTmz\nClaNKmqOq9RQt9kZrK76nea8YEnVqulxBg+s2o7zefiwJVhSLAHrE96ZRbBOht6v5viRkGNs\no53BagZ7tDjzgvW0slY0izN4YEVsDhxXBQtWyoBKED6Fb7YK1kbl4Xqa49dhOdtoZ7Aahmo3\n092A1QdmaHEGD6waa4oKWMpE5iHJgjOLYE1Xal2a49Ha3Vs7g3XdtXqcecGaDb20OIMH1oDW\nRQks57c73plFsD5QhiTTHC+BN9lGG4N1JixKjzMvWAeVxWpZnMEDa2mtp6atXKXIlmAl8sMZ\nagHc4cvohrawQc3xUboCjWRrsPZAtB5nXrCkGyqlq3EGDyx9MIAtwQrI6IYHQk5oOb62Otto\nY7CWwlt6nG7AehHUaceDCNZMTbYEK4Wf+zblGDzGmalWwaqq3D1jOX6CLB8p2RqsSTBMj9MN\nWAPgazVOvPJO5HEV+2uv5W2LYB0jTx6wHHdWLwHZGKyB3GNs7sCap91fQLCoPILVWD3eUGfW\nwFpJ7qyxHI9TFxGwMVivw0o9TjdgHQl5VI0zOGAtXJjj/KeqKIDVVXi4ySJYX5Hnx1iOf4bX\nmTP7gvUs6KOH3IEl1SzLbtUHCSyADLsX72Ja5PEwindmDaw+MEfScpwc8jBzZl+w7o5M10y3\nYDWHLSzO4IC1ZEmO85+qogDWGn28iGQZrBhQnvFRc1yjMnNmX7Aq1eTidAfWh+pNaqyxqDyC\ndSb0Qd6ZNbAahCvzwKo5fhro/DX2BesEPMLF6Q6sRdCJxYlgEXkE69xNFTnbIljlbyVxshx3\nZ0+x2BesLfyMMm7BSlLuupM4gwdWna7z/ylCYD0Hv3LOLIF1kI5PUnP8JQynzmwL1vf6vUAD\nsKTbStEpeoII1v1hEHpv758uFBGwevLrllgDawl0JnGyHK+B9tSZbcEaB59ycboFq5VyE0sK\n7qnw3OJe9UMg/KEBRQKsSfycF9bAYleu1ByfCqMTWdsXrD6QyMXpFqwR8DmNM8g11t8z6xaN\nyw3nNmjTrEhWwepOn0bUcnxLOfJl3b5gteVmoDAAaxn79hxUsLK2DGtcAq5tWyTASolowDmz\nBFZT2EfiVHP8Il2Fxr5gNYK/uDjdgnUi/F4aZ/DAGtO0HFRqPv73AGBVGMCS7iilP/9lDaw6\nJckeWo7foWcS+4JVuxwfp1uwpLqRZIxpMIfNhLbbmZOHEPuC1YxbLcYSWGnsqWEtx1NgMHFm\nW7BK1eHjdA/WK0Ce7A0iWM+UhmqtJ/9ZZMDqpw/otgbWHnDQONUcb6Rlmm3BOqo/wiYZgvUJ\nfeokmDVW5obBj0XCTa9+WzTA+gbe151ZAet76EnjVHN8OrI+cWZXsNZDBz5O92CtgldInEH+\nVngpsU4R+VYobeemQrQE1ij4gsap5fhOUqbZFqzZ0J+P0z1YKZF3kTiDCdbFn9+LCoXQ+4oG\nWGlchWEJrE7wE41Ty3Fz2CnZGKyP9fknJEOwpAZhyrw6QQRr0KMRAHW7Lfg3DyX2BEuqH6E9\nU2cJrKfYGg56jvuBspK5bcHqDov4OA3A6gjKhMDB/FZ4yxtzUgMBVWEBi5ug1hJYtcqzOLUc\nTyfnEtuCFUMOuFqcBmB9DiOkoIKVzH3OPeDnmmP8j1OV32ANhsmaMwtgpYTfx+LUcrwNWko2\nBuuBkBTONAJrA7SS8m3YTAZstT9Yifq9fStgbYFYFqeW41RyZcu2YN1YjTeNwEotfbuEYKmy\nAtY+eF5zZgGsWepsUVyO60Weti9YGexujRqnAVhSw9C/ECxVVsCSKmgDc62ANUSd2p3Lcawy\nmbVdwfqLn7zWBKxOSo2PYFFZAusBbYJaK2B1UGdq43L8ASTYF6wN2uwTNE4jsCbChwiWKktg\nvao9VWcFrEfVoQBcjmdDH/uCNRuGCnEagbVFWecewaKyBNZIdindGljXqXM1cDkmtw/tCtZI\n5XDLxWkEVnr5mgiWKktgLdKmxLAA1vGQh9Q49Rynl73NvmB1hZ+FOI3Akh4JOYxgMVkC67A2\n/ZMFsNZBOzVOLsf3hafYFqxoOCDEaQhWN5iHYDFZAkuqps4MYgGsr2GQGieX47aw3rZg3RuR\nxpvGYE2FAcEFK2PlpEkrM5RPReLKuyQ1UmcGsQBWf234Fp/jofCVbcG65mYxTkOwdsGLQQXr\nmyrKxA1VAjE9ViEB6011ZhALYL2sLTjA53ge9LQrWKfUuSfUOA3BSq98QzDBmgMNJy5fNLwG\nzC0yYI2Dj5kzz2A1DD2lxsnl+Fd4zq5gbSP3ALk4DcGSGtNFGgVngQPr7ta5ytuF+vWKDFg/\nw2vMmWewKt+kxcnnuNLNdgVrPv8YtGQKVi+YE0SwIrfR9y8jiwxYyeolBM9gHTWYQPiB0OM2\nBesL/jFoyRSsb6BPEMG6jn0RnHBTkQFLUmcG8QzWcnhDi5PP8auw0qZg9eUfg5ZMwdoPTwcR\nrG4tyanw3N2DAwDWRUVXr1zklZElmFdksTkrQzCzZcG8mCtYl2QXZ1cF86pMnb0AR6mzy6Iv\nF2fZFy9OgU+0OGXO2WcwKdMlTtnFmRinnCOYeTqdKToLYKczZcHZq7BD9OXijI/z2qpCpxVn\n5p0WO8l+0/q0HwJYC6+7Z8yiuYOuvXd5AOZ6v6DoasYFXpezBNMJlmBfvSyY2bJgXsgVLGeO\nBTsjUzAzZeqsNyykzi4JzTmis4vZFy68Bwu0OGXO2U/QI9MlTtnFmRinnC2YLp3O8KfTF611\nmqkJpIhx5u20pufgiOzizKtO09+0vhaTwTzvAZgukj9AqiqAU+FXbGYQz6fCZtqM5+Kp8DA8\nadNT4e1lzTvNx/kezMqPed4DMNc7/+NUFQBY65VFlyQrYNWLTNXiFHJc9XqbglW2jnWw5kBv\nnNGPyCJYKRF0EKVHsNLL3q7HKeT4MThtS7COwjPWwToEjREsIotgqTODeATrV30YswtY8bDG\nlmCth9etgyXdWDEXwVJkFaxm9Akoj2At0peAdgHrMxhvS7Bmw2AvwGoKfyJYiqyC1Zc8cuoZ\nrM9gjB6nANZP0MWWYH0MX3sAa+/NuipCtVqcefMEBIvKCCz6yKlnsLpyDw2LYB0LaWRLsHrA\nCg9g7a6oqwxACc6sOAbBojICaxudGcQjWM9xg+JcLkJfX82WYL0EB704FR4JgZYn+A0IFpUR\nWKklycwgHsG6rbS+NogLWE9CkhinPcB6KOScdbAOPwgANyzjnSFYREZgSfeQmUE8gZUaWY+L\nUwSrCywT/rdNwKpRxUOn+ThfJBfFrz3KOUOwiAzBak1mBvEE1k7lCSgtThEs11EC9gArLbK+\ndbAOhtDbLdysRwgWlSFYH5Lnmz2BNRfe4eIUwVqlDupS47QFWAfgeetgbWD38QZyzhAsIkOw\nEgkynsAaAV9ycYpgnQgVh/jaA6zlEG8drD/DKVj6cqwIFpMhWPvgBckzWG/wj+C5Dk2qVVEw\n7QFWAnzoRY3ViXB1FzfrEYJFZQiWVKGW5BmsxnCEi9MFrBfE5/PsAdYQmOoFWKdeCwW4bxe3\nBcGiMgbrfmVmEE9gqWte0jhdwHqXX+7JLmB1gmWewEo7ymkawGjOTEGwqIzB6qDMDOIhxxfY\nckwsThewpomTa9gDrKaw3xNYO8FYIxEsKmOwyMwgHnK8j1/QKQ9Y26CtEKctwGoQnuoJrIPR\nnJq3CKnMmXMRLCpjsBZCF49gfS9MiO4K1r/hUUKctgDrmhs9ddolTvn2UqmcjWBRGYNFZgbx\nkOPhwoQ/eR5Yub1MOmfaAqyUkAe8Betl2MQ7Q7CIjMGSql3nEayOsJ6P0xWsZrCHj9MOYO2E\nlt6CJS43gGBRmYDVCI54yvFjIcc5Mw9Y78NsPk47gLUQunsL1kqI550hWEQmYL0JSzzl+Nrr\nhThdwfqWv9dhD7AmwChvwUpXF7SnzhAsIhOwxsJoDzk+Do8JcbqCtVOYXsMWYL0PM70F63Jt\nvnpHsKhMwFoOr3nI8Vp4VYjTFaz/+EE19gArDtZ5DVaMNpGThGCpMgFLmRnEPMdTxCugeacx\nqFOC+1u2BVhPwWGvwRqKw8Uvrc4AACAASURBVGa8AkuqUdFDjvvCLCHOPGC1hG1cnHYA685S\nHr8K5wFrMV+9I1hUZmA9AwfMcxwLW4U484DVnx9QYguwytX2HqxkvnpHsKjMwOoJ88xzfG84\nv0qWG7C+hX5cnDYA6y94wnuwJL56R7CozMD6Coaa57jirWKcecDawY9ctgNYG5Xbm16DxVfv\nCBaVGVjroa1pjv/gHq8nceYBK630nVycNgDrO2WpFq/B4qt3BIvKDKyU8PtMc7wUuotx5p0f\ng1sF2BZgfQqf+wAWX70jWFRmYEm3l75iluMvtCV3WJx5weJWAbYFWL3gex/A4qt3BIvKFKxo\nOGSW456wXIwzL1iDYaoepw3AaqV8z/UaLL56R7CoTMF6D+ab5bgp/CnGmRes76C3HqcNwHoE\nPI/HdgMWV70jWFSmYE2HIWY5rlNS9OUGrL3woh6nDcC6WRnD7z1YXPWOYFGZgrUNWpvkOL1U\n3atinHnBSi9/ix5n4Qcrndzc9B4srnpHsKhMwUotebdJjvdCU49gSQ3DTmpxFn6wfofnJF/A\n4qp3BIvKFCzpnohUoVnI8Q/Q0zNY7WCtFmfhB2slvC75AhZXvSNYVOZgtYYtYlp4Z6PhC89g\nDdOfwbcBWNPJyEQfwNKrdwSLyhysQeLqyGKOO8NPnsH6Qb+IagOwhsFkySewhmp/PwgWlTlY\n38G7Ylp4Z0/DIc9g/Q5Pa3EWfrDegqWST2D9CJ1UZwgWkTlY/NUCkhbe2S3l//EMllS5hhZn\n4QfLAXsln8DSq3cEi8ocrPSKtwjNfI7PRNxrBayHQ/5S4yz8YEWFnZZ8Akuv3hEsKnOwpIdC\n+ee7hBxvgxgrYL2mTXRkA7Cqk6eOfAFLq94RLCoPYMXDKiEtnLPZ0McKWB/DODXOQg9WSiiZ\n48QXsLTqHcGi8gDWWBgvpIVzNhQmWQFrMXRW4yz0YO2m4xJ9AUur3hEsKg9grYSuQlo4Z6/C\nKitgHdGW9i38YC2mvfUFLK16R7CoPIB1Gp4U0sI5exyOWQFLqn6tGmehB2sijCDOfABLq94R\nLCoPYF295johLZyzG66RLIHVSJ1NsvCDNQBmEGe+gKVW7wgWlSewGvGTjPI5Phn6oDWwlCkg\naJyFHqyOsJo48wUstXpHsKg8gdVZxYKmRXe2AV6xBpYyBQSNs9CD9TQcIs58AUut3hEsKk9g\njVOxoGnRnU2DgdbAWk5GDEh2AKtuCTJRnE9gqdU7gkXlCayVKhY0LbqzATDdGlhJIY+wOAs9\nWBXofQafwFKrdwSLyhNYJ0P45SW4HCvP31gCS7qRTdld6MFKhsepM5/AYtU7gkXlCax/a1Ti\n06I7axh60iJYTeAgjbOwg7WZzQHtG1iseg82WNtGdIztuZ58PN4/Jm52jtaimX/2aDXqkvN9\nS5fsQgzWM/AblxbdWZUakkWw3ob5NM7CDtZcNkjIN7BY9R5ssLoNWrzmI8dS56dz7ftsX9hy\nptqgmbmdEy/0nybLWfG7CvMRq4fyCKeWFs3ZUWX2DGtgTaCXHQs/WGNgLHXmE1iseg82WKnK\nS99450tizFlZnhlziTVo5t+OS/K6HrI8fzC/H//jtNgLEqyJ8BGXFs3Zz0pRbw2s1RBH4yzs\nYPVmS7T4Bhar3vOlxpr+kvOlzxDnS7JjO9ummQpY63vIZ9ueKNRgreOXl9BzPBGGWwXrJFsX\npdCD9TK7eO4jWLR6zxew+vdyvrRJcL5kRc9n2zQzt/MPFz9IkCdMEnbhf5wWe0GClRJ+H5cW\nzdm7kGgVLKlWOXJ5qNCD9RhbxNpHsGj1nh9gbXZsdr5GJyqfY2ewjbrpLN5HXEp+5bz637/r\n27fv0CuKsrOu8LqaI5hZsticfVUwc2TBvJIrWJmyi7Ns0Zfs4izzyh1lLuu+NGet4HenM9HX\nVdnFGYszGv6kvjNNArviElg+djqLdbp2JebMJU4XZ6Kpd3oVdLuS53eXp9OiSf93hndgJbX+\nXCfpJREszfxgsTwrLn6j8nFAVFRUE0vE5qti4ZibrfdFZln2MACWBy6c4Cm31D1+7X8+9FEf\n99SvClgBK63DYLKD0amQaFvn7O1xab/FpDs/Xz537tz5vxVlXPib17krgnlBvijYV84J5lX5\nH8HOESznqVB0dlkwL8suzv77+z2YpfvSnJW9TXF2VYxTdnHG4pwCQ0ic8n9Cc7Zg/S1nic48\ndPq8GKeHTmeKzjIE8xLt9CF4hjkT48xxceYSp97p2qXS9E6rcbp2WoyT/aa9Aevsm73oEY5U\n60li8a6a2W/ulKdOkOUeG9Td+DOvdhovyBpLmg4D9ApBdfYbPCtZrrE20guPAa6xFn7GaeLk\nMZw1wacaazV0pLaPNRat3oNdY13u+eZZ+olcX5ghXm5QzYWDZHnqeCdY6wsvWFshRk+L6uxH\nZc05q2CdjmhA4gwsWK2MV6Os7BNY36h/Qb6CRar3YIM1JHr+ZqdyZPlcu95b5rdQLpCuanaK\nN52f2x6X5a1xZw60TCu8YKWWrKOnRXU2Bj6VLIMl3VEqTQo4WCsSNH0cFQo3v6vb3/oE1gj4\nitq+gkWuvQcbrPYOIuVsmNw/Jm6Wcg9nheMkb8ryxK+U12/adlyr7cf/OC32AgVLqqfPI6rl\nuBsslKyD1Qx2SkG83HDsJuUwVWIZ1+wLWF1hMbV9BSsp9AG8Ca3KAlit9IUetRy/APsl62D1\nhZlSEMHqS0+A/PLUvoDVAnZR21ewpNqlUxEsJgtgDdLnEdVyfEdp5ZqnVbBo/R80sJpSsEpx\nzb6A1TCUHZl9Bkup3hEsKgtgfQfvaGlhzlIj71LerIJF6/+ggfUyBasa1+wLWDdUZ7bPYCnV\nO4JFZQGsvfCClhbmbDdEK29WwUotUVcKIlhzKFhvcM0+gHUmTL135TNYSvWOYFFZACu9gjYz\niJrjedBLebMKlnR35Jlg3ivsQM6E/BTOPoC1h/6xSH6ApVTvCBaVBbCcxYc6M4ia45H0yXvL\nYL2kzAwYYLB619dUDcKgDFyv2Y/5AtZSeIvZPoOljJxBsKisgBVHH7eT9By/AeS7vWWwBsC0\nQn+BdBIMY7bvYDmrdwSLygpYI7SZQdQcN4bDyptlsGYpax8F7VQ4Ano5Oz0CWuibfABroLa2\nou9gOat3BIvKClgLtJlB1BzfXJG8WQZrNziCB1ZqzcjfnJ1OrcfG1ivyAazXYSWzfQfLWb0j\nWFRWwDqszQzCcpwS9j/ybhms9LK3Bw+sqfAK6fTK0Fu0WwQ+gPUse5jIH7Cc1TuCRWUFLKnq\n9WpaqLPN0Jq8WwaLrMUaLLCiQjbRTrfTx2H4ANbdkenM9h0sZ/V+HsEisgTW4+rMICzH38L7\n5N06WG1gQ7DA+hGeYZ0+UrnkbrbRB7Aq11RtP8CKgd0IFpElsDqRWaolLceD4Wvybh2sITAp\nWGA9C4vUTo/RLuV6D9YJeES1/QBrKHyNYBFZAmsMfMLSQp21Z+uYWAdrHvQMElhbQ+tLaqfT\nGsJsutV7sLaw07vkF1g/QlcEi8gSWMvU2yUsxw+H0MdZrIO1H54PEljtYIqkdXpDeI0TZKv3\nYH1PbyYo8gOspNCHESwiS2AlqTODsBxXZ9P8WQdLqlQzOGD9UaLGGUnv9BvsKXnvwRpHhi4S\n+QGWVLu0+NtAsKjcgyWpM4PQHCerExN5Adb9oceDAtY7yoOzeqf/qh65VXn3Hqw+yoOSVP6A\nFUPGNHJxIlhEBmA9zWYGoTlew56Z9wasDrAqGGCdqFwxmcSpdvpLOkmz92C11ZdF9wesoeTM\nzMWJYBEZgNWdzQxCczwFPqStXoA1EsYHA6yRzi8FJE6t04+SOzPeg9UI1KVZ/AKLPmXCxYlg\nERmApc4MQnPcj4w0lrwCawF0CwJYqTUjD9A4tU5vjrg+2RewapfVbH/ASgp9SIwTwSIyAGsd\nvELTQpy1UpfH9AKsw/BUEMBKgDYsTr3T3eBtX8AqrT+L5A9Y0m2lhUVpESwqA7BSwqNoWoiz\nqDB2T84LsKQqNwQBrP+FbGBx6p0+USN8g/dgOcHXbL/AaqWttUrjRLCIDMBy/h2mkbQQZ5XU\nmx/egPVoyJmAg7UEmqhxcp2eBg+mew3WWuig2X6BNVJfq5jEiWARGYHlAHIXjuRY/+P2Bqw3\nYF3AwXoOFqhx8p1uAhO9Bmsm9Ndsv8D6WVtrlcaJYBEZgdUHZpG0KM6WQTxr9QasT+HLQIO1\nLfQubUAC3+kdJa75R/jPFsAaCRM02y+w0pSnVrk4ESwiI7Cm0REpJMfjYSRr9QaspdAt0GDF\nkaXBaZxCp3tDN+E/WwDrbeVWturMH7Au3VaGr94RLJYWA7C20JlBSI57sqk6vQPrGDQOMFh/\nlLz+tBan0OmTN4et5f+zBbBaclfM/QNLrN4RLJYWA7BSS9YlaVGcOWAPa/UGLOm66gEG611u\n2l2XTs+Fe9M40wJY94doo0/9BGuEUL0jWCwtBmBJ9SKVowPJ8V2R6rHeK7AaQ3pAwTpRudwx\nPU6XTkezmbVZnJ7BupF7jto/sJYL1TuCxdJiBBY9wCs5Ti99p9rqFVhvwfqAgjUKunNxunQ6\nqXSlw7rlGazU8Hs5Z36BdUao3hEslhYjsAaSQaNKjvfBi2qrR7B2/qCrC7y9kDN/SPUPrP9q\nRezj4nTt9ABor1uewdoPTTlnfoF14Va+ekewWFqMwJpDBjopOV6gHyk8gvWO8UOlkOwfWDPZ\nwjcsTtdOp9weqs+X5RmsZfAm58w/sGL46h3BYmkxAmsPOU4pOf4ExqmtHsGa113V2zUITc21\nDd1T/APrfljPx5mn0z+G1DmjxekRrKkwlHPmH1hD+eodwWJpMQIrvbwyM4iS47fUie+8qrG+\npoepWlyzX2CtFVdBd9Pp5trlNgtgDYYEzpl/YP3IV+8IFkuLEVhSw9ATNMfccmBegNWVnQC5\nktovsKLhByHOvJ0+UK7872qcHsGKh+WcM//A+ouv3hEslhZDsMjMIEqOa5fTWr0AqxflKiRZ\n3+QPWNtD64lxuun0RxCrxukRrBfhV86Zf2BJtbnqHcFiaTEEi8wM4szxmcj6WqsXYC2jYD3K\nNfsD1qv69JU0TjedPnMXmYFXsgLWPRHcNzl/weKrdwSLpcUQrAXK/TdnjrdDS63VI1ij+Tms\nnAqto2844QdYh0reIHbSbad/CrmD3vPxDFaVm3hnfoLFV+8IFkuLIVhksIwzx98pMxIxFdjl\nhj4wysrqXy/DYBqnJ7DSQvgBxf6CxVfvCBZLiyFYUtUbSI6HqdPsS15eeXfmeDy/9qEfp8JT\n15RLtQLW4cqlyG1Nj2DtgZd4Z36ClcRV7wgWS4sxWI/Bn0qOX4MV2iZvwZJqh23Vbd/BGg3d\nrK1XOFqZl8sCWIvZwz7MmZ9gSdy1dwSLpcUYrHj4SclxIziqbfIWrH8nQivd9hmstNsi9lkD\nKy0KvpMsgDURRvPO/AWLq94RLJYWY7A+g0+UHN9YVW/1GqzU28N+0WyfwfoGWltdYXV1WK1T\nFsDqr04mQp35CxZXvSNYLC3GYCkzg2TnnKRrtVN5DZY0hftO6TNYDWGd5aV7X4V+FsDqABt4\nZ/6CxVXvCBZLizFYSSGPOHO8UX2ST5H3YKXdFar9Cn0Fa4XyFL1VsI5WLbnLM1hPcef3AIDF\nXXtHsFhajMGSalR25phfFtMHsKTptJxW5CtYTZXn/S0vNj7eiaFHsO4oIzjzFyyuekewWFpM\nwHoafs/O+UCbtFryCaz0BiHrmO0jWLvC6qR7AVb6w/CtR7DK3iE48xssvXpHsFhaTMDqDj9k\n53CTsvgEljQTnme2j2C9Ripjy2BJGyNuPOkBrH/pFDWaM7/B0qt3BIulxQSsL2FYds4DISf0\nLb6AJd2nXgjzDawjpa9THnvwBFa6PlS1Kdzf5rVx3NjV7a5g7eOHmwYCLL16R7BYWkzAWguv\nZOdUvZFr9QmsRHia2r6B9R69TeMJrFSTm0ldXMFaonx15Jz5DZZevSNYLC0mYKWER2X/C424\nVp/Akh5kY598AiulWlmyypcnsNL0oap3EJrC2mgb5riCNVFb04U68xssvXpHsFhaTMCSbiuT\ntQ06cht8A+sHeIK8+wTWZ2yNLus11plIepzibtq4gtXfZdSg/2Bp1TuCxdJiBpYDjs7iHhL1\nFSzpIViivPkCVlrtiL3UmWWwktgJ8MbBK9VrAK5gtYNtgjP/wdKqdwSLpcUMrD6waBDM4Tb4\nCNYiOt7PF7BmqsMQrIMl1dCKq3LPDFmtwOUKViP+G0lAwFqkVu8IFkuLGVjTYNjLsJ3b4CNY\n0mNkaKcvYD3Ali7wq3iPPesSZ82qgh0AsLTqHcFiaTEDawu0/V/4aW6Dr2AtA+WGow9grdS+\nO3gs3vWhqvVvioSQinWVT3VvrqJUXGWfHLiam9vhQmQD0Zn/YGnVe2EB69JARR8NYY/EfUbM\nD9kSSXOINXA1BWsdtRIoWIeoNYzl+CNqKs/EONPyNbWUu3ROsH6iFp3W/PxBarGpDs6OGkLM\nU9T8YvhgxdpJre/CrytZZeBA9vTXxoEDBw0fOJDNJHRUiXPUR2w6ZWkk6cZQ9pjMdBrbLprj\nnwcOvBVeGTiTgrWf/vzRFKx0ag1MomB9Sa0tFKwFA+s49xtIJlvLOLeVttFa5uqFQdRkE2ZN\npNZ+as0eMlSxfibGgUH3VXDCFXFbt5k7du3ataLbczWgTKs+u6h6duvW39lpdutwirLbiJHs\nmvAS4nPQT9TaRX/EBApWCgs8hYI19m54y2ntpmAl0ralFKwN1PqagnXY+fHT4IOVzo7WF7OJ\nbqPWamrFUWuonKNYE6n1fHauYu6jVsXs7FzZaZaj5q/Oj07zGWpNVnaTcwdRqyPxmbOCWnfS\nH3GB/fx0at5DrR+p9Sa1+lNrOrWeoNYhapWgVnY1au6gVjNqfUGtkdR6WSbWBmrd7AzMaV1l\nP/94do5iPkCtRGeczk6zJ316Krvl5syl1v3ES24K2zGT/oya1FpPrTbUGkGtzw3OkLz+oP+1\nMbWmUWsAtd6k1hJq1SNxZ//Ndvwvh/xy6lBrOf1tvEatQfS3MYVaT9NuHHB+rBV8sK4kKJo1\ng31/SSTmNyeptZJYCbvoEWsXtZbSI9Yxas1gR6xvqPkXPWItodZuesTaTK1V9IiVRK259Eec\nmzeDmGxOn++/m65Y7EHCNQ8505GQwP5+9yQkTPsuIeFHaiUrcc6bpd5InKnsNvNb9oe/jPic\nfZQesbY6P9eHHj/TI9Zh+vPnsCMWtRJO0iPWAmrtp0es9U/Ba05rPT1i7adtdFXVq5fZjuyI\ntZRa7CnGlfNmKxab63lHwoxZ7zdq9NiDNUs6f6nsYkREuziiJxo1+tTZafaU2o/Kbolz2bRN\nG4nPaazK/I3+iAX0iHWa/fwz9Ig1rw80cVoH6RFrFW3bRI9Yu6m1mB6x/nJ+/C74YBW+Gmvr\nak2zbwW4faZu/+JrjeVkNKR+utc11pHS12qTWHnxrdBkPNbmUY4y7FDDzdQWiBpLrd4LS41V\n+MB6wPh80cB3sKQX4FuvweoPA3VnAQFLUqaioFqnbwoEWGr1jmCxtOQBa3CcKnprBGprGwb4\nAdbG0Drizp7BUu/mUGf+gbUgWtWTtFclHNqWvQEBqyWQQdgIFkuLyeWGBvRXoK/g4PPlBkXR\nMFdo9QzWWH6qIT/BGmdSuG8MCFhD6LV3BIulxQQsdlLkpr7zB6xNoXXThGZPYJ2/PXyPbvsJ\nVtIuXWOebuCYw9kpAQGLXXtHsFha8oDV7GZVlShYFbUNz/sDlvNcIS7A5gmsuXTiZtVZoGos\nycNVYV/BYtU7gsXSkifHT1VUVSFc4Sq8grbhUb/A2h5+yxneNgXr8Ce9boE1vLPCDhar3hEs\nlhazHKeO79D+c352fL/AktqLq87kAWuHPqQqVrniFBqjb/il8INFq3cEi6XFuxz7BdbhiFr8\nISsPWPNNCuxZhR+sITBRQrC0tOQjWNmvwOecmQesI9og9Y8YTgO1LYcLP1i0ekewWFryE6w9\nkTdxYyVMaqzZDCxuntDCDxat3hEslpb8BEvqAJ/pZh6w1jZSpV79b6htWV74waLVO4LF0pKv\nYB0oeYO+gk1Rq7Fo9Y5gsbTkK1jSGzBKM/OAdeYo1e8OqP5KFajU9fejmk7bACxSvSNYLC35\nC9ZvpaqfVE2jGutAA2h4UDp/3sVZ4QdrkXILCsFiaclfsKTOMEw1DcBafwM0P+l+IUw+zkII\nFqneESyWlnwG61CZauoDMu7Bml4qpI8yeM+GYJHqHcFiaclnsKRuoA6TdwvW8NASk2icNgRL\nqd4RLJaW/AbrcNnKSdR0A1bKy1B9JYvThmAp1TuCxdKS32BJPdWZ3PKCdfhhqLtXjdOGYCnV\nO4LF0pLvYP1ZoQIdF5oHrG23QpMkLU4bgqVU7wgWS0u+gyX1gb7k3RWspRUgXh8KaEewlOod\nwWJpyX+wjlUqT54ScwFrXEQkP7eQLcFyVu8IFktL/oMlvQ+9lTcBrNR4qLxIiNOOYDmrdwSL\npaUAwEquUuaQJIKV9DTc+qvwn20JlrN6R7BYWgoALGkgmRSNA2vXHfDEcaPJbZkzO4DlrN4R\nLJaWggDr+DWl/+DBWlYV4k57WmzcDmA5q/eLCBZNS0GA5axFunJgTS4RNtBwqkjNmS3Aagl7\nESyalgIB69R1JQ6oYKX3gbLKiklFAqwhMA3BomkpELCkEdCJgXX8RbhpE3FWFMBaBN0QLJqW\nggEr5foS+wlYyuCrP6izogDWX6GPIFg0LQUDljQaXlfAWncDtGAj/4oEWNKtZbMRLJKWAgLr\n9I1hDz47/Gs2+Io4KxJgtYSDCBZJSwGBdbA8nUxosu6sSIA1GAb+JTpDsKizoILVUJtfhM2r\nV17b8FqRAGttTYCIrvysBAgWcxZUsO7U5hcJoWBFaBtaFwWwjtxAevU+7wzBos7y6YgVRsEq\nXRSOWL1NnodMQrCYs3w6YkXQvJcqCkesV6uoKslwqqRtOYpgMWf5VLzvI7O63as/F23j4h2P\nWIoKCVjSr6/e+1Bffqkk+4J1VJt08ie6jkNrfRrKNASLOcsvsLxYxZ46K7xgccY8ZYWOpie5\nLQgWc4Zg+XUdK+nHGZtEZwgWdYZg+QUWPqWjpgXBQrC02BEsBAvB4pwJFoKFYGlCsBAsVQiW\nhGBpsSNYCBaCxTlDsBAsNS0IFoKlxY5gIVgIFudMsBAsBEsTgoVgqUKwJARLix3BQrAQLM4Z\nglV4wLKgnxv/aNbcs3GmSeuZxkPNdv6m8Xaz5jYtzVr3Np5i1jyq8XGz5sZvmbWuMO90L9NO\npzYeYrbzDA+dbmHWuq/xZLPmj8077aoCBWtx1A9mzZ2izHKcEvW+2c6To34xa3Y8Y9a6K2q8\nWfOHUUlmzf/rYNa6JOp7s+Y3o66YtJ72r9NPm7XujvrCrHlI1F9mza5CsNwJwcorBIsKwcqr\nYgPWrr7bzJon980yaf2372yznVf1PWzWPGqYWeuxvsvNmuf1TTNr7velWevuvlvNmif3vWrS\n6qHTq807/fFHZq3H+i4za/bQaVcVKFiooisECxUUIViooKgAwTrxRddo41J024iOsT3XGzbv\n6N8uptNsk+L+XBvHaaO21Q5FSw33zV38VsuOEw0a3yM7Ow4Y7bypZ2yHzySjVnljlxbxi91s\n57JxvH9M3Owco2Z3adO3uU2b3uw2bYLHPHnTWz2lTVABgrXu9dHxxmB1G7R4zUfGvVg0bsna\nKc3HGnuf0N4ErOabnTpjuO+klgnrFhn5/lXZt19rI6Z3Oz7dsaLD29kGzXscn23/JtpNt/Rs\nnGvfZ/vCljONmt2lTd/mNm16s9u0CR7z5E1v9ZQ2QQUIVq4sDzYGK1V56Rtv6mFqS6Pfn3y0\n1WITsEwvu8sHHVtM22U5p904o6axrzv7tdGRbNDc+x3ny4RX8satZyMx5qwsz4y5ZNDsLm36\nNrdpc9nFNW18c9686a0e0iaqYGssE7CIpr9k2jy/mdFX89w+iZvNwMo1u0L2eReSThPtduwx\navq0m6wcl5IM4oqZ5Xzd7DjorpFlo49y1ybZkefmjJ4sd2njt7lJG9/sJm1qs/u8aWCZpk1U\n4Qarfy/jtozz+wzrIHnN65lmYEXHOl5dYMhOl7GTY5t/cMokrrHtc4ya9jVbcv7Eu/0MWrOb\nJTpfdzhWuGtk2WiT4HzJip5v0Cx7BstN2rRm92lTm93nTQXLPG2iCjVYmx2bjRtbOhwfG50J\nL8dtkk3A2jlz2+ZRDsNLjW1ju2/dFB9vfHU2s7XJ7dpNMQ7HexeNWuOVC7OzHXmoUcSyEa2w\nJ8fOMGiWPYLlLm1as/u0sWaDvLFWD2kTVZjBSmr9uUnrH/u+bz3GoC2hn2wGFtHoGKPjeptm\nac5iw7HOcNfNjj8M236Lnbh3XXw/I+QXRi+/sLOtY4G7NgGsl3wGy23atGb3aWPNBnnjf55x\n2kQVYrDSOgw2rM2p1hiUMmda7L94cY3jWIbZzr84/jRoie+kvMZ+a7jriDeM3b4z0Pnyp2OT\nQXP2+GjHS4nuoQ3MqdB92vhd3KSNNhvljd/ZOG2iCi9YZ9/sZQqGrFS47m+77aOXmhymY5c2\nOo4ZtAwhX6piZxnteSnGmDm51XTnS3a08Y3m88kZ290fTPniPcnX4t0gbfwubtJGm43yxu9s\nnDZRhRasyz3fPGuyJymeFzrc33C/8KtTcxzrjL7zk7/oIbFGx/Rl0c7f+x/G9d1qw4sJTnXr\n73w55Nhg/D/kLIPanr/cMMPlcoNsESyjtLFmo7TRZqO8sZ09pE1UAYKVsXlzjy6bN1923zok\ner5yOc7o29e7U5b/PK652d16kxqrz+RlS/s7DIfsZHZ6a92qjt0Nv/gN7GbyY5c6xm5d3vE1\ng17Ju6esXNCjtZuxV/DtXwAAAgBJREFUmHo2zrXrvWV+i5lGze7Spm9zmza92W3aRI+uedNb\nPaRNVAGCdZoed0+6b21PW43Oht/3aNW6xyKzESYmYM3qEhvTc7XxrunDYluN+tuo9b9mZgOq\ncpe/HRs3yvDy9JHesa2Guhvjy2UjuX9M3Kwco2Z3adO3uU2b3uw2baJH17zprZ7SJghvQqOC\nIgQLFRQhWKigCMFCBUUIFiooQrBQQRGChQqKECxUUIRgoYIiBMs/LYGFAftfRUoIln9CsAyE\nYPknBMtACJZ/QrAMhGD5J4rMleF1S1R4cY8sLwM6LPjB6lncVgQL5a0IMlefCOswceQtpXbK\n2ddGKVuPQC9+K4KF8lYEmTGgjH777/rGsvwu/O78+AHsE7YiWCgvRZC5r1aGok7hV+QD0FeW\nc2veIwtbESyUlyLIlAKm006cbsyR18OnsrAVwUJ5KYJMyXu2UmXK8jhYJb8WpgxN5rYiWCgv\nRZCpV0F/ciU9ov3l8s8rn7itCBbKSxFkPoH3iEGeQoguMxXIs8zcVgQL5aXo5YZnoNHHk/o1\nbKJsmQ/lK5CHZLitCBbKS1Fksj6PKl269isrlS2ZlYE9ga9vRbBQqMAIwUIFRQgWKihCsFBB\nEYKFCooQLFRQhGChgiIECxUUIViooAjBQgVFCBYqKEKwUEERgoUKihAsVFD0f2PClYT70UN6\nAAAAAElFTkSuQmCC"},"metadata":{},"output_type":"display_data"}],"execution_count":188,"cell_type":"code","source":"# Adding standard error bars\nggplot(difficulty, aes(x = level, y = p_win)) +\n     geom_line() +\n     scale_x_continuous(breaks = 1:15) +\n     scale_y_continuous(label = scales::percent) + \n     geom_point() +\n     geom_hline(yintercept = 0.1, linetype = 'dashed') +\n     geom_errorbar(aes(ymin = p_win - error, ymax = p_win + error))","metadata":{"trusted":true,"dc":{"key":"52"},"tags":["sample_code"]}},{"cell_type":"markdown","source":"## 9. A final metric\n<p>It looks like our difficulty estimates are pretty precise! Using this plot, a level designer can quickly spot where the hard levels are and also see if there seems to be too many hard levels in the episode.</p>\n<p>One question a level designer might ask is: \"How likely is it that a player will complete the episode without losing a single time?\" Let's calculate this using the estimated level difficulties!</p>","metadata":{"deletable":false,"dc":{"key":"59"},"tags":["context"],"run_control":{"frozen":true},"editable":false}},{"outputs":[{"traceback":["Error in eval(expr, envir, enclos): object '....' not found\nTraceback:\n"],"evalue":"Error in eval(expr, envir, enclos): object '....' not found\n","ename":"ERROR","output_type":"error"}],"execution_count":190,"cell_type":"code","source":"# The probability of completing the episode without losing a single time\np <- ....\n\n# Printing it out\np","metadata":{"trusted":true,"dc":{"key":"59"},"tags":["sample_code"]}},{"cell_type":"markdown","source":"## 10. Should our level designer worry?\n<p>Given the probability we just calculated, should our level designer worry about that a lot of players might complete the episode in one attempt?</p>","metadata":{"deletable":false,"dc":{"key":"66"},"tags":["context"],"run_control":{"frozen":true},"editable":false}},{"outputs":[],"execution_count":null,"cell_type":"code","source":"# Should our level designer worry about that a lot of \n# players will complete the episode in one attempt?\nshould_the_designer_worry = .... # TRUE / FALSE","metadata":{"trusted":true,"dc":{"key":"66"},"tags":["sample_code"],"collapsed":true}}],"metadata":{"language_info":{"pygments_lexer":"r","codemirror_mode":"r","file_extension":".r","name":"R","mimetype":"text/x-r-source","version":"3.4.1"},"kernelspec":{"language":"R","name":"ir","display_name":"R"}},"nbformat_minor":2}