{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" height\u003d\"227px\" src\u003d\"CDN_BASE_URL/714b7cb832398002c42e79fac2bd928e?v\u003d1715156291\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\" width\u003d\"227px\"\u003e \u003c/center\u003e Tania is a marine biologist. Her goal is to measure the impact of climate change on the population of Macaroni penguins. As most species of penguins, Macaroni penguins live in the southern hemisphere, near Antarctica. Tania is primarily focused on the population of Macaroni penguins near the \"Îles Nuageuses\" (in English, \"Cloudy Islands\").\u003cp\u003eDuring summer, the ice around the islands melt and the islands become too small to host all the birds. Some penguins live on the icebergs floating around. For her study, Tania needs to measure the area of those icebergs.\u003c/p\u003e\u003cp\u003eUsing satellite imagery and image recognition, Tania has obtained a map of the icebergs and your goal is to measure their area. The island studied by Tania is quite small and the Earth can locally be approximated as a flat surface. Tania\u0027s map thus uses the usual 2D Cartesian coordinate system, and areas are computed in the usual manner. For instance, a rectangle parallel to the axes defined by the equations $$$x_1 \\le x \\le x_2$$$ and $$$y_1 \\le y \\le y_2$$$ has an area of $$$( x_2 - x_1 ) \\times (y_2 - y_1 )$$$.\u003c/p\u003e\u003cp\u003eIn Tania\u0027s representation, an iceberg is a polygon represented by its boundary. For each iceberg, Tania has noted the sequence of points $$$p_1,\\ldots, p_k$$$ defining the border of the iceberg. The various icebergs never touch each other and they never overlap. Furthermore, the boundary $$$p_1, \\ldots , p_k$$$ of an iceberg is always a \"simple\" polygon, i.e. no two segments in $$$[ p_1 ; p_2 ], \\ldots, [ p_k ; p_1 ]$$$ cross each other.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe input consists of the following lines: \u003c/p\u003e\u003cul\u003e \u003cli\u003e on the first line, an integer N, describing the number of polygons; \u003c/li\u003e\u003cli\u003e then N blocks of lines follow, each describing a polygon and composed of: \u003cul\u003e \u003cli\u003e on the first line, an integer P, the number of points defining the polygon border, \u003c/li\u003e\u003cli\u003e on the next P lines, two space-separated integers $$$x$$$ and $$$y$$$, the coordinates of each border point. \u003c/li\u003e\u003c/ul\u003e \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eLimits \u003c/p\u003e\u003cul\u003e \u003cli\u003e The number $$$N$$$ of polygons is such that $$$1 \\le N \\le 1000$$$. \u003c/li\u003e\u003cli\u003e Each polygon is described by $$$P$$$ points with $$$3 \\le P \\le 50$$$. \u003c/li\u003e\u003cli\u003e All coordinates are such that $$$0 \\le x, y \\le 10^6$$$ . \u003c/li\u003e\u003c/ul\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eThe output should contain a single integer: the total area rounded to the nearest integer below. In other words, the output should be a single line containing a single integer $$$I$$$ such that the total area $$$A$$$ of the polygons described in the input is comprised between $$$I$$$ included and $$$I + 1$$$ excluded ($$$I \\le A \u0026lt; I + 1$$$).\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e1\n4\n0 0\n1 0\n1 1\n0 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e2\n5\n98 35\n79 90\n21 90\n2 36\n50 0\n3\n0 0\n20 0\n0 20\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e6100\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003eSample Explanation 1\u003c/span\u003e\u003c/p\u003e\u003cp\u003eThis sample has a unique iceberg, which is a square of side 1.\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003eSample Explanation 2\u003c/span\u003e\u003c/p\u003e\u003cp\u003eIn this sample (depicted below) there are two icebergs, a triangle of area 200 and a pentagon of area 5900.5. \u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/d652a1c1c4e3ec9947705e4697f32d26?v\u003d1715156291\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e"}}]}