{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eGiven $$$n$$$ points $$$P_1, P_2, \\cdots, P_n$$$ on 2D plane and $$$q$$$ queries. In $$$i$$$-th query, a point $$$A_i$$$ is given, and you should determine the number of tuples $$$(u, v)$$$ that $$$1 \\le u \u0026lt; v \\le n$$$ and $$$A_i, P_u, P_v$$$ form a non-degenerate right-angled triangle.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains two positive integers $$$n,q~(2\\le n \\le 2\\,000, 1\\le q \\le 2\\,000)$$$, denoting the number of given points and the number of queries.\u003c/p\u003e\u003cp\u003eNext $$$n$$$ lines each contains two integers $$$x_i, y_i~(|x_i|,|y_i| \\le 10^9)$$$, denoting a given point $$$P_i$$$.\u003c/p\u003e\u003cp\u003eNext $$$q$$$ lines each contains two integers $$$x_i, y_i~(|x_i|,|y_i| \\le 10^9)$$$, denoting a query point $$$A_i$$$.\u003c/p\u003e\u003cp\u003eIt is guaranteed that the input $$$n+q$$$ points are all pairwise distinct.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput $$$q$$$ lines each contains a non-negative integer, denoting the answer to corresponding query.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e4 2\n0 1\n1 0\n0 -1\n-1 0\n0 0\n1 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4\n3\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eFor query $$$(0,0)$$$, the 4 right-angled triangles are \u003c/p\u003e\u003cul\u003e \u003cli\u003e $$$\\{(0,0),(0,1),(1,0)\\}$$$ \u003c/li\u003e\u003cli\u003e $$$\\{(0,0),(0,1),(-1,0)\\}$$$ \u003c/li\u003e\u003cli\u003e $$$\\{(0,0),(0,-1),(1,0)\\}$$$ \u003c/li\u003e\u003cli\u003e $$$\\{(0,0),(0,-1),(-1,0)\\}$$$ \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eFor query $$$(1,1)$$$, the 3 right-angled triangles are \u003c/p\u003e\u003cul\u003e \u003cli\u003e $$$\\{(1,1),(0,1),(1,0)\\}$$$ \u003c/li\u003e\u003cli\u003e $$$\\{(1,1),(0,1),(0,-1)\\}$$$ \u003c/li\u003e\u003cli\u003e $$$\\{(1,1),(1,0),(-1,0)\\}$$$ \u003c/li\u003e\u003c/ul\u003e"}}]}