{"raw_statement":[{"iden":"problem statement","content":"You are given two sets $S={(a_1,b_1),(a_2,b_2),\\ldots,(a_N,b_N)}$ and $T={(c_1,d_1),(c_2,d_2),\\ldots,(c_N,d_N)}$ of $N$ points each on a two-dimensional plane.\nDetermine whether it is possible to do the following operations on $S$ any number of times (possibly zero) in any order so that $S$ matches $T$.\n\n*   Choose a real number $p\\ (0 \\lt p \\lt 360)$ and rotate every point in $S$ $p$ degrees clockwise about the origin.\n*   Choose real numbers $q$ and $r$ and move every point in $S$ by $q$ in the $x$\\-direction and by $r$ in the $y$\\-direction. Here, $q$ and $r$ can be any real numbers, be it positive, negative, or zero."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 100$\n*   $-10 \\leq a_i,b_i,c_i,d_i \\leq 10$\n*   $(a_i,b_i) \\neq (a_j,b_j)$ if $i \\neq j$.\n*   $(c_i,d_i) \\neq (c_j,d_j)$ if $i \\neq j$.\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$a_1$ $b_1$\n$a_2$ $b_2$\n$\\hspace{0.6cm}\\vdots$\n$a_N$ $b_N$\n$c_1$ $d_1$\n$c_2$ $d_2$\n$\\hspace{0.6cm}\\vdots$\n$c_N$ $d_N$"},{"iden":"sample input 1","content":"3\n0 0\n0 1\n1 0\n2 0\n3 0\n3 1"},{"iden":"sample output 1","content":"Yes\n\nThe figure below shows the given sets of points, where the points in $S$ and $T$ are painted red and green, respectively:\n![image](https://img.atcoder.jp/ghi/39ad67d4e10490f509f252a1f0e4935b.png)\nIn this case, we can match $S$ with $T$ as follows:\n\n1.  Rotate every point in $S$ $270$ degrees clockwise about the origin.\n2.  Move every point in $S$ by $3$ in the $x$\\-direction and by $0$ in the $y$\\-direction."},{"iden":"sample input 2","content":"3\n1 0\n1 1\n3 0\n-1 0\n-1 1\n-3 0"},{"iden":"sample output 2","content":"No\n\nThe figure below shows the given sets of points:\n![image](https://img.atcoder.jp/ghi/02c4ca4a8329110dc131b37720283d2a.png)\nAlthough $S$ and $T$ are symmetric about the $y$\\-axis, we cannot match $S$ with $T$ by rotations and translations as stated in Problem Statement."},{"iden":"sample input 3","content":"4\n0 0\n2 9\n10 -2\n-6 -7\n0 0\n2 9\n10 -2\n-6 -7"},{"iden":"sample output 3","content":"Yes"},{"iden":"sample input 4","content":"6\n10 5\n-9 3\n1 -5\n-6 -5\n6 9\n-9 0\n-7 -10\n-10 -5\n5 4\n9 0\n0 -10\n-10 -2"},{"iden":"sample output 4","content":"Yes"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}