{"raw_statement":[{"iden":"problem statement","content":"There are villages at some number of points in the $xy$\\-plane.  \nTakahashi will construct a moat to protect these villages from enemies such as civil armies and witches.\nYou are given a $4 \\times 4$ matrix $A = (A_{i, j})$ consisting of $0$ and $1$.  \nFor each pair of integers $(i, j)$ $(1 \\leq i, j \\leq 4)$ such that $A_{i, j} = 1$, there is a village at the coordinates $(i-0.5, j-0.5)$.\nThe moat will be a polygon in the plane. Takahashi will construct it so that the following conditions will be satisfied. (See also the annotation at Sample Input/Output 1.)\n\n1.  There is no self-intersection.\n2.  All villages are contained in the interior of the polygon.\n3.  The $x$\\- and $y$\\-coordinates of every vertex are integers between $0$ and $4$ (inclusive).\n4.  Every edge is parallel to the $x$\\- or $y$\\-axis.\n5.  Every inner angle is $90$ or $270$ degrees.\n\nPrint the number of ways in which Takahashi can construct the moat."},{"iden":"constraints","content":"*   $A_{i, j} \\in \\lbrace 0, 1\\rbrace$\n*   There is at least one pair $(i, j)$ such that $A_{i, j} = 1$."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$A_{1, 1}$ $A_{1, 2}$ $A_{1, 3}$ $A_{1, 4}$\n$A_{2, 1}$ $A_{2, 2}$ $A_{2, 3}$ $A_{2, 4}$\n$A_{3, 1}$ $A_{3, 2}$ $A_{3, 3}$ $A_{3, 4}$\n$A_{4, 1}$ $A_{4, 2}$ $A_{4, 3}$ $A_{4, 4}$"},{"iden":"sample input 1","content":"1 0 0 0\n0 0 1 0\n0 0 0 0\n1 0 0 0"},{"iden":"sample output 1","content":"1272\n\nThe two ways to construct the moat shown in the images below are **valid**.\n![image](https://img.atcoder.jp/ghi/7b3181deb4e1df72e4c0661b1137db4d.png) ![image](https://img.atcoder.jp/ghi/a1e46c7db32d63942caa7119a4f3a593.png)\nThe four ways to construct the moat shown in the images below are **invalid**.\n![image](https://img.atcoder.jp/ghi/335053c01a13eb99e55767a3dc02eb38.png) ![image](https://img.atcoder.jp/ghi/c4df3d1fa24557b0d4d94ac0eaa8b9ab.png) ![image](https://img.atcoder.jp/ghi/be93de595e9222d5e20c90bd28d24563.png) ![image](https://img.atcoder.jp/ghi/37dac3af065c013ce0b8c0ee7591b97a.png)\nHere are the reasons the above ways are invalid.\n\n*   The first way violates the condition: \"There is no self-intersection.\"\n*   The second way violates the condition: \"All villages are contained in the interior of the polygon.\"\n*   The third way violates the condition: \"The $x$\\- and $y$\\-coordinates of every vertex are integers between $0$ and $4$.\" (Some vertices have non-integer coordinates.)\n*   The fourth way violates the condition: \"Every edge is parallel to the $x$\\- or $y$\\-axis.\""},{"iden":"sample input 2","content":"1 1 1 1\n1 1 1 1\n1 1 1 1\n1 1 1 1"},{"iden":"sample output 2","content":"1"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}