Moat

There are villages at some number of points in the $xy$\-plane. Takahashi will construct a moat to protect these villages from enemies such as civil armies and witches. You are given a $4 \times 4$ matrix $A = (A_{i, j})$ consisting of $0$ and $1$. For 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 $(i-0.5, j-0.5)$. The 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.) 1. There is no self-intersection. 2. All villages are contained in the interior of the polygon. 3. The $x$\- and $y$\-coordinates of every vertex are integers between $0$ and $4$ (inclusive). 4. Every edge is parallel to the $x$\- or $y$\-axis. 5. Every inner angle is $90$ or $270$ degrees. Print the number of ways in which Takahashi can construct the moat. ## Constraints * $A_{i, j} \in \lbrace 0, 1\rbrace$ * There is at least one pair $(i, j)$ such that $A_{i, j} = 1$. ## Input Input is given from Standard Input in the following format: $A_{1, 1}$ $A_{1, 2}$ $A_{1, 3}$ $A_{1, 4}$ $A_{2, 1}$ $A_{2, 2}$ $A_{2, 3}$ $A_{2, 4}$ $A_{3, 1}$ $A_{3, 2}$ $A_{3, 3}$ $A_{3, 4}$ $A_{4, 1}$ $A_{4, 2}$ $A_{4, 3}$ $A_{4, 4}$ [samples]