Walk of Length 6

Bobo has an undirected graph with $n$ vertices which are conveniently labeled with $1, 2, \dots, n$. Let $V$ be the set of vertices and $E$ be the set of edges. He would like to count the number of tuples $(v\_1, v\_2, \dots, v\_6)$ where:

• $v\_1, v\_2, \dots, v\_6 \in V$,
• $\\{v\_1, v\_2\\}, \\{v\_2, v\_3\\}, \dots, \\{v\_5, v\_6\\}, \\{v\_6, v\_1\\} \in E$;
• $\mathcal{C} = (\\{v\_1, v\_2\\}, \\{v\_2, v\_3\\}, \dots, \\{v\_5, v\_6\\}, \\{v\_6, v\_1\\})$ is not a simple cycle of length $6$.

The input contains zero or more test cases, and is terminated by end-of-file. For each test case:

The first line contains an integer $n$ ($1 \leq n \leq 1000$). 

The $i$-th of the following $n$ lines contains a string $g\_i$ of length $n$ where $g\_{i, j}$ denotes the existence of edge $\\{i, j\\}$ ($g\_{i, j} \in \\{0, 1\\}$, $g\_{i, i} = 0$, $g\_{i, j} = g\_{j, i}$). 

It is guaranteed that the sum of $n$ does not exceed $1000$.

For each test case, output an integer which denotes the number of tuples.