Counting four cycles

You are given an undirected graph. Count the four cycles it contains.

A four cycle is a cycle of length 4 on four distinct vertices. Vertices $v_1, v_2, v_3, v_4$ in this order form one when they are pairwise distinct and $v_1 v_2$, $v_2 v_3$, $v_3 v_4$, $v_4 v_1$ are all edges.

Orders that visit the vertices differently count as different four cycles. For example, 1 -> 2 -> 3 -> 4 -> 1 and 2 -> 3 -> 4 -> 1 -> 2 are counted separately.

The first line has the number of vertices $N$. ($1 \le N \le 250$)

Each of the next $N$ lines holds one row of the adjacency matrix $A$ of the undirected graph, given as $N$ integers separated by spaces, each of them 0 or 1. $A_{ij}$ is 1 when an edge joins vertex $i$ and vertex $j$, and 0 when it does not. No $A_{ii}$ is 1.

Print the number of four cycles on one line.