Problem Statement

You are given a simple undirected graph G with N vertices.
G is given as the $N \times N adjacency matrix A$. That is, there is an edge between Vertices i and j if A_{i,j} is 1, and there is not if A_{i,j} is 0.
Find the number of triples of integers $(i,j,k) satisfying 1 \le i < j < k \le N$ such that there is an edge between Vertices i and j, an edge between Vertices j and k, and an edge between Vertices i and k.

Input

Input is given from Standard Input in the following format:
N
$A_{1,1}A_{1,2}\dots A_{1,N}$
$A_{2,1}A_{2,2}\dots A_{2,N}$
$\vdots$
$A_{N,1}A_{N,2}\dots A_{N,N}$

Output

Print the answer.

Constraints

• $3 \le N \le 3000$
• A is the adjacency matrix of a simple undirected graph G.
• All values in input are integers.

Sample Input 1

4
0011
0011
1101
1110

Sample Output 1

2

(i,j,k)=(1,3,4),(2,3,4) satisfy the condition.
(i,j,k)=(1,2,3) does not satisfy the condition, because there is no edge between Vertices 1 and 2.
Thus, the answer is 2.

Sample Input 2

10
0000000000
0000000000
0000000000
0000000000
0000000000
0000000000
0000000000
0000000000
0000000000
0000000000

Sample Output 2

0

见题面 Input 部分

见题面 Output 部分