Problem Statement
Utkarsh has recently put on some weight. In order to lose weight, he has to run on boundary of gardens.
But he lives in a country where there are no gardens. There are just many bidirectional roads between cities.
Due to the situation, he is going to consider any cycle of length four as a garden. Formally a garden is considered to be a unordered set of 4 roads {r0, r1, r2, r3} where ri and ri+1 mod 4 share a city.
Now he wonders how many distinct gardens are there in this country.
Input format:
The first integer contains N, the number of cities in the country.
It is followed by space separated elements of N*N binary matrix G.
G[i][j] = 1 denotes there is a road between ith city and jth city.
A pair of cities has atmost one road connecting them.
No road connects a city to itself.
G is symmetric.
Output format:
Print the total number of gardens.
Constraints:
1 ≤ N ≤ 2000
8 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 0
The Country here is a cube. A cube consists of 6 square faces denoting 6 gardens.
