Bobo has a matrix A with n rows and n columns.
For submatrix with upper-left corner (x₁, y₁) and lower-right corner (x₂, y₂) (1≤ x₁≤ x₂≤ n, 1≤ y₁ ≤y₂ ≤n), 
he defined its skewness S(x₁, y₁, x₂, y₂) =(ΣiΣj A_i,_j)³.i=x₁ to x₂, j=y₁ to y₂.
Bobo would like to know the sum of skewness of all submatrices modulo (10⁹ + 7).

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.
The i-th of following n lines contains n integers A_i,1,A_i,2, . . . ,A_i,n.
• 1≤ n≤1000
• 0≤A_i,j≤10⁹
• The number of test cases does not exceed 10.

For each case, output an integer which denotes the sum.

2
0 1
1 0
3
0 1 0
1 1 0
1 0 1

14
448

2017年四川省赛