Laplacian Matrices (1) X84325

A square matrix M of size n×n that contains only zeros and ones, and only zeros in the diagonal, is called a binary matrix.

The Laplacian of a binary matrix M is another n×n square matrix L with the following content:

• All cells L_ii (i.e. the diagonal of L), are equal to the number of ones in row i of M.
• Any other cell in L contains the same value than the corresponding cell in M but with opposite sign (since M contains only 0 and 1, these L cells will contain 0 or -1 accordingly).

For example, the following binary matrix 5×5:

 0  1  1  0  0
 1  0  0  1  1
 0  1  0  0  1 
 1  1  1  0  1
 0  0  0  0  0

has as Laplacian the following Matrix:

 2 -1 -1  0  0
-1  3  0 -1 -1
 0 -1  2  0 -1 
-1 -1 -1  4 -1
 0  0  0  0  0

Write a program that reads one binary matrix and prints its Laplacian following the format shown in the examples.

Input

Input consists of a number n > 0, the dimension of the binary matrix, followed by n×n integers describing the matrix: all of them either 0 or 1, where all the diagonal entries are zero.

Output

The output must contain the Laplacian transform of the input matrix.