Laplacian Matrices (1)

A square matrix $M$ of size $n\times{n}$ 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 $n\times{n}$ 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 $5\times5$ :

 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 $n\times{n}$ 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.

Problem information

Author: ProAl1 professors

Generation: 2026-01-25T16:46:44.879Z