Laplacian Matrices (1)

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.

Problem information

Author: ProAl1 professors

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

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