Laplacian Matrices (1) X11939


Statement
 

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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 Lii (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.

Public test cases

  • Input

    3
0 1 0
0 0 1
1 1 0

    Output

    1 -1 0 
0 1 -1 
-1 -1 2

  • Input

    4
0 1 1 0
1 0 0 1
1 1 0 1
0 1 1 0

    Output

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

  • Input

    3
0 0 0
0 0 0
0 0 0

    Output

    0 0 0 
0 0 0 
0 0 0
    • Information
    Author
    ProAl1 professors
    Language
    English
    Official solutions
    Python
    User solutions
    Python