Cross Balance of Ones

Medium

You get a rectangular m × n table grid of zeros and ones. For every cell (i, j) look at its "cross": row i together with column j. Compute: - the number of ones in row i plus the number of ones in column j, - minus the number of zeros in row i and minus the number of zeros in column j. Return a table of the same size where cell (i, j) holds that value.

Example 1

grid=[[1, 0, 1], [0, 0, 1]] → [[1, -1, 3], [-1, -3, 1]]

For cell (0, 0): row 0 has two ones and one zero, column 0 has one one and one zero: 2 + 1 - 1 - 1 = 1. For cell (1, 2): row 1 has one one and two zeros, column 2 has two ones: 1 + 2 - 2 - 0 = 1.

Example 2

grid=[[0, 0], [0, 0]] → [[-4, -4], [-4, -4]]

There are no ones at all: every row and column has two zeros, 0 + 0 - 2 - 2 = -4.

Example 3

grid=[[1], [1], [0]] → [[2], [2], [0]]

Constraints

1 ≤ m, n
m · n ≤ 10⁵
all rows have the same length
grid[i][j] is 0 or 1

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Topics

Array Matrix Simulation

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Input

grid=[[1, 0, 1], [0, 0, 1]]

Expected

[[1, -1, 3], [-1, -3, 1]]

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