Zero Matrix

Given a two-dimensional matrix of integers, for each zero in the original matrix, replace all values in its row and column with zero, and return the resulting matrix.

Constraints

• n * m ≤ 100,000 where n and m are the number of rows and columns in matrix

https://binarysearch.com/problems/Zero-Matrix

Examples

Example 1

Input

• matrix =

[[ 5, 0, 0, 5, 8],
 [ 9, 8,10, 3, 9],
 [ 0, 7, 2, 3, 1],
 [ 8, 0, 6, 7, 2],
 [ 4, 1, 8, 5,10]]

Output

• answer = [[0, 0, 0, 0, 0], [0, 0, 0, 3, 9], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 5, 10]]

Explanation

These rows contain a 0: [0, 2, 3] and the returned matrix contains 0 in those rows. These columns contain a 0: [0, 1, 2] and the returned matrix contains 0 in those columns.

Solution