Largest Elements in Their Row and Column

You are given a two-dimensional list of integers matrix containing 1s and 0s. Return the number of elements in matrix such that:

• matrix[r][c] = 1
• matrix[r][j] = 0 for every j ≠ c and matrix[i][c] = 0 for every i ≠ r

Constraints

• 0 ≤ n, m ≤ 250 where n and m are the number of rows and columns in matrix

https://binarysearch.com/problems/Largest-Elements-in-Their-Row-and-Column

Examples

Example 1

Input

• matrix =

[[0,0,1],
 [1,0,0],
 [0,1,0]]

Output

• answer = 3

Explanation

We have matrix[0][2], matrix[1][0] and matrix[2][1] meet the criteria.

Example 2

Input

• matrix =

[[0,0,1],
 [1,0,0],
 [1,0,0]]

Output

• answer = 1

Explanation

Only matrix[0][2] meet the criteria. The other two 1s share the same column.

Solution