You are given a 0-indexed m x n integer matrix grid. The width of a column is the maximum length of its integers.

• For example, if grid = [[-10], [3], [12]], the width of the only column is 3 since -10 is of length 3.

Return an integer array ans of size n where ans[i] is the width of the ith column.

The length of an integer x with len digits is equal to len if x is non-negative, and len + 1 otherwise.

 

Example 1:

Input: grid = [[1],[22],[333]]
Output: [3]
Explanation: In the 0th column, 333 is of length 3.

Example 2:

Input: grid = [[-15,1,3],[15,7,12],[5,6,-2]]
Output: [3,1,2]
Explanation: 
In the 0th column, only -15 is of length 3.
In the 1st column, all integers are of length 1. 
In the 2nd column, both 12 and -2 are of length 2.

 

Constraints:

• m == grid.length
• n == grid[i].length
• 1 <= m, n <= 100
• -109 <= grid[r][c] <= 109