You are given an $m \times n$ $0$ indexed $2 {D}$ array of integers heights representing the heights of people standing in a grid.

A person at cell $(r_1, c_1)$ can see a person at cell $(r_2, c_2)$ if they are either in the same row looking to the right or in the same column looking downwards. Specifically, the person at $(r_1, c_1)$ can see the person at $(r_2, c_2)$ if:

• In the same row: $r_1 = r_2$, $c_1 < c_2$, and every person in cell $(r_1, k)$ with $c_1 < k < c_2$ is strictly shorter than $\min($heights$[r_1][c_1],$ heights$[r_2][c_2])$.

• In the same column: $c_1 = c_2$, $r_1 < r_2$, and every person in cell $(k, c_1)$ with $r_1 < k < r_2$ is strictly shorter than $\min($heights$[r_1][c_1],$ heights$[r_2][c_2])$.

Return an $m \times n$ $2 {D}$ array of integers ans where ans[i][j] is the total number of people that the person at cell $(i, j)$ can see to their right and downwards.

Constraints:

• $1 \leq$ heights.length $\leq 400$

• $1 \leq$ heights[i].length $\leq 400$

• $1 \leq$ heights[i][j] $\leq 10^5$

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