A farmer owns a rectangular grid grid of size $m imes n$, where each cell is either $0$ representing infertile land or $1$ representing fertile land.

A pyramidal plot of height $h > 1$ with its apex at cell $(r, c)$ consists of a set of cells satisfying the following conditions:

• The apex cell $(r, c)$ is fertile.

• For each level $i$ where $0 \leq i < h$, all cells in row $r + i$ from column $c - i$ through column $c + i$ inclusive are fertile.

• The height $h$ is strictly greater than $1$.

An inverse pyramidal plot of height $h > 1$ with its apex at cell $(r, c)$ consists of a set of cells satisfying the following conditions:

• The apex cell $(r, c)$ is fertile.

• For each level $i$ where $0 \leq i < h$, all cells in row $r - i$ from column $c - i$ through column $c + i$ inclusive are fertile.

• The height $h$ is strictly greater than $1$.

Return the total count of all pyramidal and inverse pyramidal plots present in grid.

Constraints:

• m == grid.length

• n == grid[i].length

• $1 \leq$ m, n $\leq 1000$

• $1 \leq$ m $ imes$ n $\leq 10^5$

• grid[i][j] is either $0$ or $1$.

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