![](\"https://assets.leetcode.com/uploads/2021/11/08/image.png\")
A farmer has a rectangular grid of land with m rows and n columns that can be divided into unit cells. Each cell is either fertile (represented by a 1) or barren (represented by a 0). All cells outside the grid are considered barren.
A pyramidal plot of land can be defined as a set of cells with the following criteria:
\n\n1 and all cells must be fertile.(r, c) be the apex of the pyramid, and its height be h. Then, the plot comprises of cells (i, j) where r <= i <= r + h - 1 and c - (i - r) <= j <= c + (i - r).An inverse pyramidal plot of land can be defined as a set of cells with similar criteria:
\n\n1 and all cells must be fertile.(r, c) be the apex of the pyramid, and its height be h. Then, the plot comprises of cells (i, j) where r - h + 1 <= i <= r and c - (r - i) <= j <= c + (r - i).Some examples of valid and invalid pyramidal (and inverse pyramidal) plots are shown below. Black cells indicate fertile cells.
\n\nGiven a 0-indexed m x n binary matrix grid representing the farmland, return the total number of pyramidal and inverse pyramidal plots that can be found in grid.
\n
Example 1:
\n![\"\"](\"https://assets.leetcode.com/uploads/2021/12/22/1.JPG\")
\n\nInput: grid = [[0,1,1,0],[1,1,1,1]]\nOutput: 2\nExplanation: The 2 possible pyramidal plots are shown in blue and red respectively.\nThere are no inverse pyramidal plots in this grid. \nHence total number of pyramidal and inverse pyramidal plots is 2 + 0 = 2.\n\n\n
Example 2:
\n![\"\"](\"https://assets.leetcode.com/uploads/2021/12/22/2.JPG\")
\n\nInput: grid = [[1,1,1],[1,1,1]]\nOutput: 2\nExplanation: The pyramidal plot is shown in blue, and the inverse pyramidal plot is shown in red. \nHence the total number of plots is 1 + 1 = 2.\n\n\n
Example 3:
\n![\"\"](\"https://assets.leetcode.com/uploads/2021/12/22/3.JPG\")
\n\nInput: grid = [[1,1,1,1,0],[1,1,1,1,1],[1,1,1,1,1],[0,1,0,0,1]]\nOutput: 13\nExplanation: There are 7 pyramidal plots, 3 of which are shown in the 2nd and 3rd figures.\nThere are 6 inverse pyramidal plots, 2 of which are shown in the last figure.\nThe total number of plots is 7 + 6 = 13.\n\n\n
\n
Constraints:
\n\nm == grid.lengthn == grid[i].length1 <= m, n <= 10001 <= m * n <= 105grid[i][j] is either 0 or 1.有一个 矩形网格 状的农场，划分为 m 行 n 列的单元格。每个格子要么是 肥沃的 （用 1 表示），要么是 贫瘠 的（用 0 表示）。网格图以外的所有与格子都视为贫瘠的。
农场中的 金字塔 区域定义如下：
\n\n1 且所有格子都是 肥沃的 。(r, c) 为金字塔的顶端且高度为 h ，那么金字塔区域内包含的任一格子 (i, j) 需满足 r <= i <= r + h - 1 且 c - (i - r) <= j <= c + (i - r) 。一个 倒金字塔 类似定义如下：
\n\n1 且所有格子都是 肥沃的 。(r, c) 为金字塔的顶端且高度为 h ，那么金字塔区域内包含的任一格子 (i, j) 需满足 r - h + 1 <= i <= r 且 c - (r - i) <= j <= c + (r - i) 。下图展示了部分符合定义和不符合定义的金字塔区域。黑色区域表示肥沃的格子。
\n\n
给你一个下标从 0 开始且大小为 m x n 的二进制矩阵 grid ，它表示农场，请你返回 grid 中金字塔和倒金字塔的 总数目 。
\n\n
示例 1：
\n\n![\"\"](\"https://assets.leetcode.com/uploads/2021/10/23/eg11.png\")
![\"\"](\"https://assets.leetcode.com/uploads/2021/10/23/exa12.png\")
![\"\"](\"https://assets.leetcode.com/uploads/2021/10/23/exa13.png\")
输入：grid = [[0,1,1,0],[1,1,1,1]]\n输出：2\n解释：\n2 个可能的金字塔区域分别如上图蓝色和红色区域所示。\n这个网格图中没有倒金字塔区域。\n所以金字塔区域总数为 2 + 0 = 2 。\n\n\n
示例 2：
\n\n![\"\"](\"https://assets.leetcode.com/uploads/2021/10/23/eg21.png\")
![\"\"](\"https://assets.leetcode.com/uploads/2021/10/23/exa22.png\")
![\"\"](\"https://assets.leetcode.com/uploads/2021/10/23/exa23.png\")
输入：grid = [[1,1,1],[1,1,1]]\n输出：2\n解释：\n金字塔区域如上图蓝色区域所示，倒金字塔如上图红色区域所示。\n所以金字塔区域总数目为 1 + 1 = 2 。\n\n\n
示例 3：
\n\n![\"\"](\"https://assets.leetcode.com/uploads/2021/10/23/eg3.png\")
输入：grid = [[1,0,1],[0,0,0],[1,0,1]]\n输出：0\n解释：\n网格图中没有任何金字塔或倒金字塔区域。\n\n\n
示例 4：
\n\n![\"\"](\"https://assets.leetcode.com/uploads/2021/10/23/eg41.png\")
![\"\"](\"https://assets.leetcode.com/uploads/2021/10/23/eg42.png\")
![\"\"](\"https://assets.leetcode.com/uploads/2021/10/23/eg43.png\")
![\"\"](\"https://assets.leetcode.com/uploads/2021/10/23/eg44.png\")
输入：grid = [[1,1,1,1,0],[1,1,1,1,1],[1,1,1,1,1],[0,1,0,0,1]]\n输出：13\n解释：\n有 7 个金字塔区域。上图第二和第三张图中展示了它们中的 3 个。\n有 6 个倒金字塔区域。上图中最后一张图展示了它们中的 2 个。\n所以金字塔区域总数目为 7 + 6 = 13.\n\n\n
\n\n
提示：
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