You are given a 0-indexed 2D matrix grid of size n x n, where (r, c) represents:
grid[r][c] = 1grid[r][c] = 0You are initially positioned at cell (0, 0). In one move, you can move to any adjacent cell in the grid, including cells containing thieves.
The safeness factor of a path on the grid is defined as the minimum manhattan distance from any cell in the path to any thief in the grid.
\n\nReturn the maximum safeness factor of all paths leading to cell (n - 1, n - 1).
An adjacent cell of cell (r, c), is one of the cells (r, c + 1), (r, c - 1), (r + 1, c) and (r - 1, c) if it exists.
The Manhattan distance between two cells (a, b) and (x, y) is equal to |a - x| + |b - y|, where |val| denotes the absolute value of val.
\n
Example 1:
\n![\"\"](\"https://assets.leetcode.com/uploads/2023/07/02/example1.png\")
\n\nInput: grid = [[1,0,0],[0,0,0],[0,0,1]]\nOutput: 0\nExplanation: All paths from (0, 0) to (n - 1, n - 1) go through the thieves in cells (0, 0) and (n - 1, n - 1).\n\n\n
Example 2:
\n![\"\"](\"https://assets.leetcode.com/uploads/2023/07/02/example2.png\")
\n\nInput: grid = [[0,0,1],[0,0,0],[0,0,0]]\nOutput: 2\nExplanation: The path depicted in the picture above has a safeness factor of 2 since:\n- The closest cell of the path to the thief at cell (0, 2) is cell (0, 0). The distance between them is | 0 - 0 | + | 0 - 2 | = 2.\nIt can be shown that there are no other paths with a higher safeness factor.\n\n\n
Example 3:
\n![\"\"](\"https://assets.leetcode.com/uploads/2023/07/02/example3.png\")
\n\nInput: grid = [[0,0,0,1],[0,0,0,0],[0,0,0,0],[1,0,0,0]]\nOutput: 2\nExplanation: The path depicted in the picture above has a safeness factor of 2 since:\n- The closest cell of the path to the thief at cell (0, 3) is cell (1, 2). The distance between them is | 0 - 1 | + | 3 - 2 | = 2.\n- The closest cell of the path to the thief at cell (3, 0) is cell (3, 2). The distance between them is | 3 - 3 | + | 0 - 2 | = 2.\nIt can be shown that there are no other paths with a higher safeness factor.\n\n\n
\n
Constraints:
\n\n1 <= grid.length == n <= 400grid[i].length == ngrid[i][j] is either 0 or 1.grid.给你一个下标从 0 开始、大小为 n x n 的二维矩阵 grid ，其中 (r, c) 表示：
grid[r][c] = 1 ，则表示一个存在小偷的单元格grid[r][c] = 0 ，则表示一个空单元格你最开始位于单元格 (0, 0) 。在一步移动中，你可以移动到矩阵中的任一相邻单元格，包括存在小偷的单元格。
矩阵中路径的 安全系数 定义为：从路径中任一单元格到矩阵中任一小偷所在单元格的 最小 曼哈顿距离。
\n\n返回所有通向单元格 (n - 1, n - 1) 的路径中的 最大安全系数 。
单元格 (r, c) 的某个 相邻 单元格，是指在矩阵中存在的 (r, c + 1)、(r, c - 1)、(r + 1, c) 和 (r - 1, c) 之一。
两个单元格 (a, b) 和 (x, y) 之间的 曼哈顿距离 等于 | a - x | + | b - y | ，其中 |val| 表示 val 的绝对值。
\n\n
示例 1：
\n\n\n输入：grid = [[1,0,0],[0,0,0],[0,0,1]]\n输出：0\n解释：从 (0, 0) 到 (n - 1, n - 1) 的每条路径都经过存在小偷的单元格 (0, 0) 和 (n - 1, n - 1) 。\n\n\n
示例 2：
\n\n\n输入：grid = [[0,0,1],[0,0,0],[0,0,0]]\n输出：2\n解释：\n上图所示路径的安全系数为 2：\n- 该路径上距离小偷所在单元格（0，2）最近的单元格是（0，0）。它们之间的曼哈顿距离为 | 0 - 0 | + | 0 - 2 | = 2 。\n可以证明，不存在安全系数更高的其他路径。\n\n\n
示例 3：
\n\n\n输入：grid = [[0,0,0,1],[0,0,0,0],[0,0,0,0],[1,0,0,0]]\n输出：2\n解释：\n上图所示路径的安全系数为 2：\n- 该路径上距离小偷所在单元格（0，3）最近的单元格是（1，2）。它们之间的曼哈顿距离为 | 0 - 1 | + | 3 - 2 | = 2 。\n- 该路径上距离小偷所在单元格（3，0）最近的单元格是（3，2）。它们之间的曼哈顿距离为 | 3 - 3 | + | 0 - 2 | = 2 。\n可以证明，不存在安全系数更高的其他路径。\n\n
\n\n
提示：
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collections<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n \\u6ce8\\u610f Python 2.7 \\u5c06\\u57282020\\u5e74\\u540e\\u4e0d\\u518d\\u7ef4\\u62a4<\\/a>\\u3002 \\u5982\\u60f3\\u4f7f\\u7528\\u6700\\u65b0\\u7248\\u7684Python\\uff0c\\u8bf7\\u9009\\u62e9Python 3\\u3002<\\/p>\"],\"c\":[\"C\",\" \\u7248\\u672c\\uff1a \\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528 \\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n \\u5982\\u60f3\\u4f7f\\u7528\\u54c8\\u5e0c\\u8868\\u8fd0\\u7b97, \\u60a8\\u53ef\\u4ee5\\u4f7f\\u7528 uthash<\\/a>\\u3002 \\\"uthash.h\\\"\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5bfc\\u5165\\u3002\\u8bf7\\u770b\\u5982\\u4e0b\\u793a\\u4f8b:<\\/p>\\r\\n\\r\\n 1. 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