Wait as Long as Possible before Escaping a Spreading Fire

### Problem You are given a rectangular `grid` in which `0` is grass, `1` is fire, and `2` is a wall. You start at the top-left grass cell and want to reach the bottom-right grass cell, the safehouse. You may first wait at the starting cell for a nonnegative number of minutes. Each minute after you start moving, move one cell north, south, east, or west onto grass; then the fire spreads one cell in those same directions through every non-wall cell. Walls block both you and the fire. Return the greatest initial waiting time that still lets you reach the safehouse safely. Return `-1` if leaving immediately cannot succeed, or `10^9` if you can wait arbitrarily long. Arriving at the safehouse in the same minute that fire reaches it is allowed; this exception does not apply to other cells. ```cpp class Solution { public: int maximumMinutes(vector<vector<int>>& grid); }; ``` ### Examples **Example 1:** ```text Input: grid = [[0,1],[0,0]] Output: -1 Explanation: The safehouse burns at minute 1, while the shortest walk needs two moves. ``` **Example 2:** ```text Input: grid = [[0,0],[2,0]] Output: 1000000000 Explanation: No fire exists. The two-step path remains safe after any initial wait. ``` ### Constraints - `2 <= m, n <= 300`, with `4 <= m*n <= 20000`. - Cells are 0, 1, or 2. - Both corner endpoints are 0. ### Clarifying Questions - Does fire spread while you wait at the start? Yes; you must remain safe there. - Can you enter a wall or an initially burning cell? No. - Is arrival at the same time as fire allowed anywhere else? No; only the safehouse has that exception. ```hint Check the boundary Separate the timing rule for an ordinary grass cell from the safehouse rule. Equality is permitted only at the destination. ```