**Physical Address**

304 North Cardinal St.

Dorchester Center, MA 02124

You are given a **0-indexed** 2D integer array `grid`

of size `m x n`

which represents a field. Each cell has one of three values:

`0`

represents grass,`1`

represents fire,`2`

represents a wall that you and fire cannot pass through.

You are situated in the top-left cell, `(0, 0)`

, and you want to travel to the safehouse at the bottom-right cell, `(m - 1, n - 1)`

. Every minute, you may move to an **adjacent** grass cell. **After** your move, every fire cell will spread to all **adjacent** cells that are not walls.

Return *the maximum number of minutes that you can stay in your initial position before moving while still safely reaching the safehouse*. If this is impossible, return

`-1`

. If you can `10`^{9}

.Note that even if the fire spreads to the safehouse immediately after you have reached it, it will be counted as safely reaching the safehouse.

A cell is **adjacent** to another cell if the former is directly north, east, south, or west of the latter (i.e., their sides are touching).

**Example 1:**

```
Input: grid = [[0,2,0,0,0,0,0],[0,0,0,2,2,1,0],[0,2,0,0,1,2,0],[0,0,2,2,2,0,2],[0,0,0,0,0,0,0]]
Output: 3
Explanation: The figure above shows the scenario where you stay in the initial position for 3 minutes.
You will still be able to safely reach the safehouse.
Staying for more than 3 minutes will not allow you to safely reach the safehouse.
```

**Example 2:**

```
Input: grid = [[0,0,0,0],[0,1,2,0],[0,2,0,0]]
Output: -1
Explanation: The figure above shows the scenario where you immediately move towards the safehouse.
Fire will spread to any cell you move towards and it is impossible to safely reach the safehouse.
Thus, -1 is returned.
```

**Example 3:**

```
Input: grid = [[0,0,0],[2,2,0],[1,2,0]]
Output: 1000000000
Explanation: The figure above shows the initial grid.
Notice that the fire is contained by walls and you will always be able to safely reach the safehouse.
Thus, 109 is returned.
```

**Constraints:**

`m == grid.length`

`n == grid[i].length`

`2 <= m, n <= 300`

`4 <= m * n <= 2 * 10`

^{4}`grid[i][j]`

is either`0`

,`1`

, or`2`

.`grid[0][0] == grid[m - 1][n - 1] == 0`

```
class Solution(object):
def maximumMinutes(self, A):
m, n = len(A), len(A[0])
inf = 10 ** 10
d = [[0,1],[1,0],[0,-1],[-1,0]]
fires = [[i, j, 0] for i in range(m) for j in range(n) if A[i][j] == 1]
A = [[inf if a < 2 else -1 for a in r] for r in A]
def bfs(queue, seen):
for i, j, t in queue:
if seen[i][j] < inf: continue
seen[i][j] = t
for di,dj in d:
x, y = i + di, j + dj
if 0 <= x < m and 0 <= y < n and seen[x][y] >= inf and t + 1 < A[x][y]:
queue.append([x, y, t + 1])
def die(t):
seen = [[inf + 10] * n for i in range(m)]
bfs([[0, 0, t]], seen)
return seen[-1][-1] > A[-1][-1]
bfs(fires, A)
A[-1][-1] += 1
return bisect_left(range(10**9 + 1), True, key=die) - 1
```

```
int[][] directions = new int[][]{{0,1},{0,-1},{1,0},{-1,0}};
public int maximumMinutes(int[][] grid) {
int m = grid.length, n = grid[0].length;
List<int[]> fires = new ArrayList<>();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (grid[i][j] == 1) {
fires.add(new int[]{i, j});
}
}
}
int l = -1, r = m * n;
while (l < r) {
int mid = l + (r - l) / 2 + 1;
if (reachable(grid, mid, fires)) l = mid;
else r = mid - 1;
}
return l == m * n ? (int) 1e9 : l;
}
boolean reachable(int[][] grid, int move, List<int[]> fires) {
int m = grid.length, n = grid[0].length;
int[][] copy = clone(grid);
Queue<int[]> fire = new LinkedList<>();
fire.addAll(fires);
while (!fire.isEmpty() && move-- > 0) {
if (spread(fire, copy)) return false;
}
Queue<int[]> person = new LinkedList<>();
person.add(new int[]{0, 0});
while (!person.isEmpty()) {
boolean onFire = spread(fire, copy);
if (spread(person, copy)) return true;
if (onFire) return false;
}
return false;
}
// return true if it spreads to safehouse
boolean spread(Queue<int[]> queue, int[][] grid) {
int m = grid.length, n = grid[0].length;
int size = queue.size();
while (size-- > 0) {
int[] cell = queue.remove();
for (int[] d : directions) {
int x = cell[0] + d[0] , y = cell[1] + d[1];
if (x == m - 1 && y == n - 1) return true;
if (x >= 0 && x < m && y >= 0 && y < n && grid[x][y] == 0) {
grid[x][y] = -1;
queue.add(new int[]{x, y});
}
}
}
return false;
}
int[][] clone(int[][] grid) {
int m = grid.length, n = grid[0].length;
int[][] copy = new int[m][n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
copy[i][j] = grid[i][j];
}
}
return copy;
}
```

```
int maximumMinutes(vector<vector<int>>& g) {
int m = g.size(), n = g[0].size();
deque<pair<int, int>> fire, person({{0, 0}});
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j)
if (g[i][j] == 1)
fire.push_back({i, j});
auto steps = [&](deque<pair<int, int>> &pos) {
vector<vector<int>> st(m, vector<int>(n));
while(!pos.empty()) {
auto [i, j] = pos.front();
pos.pop_front();
for (auto [di, dj] : vector<pair<int, int>>{{0, 1}, {1, 0}, {0, -1}, {-1, 0}}) {
int x = i + di, y = j + dj;
if (min(x, y) >= 0 && x < m && y < n && g[x][y] == 0 && st[x][y] == 0) {
st[x][y] = st[i][j] + 1;
pos.push_back({x, y});
}
}
}
return array<int, 3>{st[m - 1][n - 1], st[m - 2][n - 1], st[m - 1][n - 2]};
};
auto f = steps(fire), p = steps(person);
if (f[0] == 0 && p[0] != 0)
return 1000000000;
if (int diff = f[0] - p[0]; p[0] != 0 && diff >= 0)
return diff - (f[1] - p[1] <= diff && f[2] - p[2] <= diff);
return -1;
}
```

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