You are given an m x n grid where each cell can have one of three values:
Every minute, any fresh orange that is $4$-directionally adjacent to a rotten orange becomes rotten.
Return the minimum number of minutes that must elapse until no cell has a fresh orange. If this is impossible, return $-1$.
Example 1
Input: grid = $[[2,1,1],[1,1,0],[0,1,1]]$
Output: $4$
Example 2:
Input: grid = $[[2,1,1],[0,1,1],[1,0,1]]$
Output: $-1$
Explanation: The orange in the bottom left corner (row $2$, column $0$) is never rotten, because rotting only happens $4$-directionally.
Example 3:
Input: grid = $[[0,2]]$
Output: $0$
Explanation: Since there are already no fresh oranges at minute 0, the answer is just 0.
Constraints:
$m$ == grid.length
$n$ == grid[$i$].length
$1 \le m, n \le 10$
grid[$i$][$j$] is $0$, $1$, or $2$.
Solve $x^3-3x+1=0$.
Simplify: $\left(\frac{1-\sqrt{5}}{2}\right)^{12}$.