You are given an m x n grid where each cell can have one of three values:

• $0$ representing an empty cell,
• $1$ representing a fresh orange, or
• $2$ representing a rotten orange.

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: $\left(\frac{1-\sqrt{5}}{2}\right)^{12}$.