650. Minimum Number of Flips to Convert Binary Matrix to Zero

Given a binary matrix mat, one flip toggles a chosen cell and its four direct neighbors. Return the minimum number of flips to turn the whole matrix into zeros, or -1 if impossible. The input is JSON {mat}.

Input: JSON {mat}.

Output: Integer — the minimum flips, or -1.

Examples

Input: {"mat":[[0,0],[0,1]]}
Output: 3
Explanation: Three flips clear the matrix.

Input: {"mat":[[0]]}
Output: 0
Explanation: Already zero.

Input: {"mat":[[1,0,0],[1,0,0]]}
Output: -1
Explanation: Cannot be cleared.

Constraints

• 1<=rows,cols<=3

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