Given a m x n binary matrix mat. In one step, you can choose one cell and flip it and all the four neighbours of it if they exist (Flip is changing 1 to 0 and 0 to 1). A pair of cells are called neighboors if they share one edge.

Return the minimum number of steps required to convert mat to a zero matrix or -1 if you cannot.

Binary matrix is a matrix with all cells equal to 0 or 1 only.

Zero matrix is a matrix with all cells equal to 0.

Example 1:

Input: mat = [[0,0],[0,1]]
Output: 3
Explanation: One possible solution is to flip (1, 0) then (0, 1) and finally (1, 1) as shown.


Example 2:

Input: mat = []
Output: 0
Explanation: Given matrix is a zero matrix. We don't need to change it.


Example 3:

Input: mat = [[1,1,1],[1,0,1],[0,0,0]]
Output: 6


Example 4:

Input: mat = [[1,0,0],[1,0,0]]
Output: -1
Explanation: Given matrix can't be a zero matrix


Constraints:

• m == mat.length
• n == mat.length
• 1 <= m <= 3
• 1 <= n <= 3
• mat[i][j] is 0 or 1.

Time complexity: O(2^(m*n))
Space complexity: O(2^(m*n))

## C++

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