Chessboard

Input

The first line contains two integers $n$ and $m$ (2 \leq n,m \leq 2000) — the number of rows and columns in the table.

Each of the next $n$ lines contains a string of length $m$, consisting only of the characters $0$ and $1$.

Output

Print one integer — the minimum number of operations needed to change cell values.

Examples

Note

In the first example, deleting the second row and the second column leaves a table with rows 01 and 10. No cell values need to be changed.

In the second example, you can delete the third row and the fifth column. In the remaining table, it is enough to change the cell in the third row and the first column from $1$ to $0$. It is impossible to obtain the required table without changing any cell values.

In the third example, no matter which row and column are deleted, a single cell containing $1$ remains. Its value must be changed to $0$.

Scoring

1. $30$ points — n,m \leq 20.

2. $50$ points — \min(n,m) \leq 20.

3. $120$ points — no additional constraints.