Given a binary matrix with $n$ rows and $m$ columns. Find the maximum area submatrix with at most $k$ number $1$.
### Input
- The first line contains three integers $n, m,k$.
- The next $n$ lines, each line contains a binary string of length $n$.
### Output
- Print the area of the largest submatrix with at most $k$ number $1$.
### Constraints
- $1 \le n, m \le 500$.
- $1 \le k \le n \times m $.
### Example
Input:
```
3 3 2
100
100
001
```
Output:
```
6
```
