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≤n,m≤500.
- 1≤k≤n×m.
### Example
Input:
332100100001
Output:
6