Given a binary matrix A of n rows and m columns.
You can do the following operation on the matrix:
- Select a row or a column and reverse every numbers on that row or column (.i.e 1 turn into 0, and 0 turn into 1).
You are given q queries of form (a,b,c,d). Determine if the submatrix with upper-left corner at (a,b) and lower-right corner at (c,d) can be transformed into a matrix full of 0 by applying the above operation?
### Input
- The first line contains 3 integers n,m,q.
- The next n lines, each line contains a binary string of length m.
- The next q lines, each line contains 4 integers a,b,c,d, a query.
### Output
- For each query, print YES if the submatrix can be transformed into a matrix full of 0, otherwise print NO.
### Constraints
- 1≤n,m≤500.
- 1≤q≤105.
- 1≤a,c≤n.
- 1≤b,d≤m.
### Example
Input:
333101001110213222331123
Output:
YESYESNO