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
- $1 \le n, m \le 500$.
- $1 \le q \le 10^5$.
- $1 \le a, c \le n$.
- $1 \le b, d \le m$.
### Example
Input:
```
3 3 3
101
001
110
2 1 3 2
2 2 3 3
1 1 2 3
```
Output:
```
YES
YES
NO
```
