K. Distinctness Queries

You are given a matrix with $n$ rows and $m$ columns. You will have to answer $q$ queries of the following type:

• i1 j1 i2 j2 — in the submatrix whose top-left corner is $(i1,j1)$ and its bottom-right corner is $(i2,j2)$, are all of the elements distinct?

Input

The first line of input contains two integers $n$ and $m$ ($1 \le n,m,n \cdot m \le 10^5$) — the height, and width, of the matrix, respectively.

Each of the next $n$ lines of input contain $m$ integers $a_{i,1},a_{i,2},\ldots,a_{i,m}$ ($1 \le a_{i,j} \le n \cdot m$) — the elements of the $i$-th row of the given matrix.

The next line contains a single integer $q$ ($1 \le q \le 10^5$) — the number of queries.

Each of the following $q$ lines contain $4$ integers $i_1$, $j_1$, $i_2$, $j_2$ ($1 \le i_1 \le i_2 \le n$, $1 \le j_1 \le j_2 \le m$) — the submatrix's corner cells' coordinates.

Output

For each query, print YES, if all of the elements of the given submatrix are distinct, or NO, otherwise.

Example 1

stdin

2 2
2 1
3 2
9
1 1 1 1
1 2 1 2
2 1 2 1
2 2 2 2
1 1 1 2
2 1 2 2
1 1 2 1
1 2 2 2
1 1 2 2

stdout

YES
YES
YES
YES
YES
YES
YES
YES
NO

Example 2

stdin

4 6
1 4 7 1 2 3
2 5 8 6 5 4
3 6 9 7 8 9
1 2 3 4 5 6
10
1 1 3 3
1 4 3 6
1 1 4 6
1 2 4 3
2 1 3 4
4 1 4 6
1 4 4 4
2 5 4 5
2 1 2 6
4 6 4 6

stdout

YES
YES
NO
YES
NO
YES
YES
NO
NO
YES