Frieren is analyzing a magic barrier, whose strength at specific points can be represented as a 2D grid, $a$, with $N$ rows, $M$ columns, and unique values. Specifically, the strength of the barrier on the $r^{th}$ row and $c^{th}$ column is $a_{r,c}$. She asks you $Q$ questions in the form of $(k,r_1,c_1,r_2,c_2)$ and your task for each of them is to determine whether $k$ exists in the inclusive rectangle formed by $a_{r_1,c_1}$ and $a_{r_2,c_2}$.

Note: Fast input is highly recommended for this problem. Also, Python users should submit with PyPy as it is significantly faster.

Constraints

All values of $a_{r,c}$ are unique.

$1\le k,a_{r,c}\le {10}^9$

$1\le r_1\le r_2\le N$

$1\le c_1\le c_2\le M$

Subtask 1 [15%]

$1\le N,M,Q\le 10$

Subtask 2 [85%]

$1\le N,M\le 1000$

$1\le Q\le 2\times {10}^5$

Input Specification

The first line contains $3$ integers, $N$, $M$, and $Q$.

The next $N$ lines contain $M$ integers each, representing the barrier strength $a_{r,c}$.

The next $Q$ lines contain $5$ integers each, $k,r_1,c_1,r_2,c_2$.

Output Specification

For each question, output yes if the $k$ for that question exists in the given rectangle and no otherwise.

Sample Input 1

3 3 3
1 7 11
10 5 9
4 3 2
10 1 1 1 2
3 2 2 3 3
100 2 2 3 3

Sample Output 1

no
yes
no

Explanation for Sample Output 1

The rectangle for the first question is shown in blue. $10$ is not inside it.

The rectangle for the second question is shown in yellow. $3$ is inside it.

The rectangle for the third question is shown in yellow. $100$ is not inside it (it's not even in the grid).

Sample Input 2

2 3 2
1 2 3
4 5 6
1 1 1 1 1
1 2 2 2 3

Sample Output 2

yes
no