Problem Description

During a treasure hunt game, Little G and Little H are exploring a series of $n$ rooms numbered $1, 2, \cdots, n$, with doors between adjacent rooms. Some of these doors are locked and require specific keys to open, while others can be opened directly. Little G informs Little H about where each key is located for each locked door (each lock has exactly one corresponding key). Little G then gives Little H $p$ instructions, each directing Little H to travel from room $S_i$ to room $T_i$. However, Little G might include dead ends in his instructions, and Little H wants to avoid unnecessary effort by checking if a path exists for each instruction beforehand.

Can you help Little H determine if a path exists for each instruction?

Input Format

The first line contains three numbers: $n, m, p$, representing the number of rooms, the number of locked doors, and the number of queries, respectively. The next $m$ lines each contain two numbers $x, y$, indicating that the key for the door between room $x$ and room $x+1$ is in room $y$. The following $p$ lines each contain two integers $S_i, T_i$, representing a query.

Output Format

Output $p$ lines, each containing either YES or NO, indicating whether a path exists or not.

Sample Input and Output

Sample Input #1

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

Sample Output #1

YES
NO
YES
YES
NO

Sample Input #2

7 5 4
2 2
3 3 
4 2 
5 3 
6 6
2 1
3 4
3 7
4 5

Sample Output #2

YES
YES
NO
NO

Notes

$1 \le n, p \le 10^6$, $0 \le m < n$, $1 \le x, y, S_i, T_i < n$. It is guaranteed that $x$ values are unique.

见题面 Input 部分

见题面 Output 部分