A directed graph consists of n nodes and m edges. The edges are numbered 1,2,\dots,n.

Your task is to answer q queries of the form "can you reach node b from node a?"

Input

The first input line has three integers n, m and q: the number of nodes, edges and queries.

Then there are m lines describing the edges. Each line has two distinct integers a and b: there is an edge from node a to node b.

Finally there are q lines describing the queries. Each line consists of two integers a and b: "can you reach node b from node a?"

Output

Print the answer for each query: either "YES" or "NO".

Constraints

• 1 \le n \le 5 \cdot 10^4
• 1 \le m,q \le 10^5

Example

Input:

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

Output:

YES
NO
YES