Reachability Queries

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