Reachability Queries

• Time limit: 1.00 s
• Memory limit: 512 MB

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