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 $a$ ?"

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 $a$ ?"

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

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