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

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