Path Existence Query

You are given a directed graph representing connections between servers. The graph has n servers and m directed edges. You are also given q queries. Each query asks whether there exists a path from a starting server to an ending server using the provided connections.

Formally, you are given integers \(n, m, q\) where \(n, m, q \in \mathbb{Z}^{+}\). Then you are given \(m\) pairs of integers \((u, v)\) representing a directed edge from server \(u\) to server \(v\). Finally, you are given \(q\) pairs of integers \((a, b)\) for which you need to determine if there exists a sequence of directed edges starting at \(a\) and ending at \(b\).

You should output "YES" if a path exists for a query, and "NO" otherwise.

inputFormat

The input is given via stdin and has the following format:

n m q
u1 v1
u2 v2
... (m lines in total)
a1 b1
a2 b2
... (q lines in total)

Here, the first line contains three integers: n (number of servers), m (number of directed connections), and q (number of queries). The next m lines each contain two integers \(u\) and \(v\) representing a directed edge from server \(u\) to server \(v\). The following q lines each contain two integers \(a\) and \(b\), representing a query to check if a path exists from server \(a\) to server \(b\).

outputFormat

For each query, output a single line to stdout. Print "YES" if a path exists from the starting server to the ending server, otherwise print "NO".

## sample

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

YES
NO
YES

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