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EICON - Is connected?

Given a directed graph which contains n vertices (indexed from 1 to n) and m edges. Given q querries and each queries contains two integers a and b. For each queries, determine if there is an edge from a to b.

Input

The first line contains three integers  n, m, q (n, m, q<=10^5)

Each line in the next m lines contains two integers u and v which is an edge from v to u.

Each line in the next q lines contains two integers a and b (1 <= a, b <=n).

Output

For each query, output "Y" if there is a edge exists, otherwise output "N" (without the quote) in a single line.

Example

Input:
3 4 2
1 2
1 3
2 3
3 1
1 3
1 2
Output:
Y
N


Added by:Ha Minh Ngoc
Date:2015-12-23
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
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