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 \le 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 \le a, b \le 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

Example Output

Y
N