You are given an undirected graph that has ~n~ vertices and ~m~ edges. You are also given ~q~ queries, each of them contains two vertices ~a~ and ~b~. You should check if there is a path between ~a~ and ~b~.

Input

• The first line contains ~3~ integers ~n, m, q~ ~(0 < n, m ≤ 10^5)~.
• Each of the next ~m~ lines contains two integers ~u, v~ representing an edge connecting vertex ~u~ and vertex ~v~ ~(0 ≤ u, v < n)~.
• Each of the next ~q~ lines contains two integers ~a~ and ~b~, representing a query ~(0 ≤ a, b < n)~.

Output

• For each query, print YES if there is a path between two vertices, otherwise print NO. The output is case-sensitive.

Sample Input

5 4 3
0 1
1 2
2 3
0 3
1 3
1 0
0 4

Sample Output

YES
YES
NO

Notes

• https://drive.google.com/file/d/1Lu4JPqxvw8etw0d6OWHzeAVsqY0TJyAn/view?usp=sharing