Given a directed graph includes ~n~ vertices (from ~1~ to ~n~) and ~m~ edges. Given ~q~ queries of two integers ~a~ and ~b~. For each query, you are allowed to remove at most one edge from the graph (you may choose not to remove any edge, or remove exactly one). After the removal, check if there is a path from ~a~ to ~b~ which visite at most one intermediate vertex.

Input

• The first line contains three integers ~n, m~ and ~q~ ~(n \le 10^4, m, q \le 10^5)~
• Each line in the next ~m~ lines contains two integer ~u~ and ~v~ which represented an edge from ~u~ to ~v~.
• Each line in the next ~m~ lines contains four integer ~a~ and ~b~ which represented two vertices and ~x~ and ~y~ which represented an edge from ~x~ to ~y~.

Output

• For each query, output in one line "Yes" if there is a path from a to b, otherwise output "No"

Example Input

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

Example Output

Yes
No