TTIME

Problem

~N\;(1 \le N \le 1000)~ cows, conveniently numbered ~1~ ~...~ ~N~ all attend a tea time every day. ~M\;(1 \le M \le 2000)~ unique pairs of those cows have already met before the first tea time. Pair ~i~ of these cows who have met is specified by two differing integers ~A_i~ and ~B_i~ ~(1 \le A_i \le N; 1 \le B_i \le N)~. The input never indicates that cows have met each other more than once.

At tea time, any cow ~i~ and cow ~j~ who have met a mutual friend cow ~k~ will meet sometime during that tea time and thus expand their circle of known cows.

Determine whether ~Q\;(1 \le Q \le 100)~ pairs of cows have met after tea times are held for long enough that no new cow meetings are occurring. Query ~j~ consists of a pair of different cows ~X_j~ and ~Y_j~ ~(1 \le X_j \le N; 1 \le Y_j \le N)~.

For example, suppose that out of cows ~1~ through ~5~, we know that ~2~ has met ~5~, ~2~ has met ~3~, and ~4~ has met ~5~; see (a) below.

    2---3           2---3            2---3
     \              |\  |            |\ /|
1     \     -->  1  | \ |    -->  1  | X |
       \            |  \|            |/ \|
    4---5           4---5            4---5
     (a)             (b)              (c)

In the first tea time, cow ~2~ meets cow ~4~, and cow ~3~ meets cow ~5~; see (b) above. In the second tea time, cow ~3~ meets cow ~4~; see (c) above.

Input

In the first line of input, there will be three space separated integers ~N~, ~M~, and ~Q~.

In the next ~2~ to ~M + 1~ lines, line ~i+1~ will contain two integers separated by a space: ~A_i~ and ~B_i~

In the next ~M + 2~ to ~M + Q + 1~ lines, line ~j + M + 1~ will contain query ~j~ as two integers separated by a space: ~X_j~ and ~Y_j~

Output

The output will consist of the lines ~1~ to ~Q~, where the ~j~-th line should contain ~Y~ if the cows from the ~j~-th query have met, or ~N~ otherwise.

Example of Input - Output Files:

STDIN (ttime.in)

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

STDOUT (ttime.out)

Y
Y
N

Constraints

• ~1 \le N \le 1000~.
• ~1 \le M \le 2000~.
• ~1 \le Q \le 100~.
• Maximum execution time: ~1~ sec.
• Available memory : ~64~ MB.