Description

$N (1 \leq N \leq 1000)$ cows, conveniently numbered $1 \dots N$ all attend a tea time every day. $M (1 \leq M \leq 2,000)$ 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 $B_i$ ($1 \leq A_i \leq N, 1 \leq B_i \leq N$). 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 $Q (1 \leq Q \leq 100)$ 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 $Y_j$ ($1 \leq X_j \leq N, 1 \leq Y_j \leq N$).

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 Format

Line $1$: Three space-separated integers: $N$, $M$, and $Q$.

Lines $2 \dots M+1$: Line $i+1$ contains two space-separated integers: $A_i$ and $B_i$.

Lines $M+2 \dots M+Q+1$: Line $j+M+1$ contains query $j$ as two space-separated integers: $X_j$ and $Y_j$.

Output Format

Lines $1 \dots Q$: Line $j$ should be Y if the cows in the $j$-th query have met and N if they have not met.

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

Y 
Y 
N