Problem Statement

The Land of Zelkova is an island country consisting of $N$ islands. These $N$ islands are named island $1, \dots,$ island $N$.

Cherry-chan, a mermaid, can travel in both directions between island $a$ and island $b$ if and only if there exists an integer $i$ between $1$ and $M$, inclusive, such that $a=u_i, b=v_i$.

Cherry-chan, who easily gets lost, has decided to investigate for which pairs of a starting island and a destination island she is less likely to get lost.

Answer the following $Q$ questions. Here, the $q$-th question is given as a pair of integers $(x_q, y_q)$.

Question $q$

Does there exist exactly one sequence of integers $(p_0, p_1, \dots, p_k)$ satisfying all of the following conditions?

• $k \geq 1$
• $1 \leq p_i \leq N$
• $p_0=x_q, p_k=y_q$
• $p_0, p_1, \dots, p_k$ are all distinct.
• Cherry-chan can travel in both directions between island $p_{i-1}$ and island $p_i$.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $0 \leq M \leq \min(\frac{1}{2}N(N-1), 2 \times 10^5)$
• $1 \leq Q \leq 2 \times 10^5$
• $1 \leq u_i \leq N, 1 \leq v_i \leq N$
• $u_i \neq v_i$
• $i \neq j \Rightarrow (u_i, v_i) \neq (u_j, v_j), (u_i, v_i) \neq (v_j, u_j)$
• $1 \leq x_q \leq N, 1 \leq y_q \leq N$
• $x_q \neq y_q$
• All inputs are integers.

Input

$N$ $M$ $Q$
$u_1$ $v_1$
$\vdots$
$u_M$ $v_M$
$x_1$ $y_1$
$\vdots$
$x_Q$ $y_Q$

Output

The output consists of $Q$ lines. On the $q~(1 \leq q \leq Q)$-th line, print Yes if exactly one such sequence exists for question $q$, and No otherwise.

Do not forget the newline at the end.

Sample

Sample 1

Input

7 6 3
1 2
2 3
3 1
1 4
2 5
6 7
1 4
1 2
1 7

Output

Yes
No
No

Cherry-chan can travel between two islands connected by an arrow in the figure below.

• The $1$st question is $(x_1, y_1)=(1,4)$. Since $(1,4)$ is the only integer sequence satisfying the conditions, the answer is Yes.
• The $2$nd question is $(x_2, y_2)=(1,2)$. Since there exist two different integer sequences satisfying the conditions, $(1,2)$ and $(1,3,2)$, the answer is No.
• The $3$rd question is $(x_3 ,y_3)=(1,7)$. Since no integer sequence satisfying the conditions exists in the first place, the answer is No.

4 0 4
1 2
2 3
3 4
4 1

No
No
No
No

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

Yes
Yes
Yes
Yes
Yes