Description

Given a simple undirected graph with $N$ vertices and $M$ edges, process a sequence of $K$ queries of two types:

• Delete an edge $e$
• Output whether there exists a path between vertex $v$ and $w$

Input

The first line of the input file contains the integers $N$, $M$ and $K$ ($1 \\leq N, M, K \\leq 10^5$), separated by a space.
The next $M$ lines describe the edges. The $i$-th of these lines describes edge $i$ and it contains the integers $a_i$ and $b_i$ ($1 \\leq a_i, b_i \\leq N$), separated by a space. Edge $i$ connects vertex $a_i$ and $b_i$. The vertices are labeled $1$ to $N$.
The next $K$ lines describe the queries. Each query is either of the following two forms:

• 0 e: delete an edge $e$ ($1 \\leq e \\leq M$, and each edge never appears twice)
• 1 v w: output whether there exists a path between $v$ and $w$ ($1 \\leq v, w \\leq N$)

Output

For each query of the 2nd type, print YES or NO, one per line, in the same order that the queries appear in the input file.

Sample Input

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

Sample Output

YES
NO
YES

Source Name

The First KMCMonthly Contest