There's some unweighted graph with N nodes and M edges. You have to respond to queries of 3 forms:

Given some interval of nodes \( [l,r]\) , you need to add edges between every pair of these nodes (even if they are already connected by an edge)
You need to remove all edges added in the \(i^{th}\) query of type 1.
Given nodes u and v, you need to print the shortest path from u to v, or say that it doesn't exist.

Input Format:

First line of input contains the integers N and M.

The next M lines of input contain 2 space-separated integers u and v, indicating a bidirectional edge between nodes u and v. There can be multiple edges between the same pair of nodes, and edges starting and ending in the same node.

The next line contains the integer Q.

The next Q lines of input are of one of the following formats:

1 l r : perform the first query with the range \( [l,r] \).
2 i : remove all edges added in the \( i^{th}\) query of type 1.
3 u v : Print the length of the shortest path between nodes u and v.

It's guaranteed that for every query of type 2, the corresponding query of type 1 will appear before the type 2 query.

Output Format:

For every query of type 3, output a single line with a single integer: the requested shortest path length if it exists, or -1 if it doesn't.

Constraints :

\( 1 \le N \le 10^5 \)

\( 1 \le M \le 10^5 \)

\( 1 \le Q \le 10^4 \)

Number of queries of type \( 3 \le 3 \)