Kingdom Connectivity

You are given a kingdom with n cities and n-1 bidirectional roads connecting them. The capital city is city 1. Initially, the cities are connected by the given roads forming a tree.

You need to process Q queries. There are three types of queries:

• 0 x: Check if city x is reachable from the capital. If it is, output YES d where d is the number of roads (edges) used in the shortest path; otherwise, output NO.
• 1 a b: Close the road between cities a and b. After a road is closed, it cannot be used for travel.
• 2 a b: Reopen the road between cities a and b. The road becomes available for travel again.

It is guaranteed that initially the roads form a tree and every query of type 0, 1, or 2 is valid. Note that the distance is defined as the number of edges in the shortest path, i.e. \(d\) satisfies \(d=\text{number of roads}\).

Input/Output must be handled through standard input (stdin) and standard output (stdout).

inputFormat

The first line contains an integer n representing the number of cities.

The next n-1 lines each contain two space‐separated integers a and b representing a road between cities a and b.

The following line contains an integer Q denoting the number of queries.

The next Q lines describe the queries. Each query is in one of the following formats:

• 0 x
• 1 a b
• 2 a b

All numbers are separated by spaces or newlines.

outputFormat

For each query of type 0, output a single line containing the answer. If the city is reachable from the capital, output YES d where d is the minimum number of roads; otherwise, output NO.

## sample

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

YES 2
NO

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