DSU

In Uzlandia, there are n cities, numbered from 1 to n. Initially, there are no roads connecting these cities, but roads will be constructed over time.

Tourist Vasyl has asked you to handle q queries of two types:

1. 1 a b - Construct a bidirectional road between cities a and b.

2. 2 a b - Determine if it's possible to travel from city a to city b using the existing roads. Output "YES" if travel is possible, otherwise output "NO".

Input

The first line contains the integers n and q. (1 ≤ n, q ≤ 2 \times 10^5)

The following q lines contain the queries.

Output

Provide the answers for each query of type 2.

Examples