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DSU - MarisaOJ: Marisa Online Judge

DSU

Time limit: 1000 ms
Memory limit: 256 MB

Given a graph of n vertices and no edge. There are q queries of either form:

  • 1 u v add an edge between u and v.
  • 2 u v determine whether u and v are connected.

Input

  • The first line contains 2 integers n,q.
  • The next q lines, each line contains 3 integers t,u,v, a query.

Output

  • For each query of type 2, print YES if u and v are connected, otherwise print NO.

Constraints

  • 1≤n,q≤105.
  • 1≤u,v≤n.

Example

Input:

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

Output:

YES
NO