Disjoint Sets Union

Implement disjont sets union data structure. You have to perform queries of two types:

• union u v - unite two sets that contain u and v respectively;

• get u v - check that two elements u and v belong to the same set.

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 5 * 10^5) - the number of elements and the number of queries. Next m lines contain queries, one per line.

For a query union the line looks like union u v (1 ≤ u, v ≤ n).

For a query get the line looks like get u v (1 ≤ u, v ≤ n).

Output

Print the result of each query get one per line in the respected order: "YES", if the elements belong to the same set, and "NO" otherwise.

Examples