Union-Find Operations

You are given a union-find (disjoint set union) data structure. Your task is to implement two operations:

• Union: Merge the sets that contain two specified elements.
• Query: Determine if two elements are in the same set.

More formally, you start with \( n \) elements (numbered from 1 to \( n \)), each in its own set. There will be \( q \) operations. Each operation is either a union or a query. For a query operation, if the two elements are in the same set, output YES; otherwise, output NO.

The mathematical representation of the union-find data structure involves the following idea:

$$ \text{if } x,y \text{ are elements, then } find(x) = find(y) \Longleftrightarrow x \text{ and } y \text{ are in the same set.} $$

inputFormat

The first line contains two integers \( n \) and \( q \) \( (1 \leq n, q \leq 10^5) \) representing the number of elements and the number of operations, respectively.

Each of the following \( q \) lines contains an operation in one of the following formats:

• union x y — Merge the sets containing elements \( x \) and \( y \).
• query x y — Check if elements \( x \) and \( y \) belong to the same set.

It is guaranteed that \( 1 \leq x, y \leq n \).

outputFormat

For each query operation, output a single line containing either YES if the two elements are in the same set, or NO otherwise.

sample

5 5
union 1 2
union 3 4
query 1 2
query 1 3
query 3 4

YES
NO
YES

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