The first line of input consists of two integers $N$ and $Q$, where $1 \le N \le 1\, 000\, 000$ is the number of elements in the base set and $0 \le Q \le 1\, 000\, 000$ is the number of operations. Then follow $Q$ lines, one per operation. There are two types of operations:
“= $a$ $b$” indicate that the sets containing $a$ and $b$ are joined
“? $a$ $b$” is a query asking whether $a$ and $b$ belong to the same set
In both cases, $a$ and $b$ are distinct integers between $0$ and $N-1$.
For each query output a line containing “yes” if $a$ and $b$ are in the same set, and “no” otherwise.
Sample Input 1 | Sample Output 1 |
---|---|
10 4 ? 1 3 = 1 8 = 3 8 ? 1 3 |
no yes |
Sample Input 2 | Sample Output 2 |
---|---|
4 5 ? 0 0 = 0 1 = 1 2 = 0 2 ? 0 3 |
yes no |