Problem:
Disjoint Set

Write a program which manipulates a disjoint set S = {S1, S2, . . . , Sk}.

First of all, the program should read an integer n, then make a disjoint set where each element consists of 0, 1, ... n−1 respectively.

Next, the program should read an integer q and manipulate the set for q queries. There are two kinds of queries for different operations:

unite(x, y): unites sets that contain x and y, say Sx and Sy, into a new set.

same(x, y): determine whether x and y are in the same set.

Input

n q
com1 x1 y1
com2 x2 y2
...
comq xq yq

In the first line, n and q are given. Then, q queries are given where com represents the type of queries. '0' denotes unite and '1' denotes same operation.

Output

For each same operation, print 1 if x and y are in the same set, otherwise 0, in a line.

Constraints

1 ≤ n ≤ 10000

1 ≤ q ≤ 100000

x ≠ y

Sample Input

5 12
0 1 4
0 2 3
1 1 2
1 3 4
1 1 4
1 3 2
0 1 3
1 2 4
1 3 0
0 0 4
1 0 2
1 3 0

Sample Output

0
0
1
1
1
0
1
1

Solution in Go (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

const (
	COMMAND_UNITE = iota
	COMMAND_SAME
)

func main() {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)

	nItems := scanInt(sc)
	nQueries := scanInt(sc)

	roots := make([]int, nItems)
	for i := 0; i < nItems; i++ {
		roots[i] = i
	}

	// 各木構造の高さを保持する。
	ranks := make([]int, nItems)

	findRoot := func(x int) int {
		for roots[x] != x {
			x = roots[x]
		}
		return x
	}

	w := bufio.NewWriter(os.Stdout)
	for i := 0; i < nQueries; i++ {
		command := scanInt(sc)
		x, y := scanInt(sc), scanInt(sc)
		rx := findRoot(x)
		ry := findRoot(y)

		switch command {
		case COMMAND_UNITE:
			// なるべく木の高さを抑えるため、より高い木を unite 後のルートに選ぶ。
			if ranks[rx] > ranks[ry] {
				roots[ry] = rx
			} else if ranks[rx] < ranks[ry] {
				roots[rx] = ry
			} else {
				roots[rx] = ry
				ranks[ry] += 1
			}
		case COMMAND_SAME:
			if findRoot(x) == findRoot(y) {
				fmt.Fprintln(w, 1)
			} else {
				fmt.Fprintln(w, 0)
			}
		}
	}
	w.Flush()
}

func scanInt(sc *bufio.Scanner) int {
	sc.Scan()
	v, _ := strconv.Atoi(sc.Text())
	return v
}