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 Python3 (judge verdict: Accepted)

import sys

class UnionFind:
    def __init__(self, N:int):
        """N: 大きさ
        size: 連結成分の大きさ
        """
        self.par = [i for i in range(N)]
        self.size = [1]*N
        self.rank = [1]*N

    def root(self, x:int)->int:
        """根を求める"""
        if self.par[x] == x: # if root
            return x
        else:
            self.par[x] = self.root(self.par[x]) # 経路圧縮
            return self.par[x]

    def is_same(self, x:int, y:int)->bool:
        """x と y が同じ集合に属するか否か"""
        return self.root(x)==self.root(y)

    def unite(self, x:int, y:int):
        """y を x の属する集合に併合"""
        root_x = self.root(x)
        root_y = self.root(y)
        if root_x == root_y: return
        if self.rank[root_x] == self.rank[root_y]:
            self.rank[root_x] += 1
        elif self.rank[root_x]<self.rank[root_y]:
            root_x,root_y = root_y,root_x
        # 短いほう(y)を長いほう(x)にくっつける
        self.par[root_y] = root_x
        self.size[root_x] += self.size[root_y]
        self.size[root_y] = 0 # もういらない

    def get_size(self, x:int)->int:
        """xの属するグループのサイズ"""
        return self.size[self.root(x)]

if __name__ == "__main__":
    N,Q = map(int, sys.stdin.readline().split())
    UNITE,SAME = 0,1
    uf = UnionFind(N)
    for _ in range(Q):
        com,x,y = map(int, sys.stdin.readline().split())
        if com==UNITE:
            uf.unite(x, y)
        else: # same
            print(int(uf.is_same(x, y)))