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)

# Disjoint Set: Union Find Tree
class UnionFind:
    def __init__(self, N):
        self.N = N  # ノード数
        # 最初は全てが根であるとして初期化        
        self.parent = [-1] * N  # idxが各ノードのid, 値がそのノードの親ノードのid
        self.rank = [0] * N # idxが各ノードのid, 値がそのノードの集合における高さ

    def root(self, x):  # ノードのidを受け取って一番上の親ノードのidを帰す
        if (self.parent[x] < 0):
            return x
        self.parent[x] = self.root(self.parent[x])  # 経由したノードすべての親を上書き（経路圧縮）
        return self.parent[x]

    def unite(self, x, y): # ノード番号を2つ受け取って、そのノード同士をつなげる処理を行う。
        # 引数のノードを直接つなぐ代わりに、親同士を連結する処理にする。
        rx = self.root(x) # xの根をrx
        ry = self.root(y) # yの根をry
        if (rx == ry): # xとyの根が同じ(=同じ木にある)時はそのまま
            return False

        if (self.rank[rx] > self.rank[ry]): # 高い方に低い方をつなぐ
            self.parent[ry] = rx
        else:
            self.parent[rx] = ry
            if (self.rank[rx] == self.rank[ry]):
                self.rank[ry] += 1

        return True

    def same(self, x, y):
        return self.root(x) == self.root(y)

N, Q = map(int, input().split())
ds = UnionFind(N)
for _ in range(Q):
    com, x, y = map(int, input().split())
    if com == 0:
        # unite
        ds.unite(x, y)
    elif com == 1:
        # same?
        print(1 if ds.same(x, y) else 0)