Problem: 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.

Constraints

* 1 ≤ n ≤ 10000
* 1 ≤ q ≤ 100000
* x ≠ y

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.

Example

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


Output

0
0
1
1
1
0
1
1

Solution (in PYTHON3):

Solution:
class UnionFind():
    # 0, 1, ..., n - 1を要素とするn個の集合
    def __init__(self, n):
        self.rank = [0] * n # 木の根のみが持つ値
        self.par = list(range(n))

    # 木の根を求める
    def find(self, x):
        children = []
        while self.par[x] != x:
            children.append(x)
            x = self.par[x]

        for c in children:
            self.par[c] = x
        return x

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

    def union(self, x, y):
        if self.same(x, y):
            return
        rx = self.find(x)
        ry = self.find(y)
        if self.rank[rx] > self.rank[ry]:
            self.par[ry] = rx # yの根をxの根の子とする。
        elif self.rank[rx] == self.rank[ry]:
            self.par[ry] = rx
            self.rank[rx] += 1
        else:
            self.par[rx] = ry

n, q = [int(x) for x in input().split()]
uf = UnionFind(n)

for _ in range(q):
    cmd, x, y = [int(x) for x in input().split()]
    if cmd == 0: # unite
        uf.union(x, y)
    else: # same
        print(int(uf.same(x, y)))