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:
import sys


class UnionFind:
    def __init__(self, max_size):
        self.max_size = max_size
        self.dat = [i for i in range(self.max_size)]

    def find(self, vertex):
        if self.dat[vertex] is vertex: return vertex
        self.dat[vertex] = self.find(self.dat[vertex])
        # print("searching : " + str(vertex))
        return self.dat[vertex]

    def merge(self, child, parent):
        """
        parentとchildをマージして、parentの所属にする
        :param parent:
        :param child:
        :return:
        """
        self.dat[self.find(child)] = self.dat[self.find(parent)]

    def is_same(self, v, w):
        """
        頂点vと頂点wが同じ集合に所属しているか
        :param v:
        :param w:
        :return:
        """
        return self.find(v) == self.find(w)


n, q = map(int, input().split())
uni = UnionFind(n)
sys.setrecursionlimit(114514)
while q > 0:
    q -= 1
    com, x, y = map(int, input().split())
    if com is 0:
        uni.merge(x, y)
    else:
        print(1 if uni.is_same(x, y) else 0)