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 CPP):

Solution:
#include<iostream>
using namespace std;
#include<vector>
struct UF{
	int n;
	vector<int>parent,rank;
	UF(int n_=0):n(n_),parent(n_),rank(n_,0)
	{
		for(int i=0;i<n_;i++)parent[i]=i;
	}
	int find(int a)
	{
		return parent[a]!=a?parent[a]=find(parent[a]):a;
	}
	bool same(int a,int b)
	{
		return find(a)==find(b);
	}
	bool unite(int a,int b)
	{
		a=find(a),b=find(b);
		if(a!=b)
		{
			if(rank[a]<rank[b])
			{
				parent[a]=b;
			}
			else
			{
				parent[b]=a;
				if(rank[a]==rank[b])rank[a]++;
			}
		}
		return a!=b;
	}
};
int main()
{
	int n,q;cin>>n>>q;
	UF uf(n);
	for(;q--;)
	{
		int p,a,b;cin>>p>>a>>b;
		if(p)cout<<uf.same(a,b)<<endl;
		else uf.unite(a,b);
	}
}