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 <cstdio>
#include <set>
using namespace std;
class union_find{
	int *parent,n;
public:
	int root(int a){return parent[a]==a?a:(parent[a]=root(parent[a]));}
	union_find(int _n){n=_n;parent=new int[n];for(int i=0;i<n;i++)parent[i]=i;}
	~union_find(){delete []parent;}
	int same(int a,int b){return root(a)==root(b);}
	int unite(int a,int b){
		int x=root(a),y=root(b);
		if(x==y)return 0;
		parent[x]=y;
		return 1;
	}
	int size(){
		set<int>s;
		for(int i=0;i<n;i++)s.insert(root(i));
		return s.size();
	}
};
int main(){
	int n,q,c,x,y;
	scanf("%d%d",&n,&q);
	union_find uf(n);
	for(;q--;c?printf("%d\n",uf.same(x,y)):uf.unite(x,y))scanf("%d%d%d",&c,&x,&y);
}