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 <vector>
#include <algorithm>
using namespace std;
struct UnionFind{
	vector<int> data;
	UnionFind(int size) : data(size, -1) {}
	bool unionSet(int x,int y){
		x=root(x);y=root(y);
		if(x==y)return 0;
		if(data[y]<data[x])swap(x,y);
		data[x]+=data[y],data[y]=x;
		return 1;
	}
	bool findSet(int x,int y){
		return root(x)==root(y);
	}
	int root(int x){
		return data[x]<0 ? x : data[x]=root(data[x]);
	}
	int size(int x){
		return -data[root(x)];
	}
};
int main(){
	int n,q,c,x,y;
	scanf("%d%d",&n,&q);
	UnionFind uf(n);
	for(;q--;c?printf("%d\n",uf.findSet(x,y)):uf.unionSet(x,y))scanf("%d%d%d",&c,&x,&y);
}