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<bits/stdc++.h>
using namespace std;

struct UnionFind{
  int n;
  vector<int> p,r;
  UnionFind(){}
  UnionFind(int sz):n(sz),r(sz,1),p(sz,0){iota(p.begin(),p.end(),0);}
  int find(int x){
    if(p[x]==x)return x;
    else return p[x]=find(p[x]);
  }
  void unite(int x,int y){
    x=find(x);
    y=find(y);
    if(r[x]<r[y])p[x]=y;
    else {
      p[y]=x;
      if(r[x]==r[y])r[x]++;

    }
  }
  bool same(int x,int y){
    return find(x)==find(y);
  }
};

int main(){
  int n,q;
  cin>>n>>q;
  UnionFind uf(n);
  for(int i=0;i<q;i++){
    int c,x,y;
    cin>>c>>x>>y;
    if(c)cout<<uf.same(x,y)<<endl;
    else uf.unite(x,y);
  }
  return 0;
}