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>
#include <vector>
using namespace std;


struct UnionFind {
  vector<int> par;
  UnionFind(int n) : par(n){
    for(int i = 0; n > i; i++)par[i] = i;
  }

  int root(int n){
    if(par[n] == n)return n;
    return par[n] = root(par[n]);
  }

  void unite(int a,int b){
    int ra = root(a);
    int rb = root(b);
    if(ra==rb)return;
    par[ra] = rb;
  }

  bool same(int a, int b){
    return root(a) == root(b);
  }
};

int main(){
    int n,q;cin>>n>>q;
    UnionFind a(n);
    for(int i = 0; q > i; i++){
        int x;cin>>x;
        int y,z;cin>>y>>z;
        if(x)cout << (a.same(y,z)?1:0) << endl;
        else a.unite(y,z);
    }
}