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>

int data[10001];
int rank[10001];

int find(int x){
  if(data[x] == x){
    return x;
  }else{
    data[x] = find(data[x]);
    return data[x];
  }
}

void Union(int x,int y){
  int a = find(x);
  int b = find(y);
  if(a != b){
    if(rank[a] > rank[b]){
      data[b] = a;
      rank[a]++;
    }else{
      data[a] = b;
      rank[b]++;
    }
  }
}

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

int main(){
  int n, q, com, x, y;
  std::cin >> n >> q;
  for(int i=0;i<=n;i++){
    data[i]=i;
  }
  while(std::cin >> com >> x >> y){
    if(com){
      std::cout<< Some(x,y) << std::endl;
    }else{
      Union(x,y);
    }
  }
  return 0;
}