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 P[100000];
void init(int n);
int root(int n);
void unite(int a, int b);
bool is_in_the_same_tree(int a, int b);

using namespace std;
int main(){
  int n, q, com, x, y;
  cin >> n >> q;
  init(n+1);
  for (int i = 0; i < q; ++i){
    cin >> com >> x >> y;
    if(com==0){unite(x, y);}
    else if(com==1){cout<<is_in_the_same_tree(x,y)<<endl;}
  }
}

void init(int n){
  for (int i = 0; i < n; ++i){P[i] = i;}
}

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

void unite(int a, int b){
  P[root(a)] = root(b);
}

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