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>
using namespace std;

int P[10010];
void init(int N);
int root(int a);
bool is_same_set(int a,int b);
void unite(int a,int b);

int main() {
  int N,Q;
  cin >> N >> Q;
  init(N);
  for (int i=0;i<Q;++i) {
    int com,x,y;
    cin >> com >> x >> y;
    if (com==0)
      unite(x,y);
    else {
      if (is_same_set(x,y)==true)
	cout << 1 << endl;
      else
	cout << 0 << endl;
    }
  }
}

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

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

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

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