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;

int uf[10101];

void init(int n)
{
  for (int i = 1; i <= n; i++){
    uf[i] = i;
  }
}

int root(int x)
{
  if (uf[x] == x) return x;

  return uf[x] = root(uf[x]);
}

void unite(int x, int y)
{
  int rx = root(x),
      ry = root(y);
  uf[ry] = rx;
}

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

int main()
{
  int n, q;
  cin >> n >> q;

  init(n);

  for (int i = 0; i < q; i++){
    int f, x, y;
    cin >> f >> x >> y;

    if (f){
      cout << same(x, y) << endl;
    } else {
      unite(x, y);
    }
  }
}