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:
//HOME- DSL-DSL_1-A

#include <stdio.h>
#include <iostream>
#include <algorithm>

using namespace std;

struct List {
  int num;
  int type;
};

int main(void) {
  int n, q, com, x, y, i, j;

  cin >> n >> q;

  List l[n];

  for(i = 0; i < n; i++) {
    l[i].num = i;
    l[i].type = i;
  }

  for(i = 0; i < q; i++) {
    cin >> com >> x >> y;

    if(com)
      if(l[x].type == l[y].type)
	printf("1\n");
      else
	printf("0\n");
    else {
      int s, t;
      s = min(l[x].type, l[y].type);
      t = max(l[x].type, l[y].type);
      for(j = 0; j < n; j++)
	if(l[j].type == t)
	  l[j].type = s;
    }
  }

  return 0;
}