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>
#include <vector>
using namespace std;

vector<int> S(100000, -1);

int main(){
	long n, q;
	cin >> n >> q;
	for (long i = 0; i < n; i++){
		S[i] = i;
	}
	for (long i = 0; i < q; i++){
		long c, x, y;
		cin >> c >> x >> y;
		if (c == 0){
			long sx = S[x];
			long sy = S[y];
			for (long j = 0; j < n; j++){
				if (S[j] == sx){
					S[j] = sy;
				}
			}
		}
		else {
			if (S[x] == S[y]){
				cout << "1" << endl;
			}
			else {
				cout << "0" << endl;
			}
		}
		// for (long j = 0; j < n; j++){
		// 	if (j != 0) cout << " ";
		// 	cout << j;
		// }
		// cout << endl;
	}
	return 0;
}