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;
int s[10000];
vector<int>v[10000];
int main(void) {
	int n;
	cin >> n;
	for (int i = 0; i < n; i++) {
		s[i] = i;
		v[i].push_back(i);
	}
	int m;
	cin >> m;
	for (int i = 0; i < m; i++) {
		int k;
		cin >> k;
		if (k) {
			int a, b;
			cin >> a >> b;
			cout << (s[a] == s[b]) << endl;
		}
		else {
			int a, b;
			cin >> a >> b;
			a = s[a];
			b = s[b];
			if (a == b) continue;
			for (int j = 0; j < v[b].size(); j++) {
				v[a].push_back(v[b][j]);
				s[v[b][j]] = a;
			}
		}
	}
}