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:
// Disjoint Set: Union Find Tree

#include <iostream>

using namespace std;

const int mxn = 10000;
const int mxm = 100000;

int n, q, fa[mxn];

int find(int u) {
	if (fa[u] == u)
		return u;
	else
		return fa[u] = find(fa[u]);
}

void merge(int a, int b) {
	a = find(a);
	b = find(b);
	if (a != b)
		fa[a] = b;
}

bool check(int a, int b) {
	a = find(a);
	b = find(b);
	return a == b;
}

int main() {
	cin >> n >> q;
	for (int i = 0; i < n; ++i)
		fa[i] = i;
	for (int i = 0; i < q; ++i) {
		int k, u, v;
		cin >> k >> u >> v;
		if (k == 0)
			merge(u, v);
		else
			cout << check(u, v) << endl;
	}
	return 0;
}