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>

using namespace std;

int P[10000];

// n個の頂点を初期化する
void init(int n) {
	for (int i = 0; i < n; i++) P[i] = i;
}

// 頂点の親の番号を返す
int root(int a) {
	if (P[a] == a) return a;
	return (P[a] = root(P[a]));
}

// 親(集合)が同じか判定する
bool is_same_set(int a, int b) {
	return root(a) == root(b);
}

// aとbを同一グループにまとめる
void unite(int a, int b) {
	P[root(a)] = root(b);
}

int main(void) {
	int n, q;
	cin >> n >> q;
	int com, x, y;
	init(n);
	while(q--) {
		cin >> com >> x >> y;
		if (com == 0) unite(x, y);
		else if (com == 1) cout << noboolalpha << is_same_set(x, y) << endl;
	}
}