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;

static const int MAX = 10000;

int P[MAX], H[MAX];

void unite(int u1, int u2) {
	while (P[u1] != u1) u1 = P[u1];
	while (P[u2] != u2) u2 = P[u2];
	if (H[u1] < H[u2]) P[u1] = u2;
	else if (H[u1] > H[u2]) P[u2] = u1;
	else {
		P[u2] = u1;
		H[u1]++;
	}
} 

int same(int n1, int n2) {
	while (P[n1] != n1) n1 = P[n1];
	while (P[n2] != n2) n2 = P[n2];
	if (n1 == n2) return 1;
	else return 0;
}

int main() {
	int n, q;
	cin >> n >> q;
	for (int i = 0; i < n; i++)	{
		P[i] = i;
		H[i] = 0;
	}

	for (int i = 0 ; i < q; i++) {
		int cmd, f, s;
		cin >> cmd >> f >> s;
		if (cmd) cout << same(f, s) << endl;
		else unite(f, s);
	}
	return 0;
}