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 <algorithm>
#include <vector>
using namespace std;

class UnionFind
{
private:
	vector<int> par;
public:
	UnionFind(int n) : par(n) 
	{
		for (int i = 0; i < par.size(); i++) par[i] = i;
	}
	int root(int x)
	{
		return (par[x] == x ? x : par[x] = root(par[x]));
	}
	bool isSame(int x, int y)
	{
		return root(x) == root(y);
	}
	void unite(int x, int y)
	{
		x = root(x);
		y = root(y);
		par[x] = y;
	}
};


int main()
{
	int n, q;
	cin >> n >> q;
	UnionFind unionFind(n);

	while (q--)
	{
		int order, x, y;
		cin >> order >> x >> y;
		if (order == 0) unionFind.unite(x, y);
		if (order == 1) cout << unionFind.isSame(x, y) << endl;
	}

	return 0;
}