Problem:
Disjoint Set

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.

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.

Constraints

1 ≤ n ≤ 10000

1 ≤ q ≤ 100000

x ≠ y

Sample 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

Sample Output

0
0
1
1
1
0
1
1

Solution in C++ (judge verdict: Accepted)

#include<iostream>
#include<vector>
using namespace std;
class DisjointSet {
private:
	vector<int> rank, p;
public:
	DisjointSet(){}
	DisjointSet(int size) {
		rank.resize(size, 0);
		p.resize(size, 0);
		for(int i = 0; i < size; ++i ) makeSet(i);
	}
    void makeSet(int x) {
    	rank[x] = 0;
    	p[x] = x;
    }

    bool same(int x, int y) {
    	return findSet(x) == findSet(y);
    }
    int findSet(int x) {
    	if( x != p[x]) p[x] = findSet(p[x]);
    	return p[x];
    }
    void unite(int x, int y) {
    	int a = findSet(x);
    	int b = findSet(y);
    	if ( a != b ) {
    		if( rank[a] < rank [b] )
    			p[a] = b;
    		else {
    			p[b] = a;
    			if( rank[a] == rank[b] ) rank[a]++;
    		}
    	}
    }
};

int main(){
 	int n, q;
 	int c, x, y;
 	cin >> n >> q;
 	DisjointSet ds = DisjointSet(n);
 	while( q-- ) {
      cin >> c >> x >> y;
      if ( c == 0 ) ds.unite(x, y);
      else if( c == 1 ) {
      	if ( ds.same(x, y) ) cout << 1 << endl;
      	else cout << 0 << endl;
      }
 	}
 	return 0;
}