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 {
public:
    vector<int> par, rank;

    DisjointSet(int n) {
        par.resize(n, 0);
        rank.resize(n, 0);
        for (int i = 0; i < n; i++) {
            par[i] = i;
            rank[i] = 0;
        }
    }

    int find(int x) {
        if (par[x] == x) {
            return x;
        } else {
            return  par[x] = find(par[x]);
        }
    }

    void unite(int x, int y) {
        x = find(x);
        y = find(y);
        if (x == y) return;

        if (rank[x] < rank[y]) {
            par[x] = y;
        } else {
            par[y] = x;
            if (rank[x] == rank[y]) rank[x]++;
        }
    }

    bool same(int x, int y) {
        return find(x) == find(y);
    }
};

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

    DisjointSet ds = DisjointSet(n);

    for (int i = 0; i < q; i++) {
        int com, x, y;
        cin >> com >> x >> y;
        if (com == 0) {
            ds.unite(x, y);
        } else {
            if (ds.same(x, y)) {
                cout << 1 << endl;
            } else {
                cout << 0 << endl;
            }
        }
    }
    return 0;
}