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)

using System;
using System.Linq;
using System.Collections.Generic;
using System.IO;

public class Program{
    public static int[] array;
    public static int[] rank;
    public static void Main(){
        var reader = Console.In;
        var nq = reader.ReadLine().Split().Select(int.Parse).ToArray();
        int N = nq[0], Q = nq[1];
        array = Enumerable.Range(0, N).ToArray();
        rank = Enumerable.Repeat(1, N).ToArray();
        for(int i=0; i<Q; i++){
            var info = reader.ReadLine().Split().Select(int.Parse).ToArray();
            int query = info[0], a = info[1], b = info[2];
            if(query==0) Union(a, b);
            else{
                if(Same(a, b))Console.WriteLine("1");
                else Console.WriteLine("0");
            }
        }
    }

    //return the parrent of the group(array[target])
    public static int Find(int target){
        /*
        not root compression version
        while(target!=array[target]){
            target = array[target];
        }
        */
        //root compression version
        if(target!=array[target]){
            array[target] = Find(array[target]);
        }
        return array[target];
    }

    //if differ parrent of b from parrent of a
    public static void Union(int a, int b){
        var parent_a = Find(a);
        var parent_b = Find(b);
        if(parent_a!=parent_b){
            //join lower rank side to heigher
            if(rank[parent_a]<rank[parent_b]){
                array[parent_a] = parent_b;
            }else{
                array[parent_b] = parent_a;
                //update rank of lower side
                rank[parent_a]++;
            }
        }
    }

    //parrent of a and thats b is same?
    public static bool Same(int a, int b){
        if(Find(a)!=Find(b))return false;
        return true;
    }
}