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 JAVA):

Solution:

import java.util.*;
public class Main {

    private static List<Set<Integer>> setList = new ArrayList<Set<Integer>>();
    public static void main(String[] args) {
        //System.out.println(new App().getGreeting());
        Scanner s = new Scanner(System.in);
        int num = s.nextInt();
        int query = s.nextInt();

        //初期セット完了
        //命令処理開始
        for(int i=0;i<query;i++)
        {
            boolean result=false;
            switch(s.nextInt())
            { 
                case 0:
                    result = unite(s.nextInt(),s.nextInt());
                break;
                case 1:
                    result = same(s.nextInt(),s.nextInt());
                    System.out.println(result?1:0);
                break; 
            }
        }
    }
    private static boolean unite(int x,int y)
    {
        Set<Integer> xSet =null;
        Set<Integer> ySet =null;
        for(Set<Integer> tmpSet:setList)
        {
            //xが含まれているか？
            if(tmpSet.contains(x))
            {
                xSet = tmpSet;
                if(ySet!=null)
                {
                    break;
                }
            }
            //yが含まれているか？
            if(tmpSet.contains(y))
            {
                ySet = tmpSet;
                if(xSet!=null)
                {
                    break;
                }
            }
        }
        if(xSet==null&&ySet==null)
        {
            Set<Integer>tmpHashSet = new HashSet<Integer>();
            tmpHashSet.add(x);
            tmpHashSet.add(y);
            setList.add(tmpHashSet);
            return true;
        }
        if(xSet==null){
            ySet.add(x);
            return false;
        }
        if(ySet==null){
            xSet.add(y);
            return false;
        }
        if(xSet.equals(ySet))return false;
        //xSetもySetもnullではない
        xSet.addAll(ySet);
        setList.remove(ySet);
        return true;
    }
    private static boolean same(int x,int y)
    {
        for(Set<Integer> tmpSet:setList)
        {
            //xが含まれているか？
            if(tmpSet.contains(x))
            {
                if(tmpSet.contains(y))
                {
                    return true;
                }
                else
                {
                    return false;
                }
            }
        }
        return false;
    }
}