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.ArrayList;
import java.util.Scanner;

public class Main{
    public static void main(String[] args) {
        Scanner stdIn = new Scanner(System.in);

        int n = stdIn.nextInt();
        int q = stdIn.nextInt();

        int[] uf = new int[n];

        init_uf(uf);

        int p, a, b;
        for(int i=0; i<q; i++){
            p = stdIn.nextInt();
            a = stdIn.nextInt();
            b = stdIn.nextInt();

            if(p == 0){
                if(search_root(a, uf) != search_root(b, uf)){
                    union_group(a, b, uf);
                }
            }else{
                if(search_root(a, uf) == search_root(b, uf)){
                    System.out.println("1");
                }else{
                    System.out.println("0");
                }
            }
        }
    }

    static void init_uf(int[] uf){
        for(int i=0; i<uf.length; i++){
            uf[i] = i;
        }
    }

    static int search_root(int f, int[] uf){
        ArrayList<Integer> list = new ArrayList<Integer>();
        int idx = f;
        while(idx != uf[idx]){
            list.add(idx);
            idx = uf[idx];
        }
        // ツリー圧縮
        while(!list.isEmpty()){
            int item = list.remove(0);
            uf[item] = idx;
        }
        return idx;
    }

    static void union_group(int f1, int f2, int[] uf){
        int root1 = search_root(f1, uf);
        int root2 = search_root(f2, uf);
        uf[root2] = root1;
    }
}