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.Arrays;
import java.util.List;
import java.util.Scanner;

// disjoin set
public class Main {
    static class UnionFind {

        private int parent[];
        private int rank[];

        public UnionFind(int Num_element) {
            parent = new int[Num_element];
            rank = new int[Num_element];
            for (int i = 0; i < Num_element; i++)
                makeSet(i);
        }
        public void makeSet(int x) {
            parent[x] = x;
            rank[x] = 0;
        }

        public void union(int x, int y) {
            link(findSet(x), findSet(y));
        }

        public int findSet(int x) {
            if (parent[x] != x) {
                parent[x] = findSet(parent[x]);
            }
            return parent[x];
        }


        public void link(int x, int y) {
            if (rank[x] > rank[y]) {
                parent[y] = x;
            } else {
                parent[x] = y;
                if (rank[x] == rank[y]) {
                    rank[y]++;
                }
            }
        }
        public void command(int com, int x, int y){
            if(com == 0){
                //unite
                union(x,y);
            }else{
                //same
                if( findSet(x) == findSet(y))
                    System.out.println("1");
                else
                    System.out.println("0");
            }
        }
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        // Disjoin set element number
        int Num_element = sc.nextInt();
        //Query times
        int Num_query =  sc.nextInt();
        
        UnionFind Disjoin_set = new UnionFind(Num_element);
        for (int i=0;i<Num_query;i++){
            // '0' denotes unite and '1' denotes same operation.
            int com = sc.nextInt();
            int x = sc.nextInt();
            int y = sc.nextInt();
            Disjoin_set.command(com,x,y);
        }

    }
}