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.*;

class Main {
  static final int MAX = 10000;
  static int[] rank = new int[MAX];
  static int[] par = new int[MAX];
  static ArrayList<Integer> ansArr = new ArrayList<Integer>();

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int q = sc.nextInt();

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

    int com, x, y;
    for(int i = 0 ; i < q ; i++) {
      com = sc.nextInt();
      x = sc.nextInt();
      y = sc.nextInt();
      if(com == 0) unite(x, y);
      else same(x, y);
    }

    // 答え出力
    for(Integer ans: ansArr) System.out.println(ans);
  }

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

  static 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[y]++;
    }
  }

  static void same(int x, int y) {
    x = find(x);
    y = find(y);
    if(x == y) ansArr.add(1);
    else ansArr.add(0);
  }
}