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:
public class
Main
{
  int[ ] a;

  private void
  unite (
    int x,
    int y
    )
  {
    if ( a[ y ] != y )
      unite ( x, a[ y ] );
    else
      a[ y ] = x;
  }

  private int
  getRepresentation (
    int x
    )
  {
    if ( a[ x ] == x )
      return ( x );

    a[ x ] = getRepresentation ( a[ x ] );
    return ( a[ x ] );
  }

  private boolean
  same (
    int x,
    int y
    )
  {
    return ( getRepresentation ( x ) == getRepresentation ( y ) );
  }

  public void
  run (
    java.io.InputStream in,
    java.io.PrintStream out
    )
  {
    java.util.Scanner sc = new java.util.Scanner ( in );
    int n, q;
    int i;

    n = sc.nextInt ( );
    q = sc.nextInt ( );

    a = new int[ n ];
    for ( i = 0; i < n; ++i )
      a[ i ] = i;

    for ( i = 0; i < q; ++i )
    {
      int c, x, y;

      c = sc.nextInt ( );
      x = sc.nextInt ( );
      y = sc.nextInt ( );
      if ( c == 0 )
      {
        if ( !same ( x, y ) )
          unite ( x, y );
      }
      else
        System.out.println ( same ( x, y ) ? "1" : "0" );
    }

    sc.close ( );
  }

  public static void
  main (
    String[ ] args
    )
  {
    ( new Main ( ) ).run ( System.in, System.out );
  }
}