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:
class Main
{
	static int[] pointer;
	static int[] rank;
	
	public static void main( String[] args )
	{
		java.util.Scanner sc = new java.util.Scanner( System.in );
		
		int n = sc.nextInt();
		int q = sc.nextInt();
		
		pointer = new int[n];
		rank    = new int[n];
		for( int a = 0 ; a < n ; a++ )
		{
			pointer[a] = a;
			rank[a]    = 0;
		}
		
		char sw;
		int x,y;
		for( int a = 0 ; a < q ; a++ )
		{
			sw = ( sc.next().toCharArray()[0] );
			x  = sc.nextInt();
			y  = sc.nextInt();
			switch( sw )
			{
				case '0' : 
					union( x, y );
					break;
				case '1' :
					if( isSame( x, y ) )System.out.println( 1 );
					else System.out.println( 0 );
					break;
			}
		}
	}
	static int findRoot( int x )
	{
		if( x != pointer[x] )
			pointer[x] = findRoot( pointer[x] );
		return pointer[x];
	}
	static boolean isSame( int x, int y )
	{
		if( findRoot( x ) == findRoot( y ) )return true;
		return false;
	}
	static void union( int x, int y )
	{
		link( findRoot( x ), findRoot( y ) );
	}
	static void link( int x, int y )
	{
		if( !isSame( x, y ) )
		{
			if( rank[x] < rank[y] )
			{
				pointer[x] = y;
			}else if( rank[x] > rank[y] )
			{
				pointer[y] = x;
			}else
			{
				pointer[x] = y;
				rank[y]++;
			}
		}
	}
}