Problem:
Disjoint Set

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.

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.

Constraints

1 ≤ n ≤ 10000

1 ≤ q ≤ 100000

x ≠ y

Sample 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

Sample Output

0
0
1
1
1
0
1
1

Solution in C (judge verdict: Accepted)

#include <stdio.h>          // printf(), scanf()
#include <stdbool.h>

#define MAX_N 10000

int par[MAX_N + 1];
int rank[MAX_N + 1];

void
init_union_find(int n)
{
	int i;

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

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

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[x]++;
	}
}

bool
same(int x, int y)
{
	return find(x) == find(y);
}

int
main(int argc, char** argv)
{
	int n, q;
	int c, x, y;

	scanf("%d %d", &n, &q);
	init_union_find(n);
	while (q--)
	{
		scanf("%d %d %d", &c, &x, &y);
		if (c == 0)
			unite(x, y);
		else
			printf("%d\n", same(x, y) ? 1 : 0);
	}

	return 0;
}