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 CPP):

Solution:
#include <stdio.h>

int main(void) {
  int i, j, k, n, q, c, x, y;
  scanf("%d%d", &n, &q);
  int u[n];
  for(i = 0; i < n; ++i) u[i] = i;
  for(i = 0; i < q; ++i) {
    scanf("%d%d%d", &c, &x, &y);
    if(c) {
      while(u[x] != x) x = u[x];
      while(u[y] != y) y = u[y];
      if(x == y) printf("1\n");
      else printf("0\n");
    } else {
      while(u[x] != x) x = u[x];
      while(u[y] != y) y = u[y];
      u[y] = x;
    }
  }
  return 0;
}