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<cstdio>
#include<algorithm>
using namespace std;
struct UF{
  int a[10001];
  void init(int x){
    for(int i=0;i<x;i++) a[i] = i;
  }
  void unite(int x,int y){
    int ax = find(x);
    int ay = find(y);
    if(ax > ay) a[ax] = ay;
    if(ay > ax) a[ay] = ax;
  }
  int find(int x){
    if(x != a[x]) a[x] = find(a[x]);
    return a[x];
  }
};
int main(){
  int n,q,b,c,d;
  UF uf;
  scanf("%d %d",&n,&q);
  uf.init(n);
  while(q--){
    scanf("%d %d %d",&b,&c,&d);
    if(b == 0) uf.unite(c,d);
    if(b == 1) printf("%d\n",uf.find(c)==uf.find(d));
  }
  return 0;
}