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 <bits/stdc++.h>
using namespace std;

int n,q;
int p[10005];

int find(int x) {
    return p[x]<0?x:p[x]=find(p[x]);
}

void uni(int x,int y) {
    if ((x=find(x))==(y=find(y))) return;
    if (p[y]<p[x]) swap(x,y);
    if (p[x]==p[y]) --p[x];
    p[y]=x;
}

int main() {
    ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0);
    cin>>n>>q;
    memset(p,-1,sizeof p);
    while (q--) {
        int f,x,y; cin>>f>>x>>y;
        if (f==0) uni(x,y);
        else cout<<(find(x)==find(y))<<'\n';
    }
}