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 <algorithm>

int uf[100010];
void inituf(int n){ for(int i = 0; i < n; i++) uf[i] = -1; }
int find(int x){ return uf[x] < 0 ? x : uf[x] = find(uf[x]); }
void unite(int x, int y){ if((x = find(x)) != (y = find(y))){ uf[x] += uf[y]; uf[y] = x; } }
bool same(int x, int y){ return find(x) == find(y); }

#include <cstdio>

int main(){
    int n,q;
    scanf("%d%d",&n,&q);
    inituf(n);
    while(q--){
        int c,x,y;
        scanf("%d%d%d",&c,&x,&y);
        if(c){
            printf("%d\n",same(x,y));
        } else {
            unite(x,y);
        }
    }
}