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>
#define N 100000
using namespace std;
struct DS {
    int p[N];
    DS(int n) {
        for (int i = 0; i < n; i++) p[i] = i;
    }
    int find(int x) {
        if (x != p[x]) p[x] = find(p[x]);
        return p[x];
    }
    bool same(int x, int y) {
        return find(x) == find(y);
    }
    void unite(int x, int y) {
        p[find(x)] = find(y);
    }
};

int main() {
    int n, q, cmd, x, y;
    scanf("%d%d", &n, &q);
    DS ds(n);
    while (q--){
        scanf("%d%d%d", &cmd, &x, &y);
        if (cmd == 0) ds.unite(x, y); 
        else printf("%d\n", ds.same(x, y));
    }
    return 0;
}