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;
const int MAXN = 10000;

int F[MAXN];

inline int Root(int u) {
    return F[u] == u ? u : F[u] = Root(F[u]);
}

inline void Merge(int u, int v) {
    int root_u = Root(u);
    int root_v = Root(v);
    if (root_u != root_v) {
        F[root_u] = root_v;
    }
}

int main() {
    //ifstream cin("input.txt");
    int n, q;
    cin >> n >> q;
    for (int i = 0; i < n; i++) {
        F[i] = i;
    }
    for (int i = 1; i <= q; i++) {
        int op, x, y;
        cin >> op >> x >> y;
        if (op == 0)
            Merge(x, y);
        else
            cout << (Root(x) == Root(y)) << endl;
    }
    return 0;
}