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<iostream>
#include<vector>
using namespace std;

int main(){
    int n, q;
    cin >> n >> q;
    vector<int> color(n);
    for (int i = 0; i < n; i++) {
        color[i] = i;
    }
    for (int i = 0; i < q; i++) {
        int com, x, y;
        cin >> com >> x >> y;
        if (com == 0) {
            int col_y = color[y];
            for (int i = 0; i < n; i++) {
                if (color[i] == col_y) color[i] = color[x];
            }
        } else {
            cout << (color[x] == color[y]) << endl;
        }
    }
    return 0;
}