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>

int par[100010];
int find(int x) {
    return par[x] < 0 ? x : par[x] = find(par[x]);
}
void union_(int x, int y) {
    if ((x = find(x)) != (y = find(y))) par[y] = x;
}
void init() {
    memset(par, -1, sizeof par);
}

int main(void) {
    int n,q;
    scanf("%d%d",&n,&q);
    init();
    for(int i=0; i<q; i++) {
        int c,x,y;
        scanf("%d%d%d",&c,&x,&y);
        if(c)
            puts(find(x)==find(y) ? "1" : "0");
        else
            union_(x,y);
    }
    return 0;
}