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 JAVA):

Solution:
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);

        int n = in.nextInt(), q = in.nextInt();
        UnionFind unionFind = new UnionFind(n);
        for (int i = 0; i < q; i++) {
            int cmd = in.nextInt(),
                    x = in.nextInt(),
                    y = in.nextInt();
            if (cmd == 0) {
                unionFind.union(x, y);
            }else {
                System.out.println(unionFind.same(x, y) ? 1 : 0);
            }
        }
    }
}

class UnionFind {
    int[] parent;
    int[] depth;

    UnionFind(int n) {
        parent = new int[n];
        depth = new int[n];
        Arrays.fill(parent, -1);
    }

    private int root(int p) {
        while (parent[p] != -1) {
            p = parent[p];
        }
        return p;
    }

    void union(int p, int q) {
        int rp = root(p), rq = root(q);

        if (rp == rq) {
            return;
        }

        if (depth[rp] >= depth[rq]) {
            parent[rq] = rp;
            depth[rp] = Math.max(depth[rp], depth[rq] + 1);
        } else {
            parent[rp] = rq;
//            depth[rq] = Math.max(depth[rq], depth[rp] + 1);
        }
    }

    boolean same(int p, int q) {
        return root(p) == root(q);

    }
}