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.*;

class UnionFind {
    private int parent[];
    private int height[];

    public UnionFind(int size) {
        parent = new int[size];
        height = new int[size];
        for (int i = 0; i < size; i++)
            parent[i] = i;
    }

    public int set(int p) {
        if (parent[p] == p)
            return p;
        parent[p] = set(parent[p]);
        return parent[p];
    }

    public void union(int p, int q) {
        if (set(p) == set(q))
            return;

        p = set(p);
        q = set(q);

        if (height[p] < height[q]) {
            union(q, p);
            return;
        }

        if (height[p] == height[q])
            height[p]++;

        parent[q] = p;
    }

    public boolean same(int p, int q) {
        return set(p) == set(q);
    }

    public String toString() {
        return Arrays.toString(parent);
    }
}

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

        UnionFind uf = new UnionFind(n);

        for (int i = 0; i < q; i++) {
            int cmd = in.nextInt();
            int a = in.nextInt();
            int b = in.nextInt();
            if (cmd == 0)
                uf.union(a, b);
            if (cmd == 1)
                System.out.println(uf.same(a, b) ? 1 : 0);
        }
    }
}