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.Scanner;

public class Main {

    public static class UnionFind {

        int[] id;
        int count;
        int[] weight;  // size indexed by root id

        public UnionFind(int n) {
            id = new int[n];
            weight = new int[n];
            count = n;
            for (int idx = 0; idx < id.length; idx++) {
                id[idx] = idx;
                weight[idx] = 1;
            }
        }

        public void union(int p, int q) {
            int pRoot = find(p);
            int qRoot = find(q);
            if (pRoot == qRoot) {
                return;
            }
            // make smaller root point to larger one
            if (weight[pRoot] < weight[qRoot]) {
                id[pRoot] = qRoot;
                weight[qRoot] += weight[pRoot];
            } else {
                id[qRoot] = pRoot;
                weight[pRoot] += weight[qRoot];
            }
            count--;
        }

        public int find(int p) {
            while (id[p] != p) {
                p = id[p];
            }
            return p;
        }

        public boolean connected(int p, int q) {
            return find(p) == find(q);
        }

        public int count() {
            return count;
        }
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        UnionFind uf = new UnionFind(n);
        int q = scanner.nextInt();
        while (q-- > 0) {
            int com = scanner.nextInt();
            int x = scanner.nextInt();
            int y = scanner.nextInt();
            if (com == 0) {
                uf.union(x, y);
            } else {
                System.out.println(uf.connected(x, y) ? "1" : "0");
            }
        }
    }
}