Problem:
Disjoint Set

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.

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.

Constraints

1 ≤ n ≤ 10000

1 ≤ q ≤ 100000

x ≠ y

Sample 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

Sample Output

0
0
1
1
1
0
1
1

Solution in Rust (judge verdict: Accepted)

use std::io::Read;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();
    let q: usize = iterator.next().unwrap().parse().unwrap();

    let mut ds = DisjointSet::new(n);

    let mut result = String::new();
    for _ in 0..q {
        let command: usize = iterator.next().unwrap().parse().unwrap();
        let x: usize = iterator.next().unwrap().parse().unwrap();
        let y: usize = iterator.next().unwrap().parse().unwrap();
        if command == 0 {
            ds.unite(x, y);
        } else {
            if ds.same(x, y) {
                result.push_str(&format!("{}\n", 1));
            } else {
                result.push_str(&format!("{}\n", 0));
            }
        }
    }
    return result.trim().to_string();
}

struct DisjointSet {
    rank: Vec<usize>,
    p: Vec<usize>,
}

impl DisjointSet {
    fn new(size: usize) -> DisjointSet {
        let mut ds = DisjointSet {
            rank: vec![0; size],
            p: vec![0; size],
        };
        for i in 0..size {
            ds.make_set(i);
        }
        return ds;
    }

    fn make_set(&mut self, x: usize) {
        self.p[x] = x;
        self.rank[x] = 0;
    }

    fn same(&mut self, x: usize, y: usize) -> bool {
        return self.find_set(x) == self.find_set(y)
    }

    fn unite(&mut self, x: usize, y: usize) {
        let a = self.find_set(x);
        let b = self.find_set(y);
        self.link(a, b);
    }

    fn link(&mut self, x: usize, y: usize) {
        if self.rank[x] > self.rank[y] {
            self.p[y] = x;
        } else {
            self.p[x] = y;
            if self.rank[x] == self.rank[y] {
                self.rank[y] += 1;
            }
        }
    }

    fn find_set(&mut self, x: usize) -> usize {
        let parent = self.p[x];
        if x != parent {
            let root = self.find_set(parent);
            self.p[x] = root;
        }
        return self.p[x];
    }
}