Problem:
Score : 400 points

Problem Statement

There are N cities. There are also K roads and L railways, extending between the cities.
The i-th road bidirectionally connects the p_i-th and q_i-th cities, and the i-th railway bidirectionally connects the r_i-th and s_i-th cities.
No two roads connect the same pair of cities. Similarly, no two railways connect the same pair of cities.

We will say city A and B are connected by roads if city B is reachable from city A by traversing some number of roads. Here, any city is considered to be connected to itself by roads.
We will also define connectivity by railways similarly.

For each city, find the number of the cities connected to that city by both roads and railways.

Constraints

2 ≦ N ≦ 2*10^5

1 ≦ K, L≦ 10^5

1 ≦ p_i, q_i, r_i, s_i ≦ N

p_i < q_i

r_i < s_i

When i ≠ j, (p_i, q_i) ≠ (p_j, q_j)

When i ≠ j, (r_i, s_i) ≠ (r_j, s_j)

Input

The input is given from Standard Input in the following format:

N K L
p_1 q_1
:
p_K q_K
r_1 s_1
:
r_L s_L

Output

Print N integers. The i-th of them should represent the number of the cities connected to the i-th city by both roads and railways.

Sample Input 1

4 3 1
1 2
2 3
3 4
2 3

Sample Output 1

1 2 2 1

All the four cities are connected to each other by roads.

By railways, only the second and third cities are connected. Thus, the answers for the cities are 1, 2, 2 and 1, respectively.

Sample Input 2

4 2 2
1 2
2 3
1 4
2 3

Sample Output 2

1 2 2 1

Sample Input 3

7 4 4
1 2
2 3
2 5
6 7
3 5
4 5
3 4
6 7

Sample Output 3

1 1 2 1 2 2 2

Solution in Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::char::from_digit;
#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::fs::File;
#[allow(unused_imports)]
use std::io::prelude::*;
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufReader, BufWriter, Stdin, Stdout, Write};
#[allow(unused_imports)]
use std::mem::swap;
#[allow(unused_imports)]
use std::str::FromStr;

type BoxResult<T> = Result<T, Box<std::error::Error>>;

fn main() {
    let mut scanner = Scanner::new(stdin());
    let (n, k, l) = scanner.read_three::<usize>().unwrap();
    let mut set_1 = UnionFindTree::new(n);
    for _ in 0..k {
        let (x, y) = scanner.read_two::<usize, usize>().unwrap();
        set_1.unite(x - 1, y - 1);
    }
    let mut set_2 = UnionFindTree::new(n);
    for _ in 0..l {
        let (x, y) = scanner.read_two::<usize, usize>().unwrap();
        set_2.unite(x - 1, y - 1);
    }
    let mut map = HashMap::<(usize, usize), Vec<usize>>::new();
    for i in 0..n {
        let group_1 = set_1.climb_up(i);
        let group_2 = set_2.climb_up(i);
        if map.contains_key(&(group_1, group_2)) {
            map.get_mut(&(group_1, group_2)).unwrap().push(i);
        } else {
            map.insert((group_1, group_2), vec![i]);
        }
    }
    let mut results = vec![0; n];
    for group in map.values() {
        for i in group {
            results[*i] = group.len();
        }
    }
    println!(
        "{}",
        results
            .into_iter()
            .map(|v| v.to_string())
            .collect::<Vec<_>>()
            .join(" ")
    );
}

pub struct UnionFindTree {
    parents: Vec<usize>,
    heights: Vec<usize>,
    sizes: Vec<usize>,
    group_num: usize,
}

impl UnionFindTree {
    pub fn new(size: usize) -> UnionFindTree {
        UnionFindTree {
            parents: (0..size).collect(),
            heights: vec![0; size],
            sizes: vec![1; size],
            group_num: size,
        }
    }

    pub fn climb_up(&mut self, node: usize) -> usize {
        let mut parents_to_root = vec![];
        let mut present = node;
        while self.parents[present] != present {
            parents_to_root.push(present);
            present = self.parents[present];
        }
        for &node in parents_to_root.iter() {
            self.parents[node] = present;
        }
        present
    }

    pub fn is_same_group(&mut self, x: usize, y: usize) -> bool {
        self.climb_up(x) == self.climb_up(y)
    }

    pub fn unite(&mut self, x: usize, y: usize) {
        let root_x = self.climb_up(x);
        let root_y = self.climb_up(y);
        if root_x == root_y {
            return;
        }
        if self.heights[root_x] > self.heights[root_y] {
            self.parents[root_y] = root_x;
            self.sizes[root_x] += self.sizes[root_y];
        } else if self.heights[root_x] < self.heights[root_y] {
            self.parents[root_x] = root_y;
            self.sizes[root_y] += self.sizes[root_x];
        } else {
            self.parents[root_y] = root_x;
            self.heights[root_x] += 1;
            self.sizes[root_x] += self.sizes[root_y];
        }
        self.group_num -= 1;
    }

    pub fn group_num(&self) -> usize {
        self.group_num
    }

    pub fn group_size(&mut self, x: usize) -> usize {
        let root = self.climb_up(x);
        self.sizes[root]
    }
}

pub struct Scanner<R> {
    reader: BufReader<R>,
    buffer: String,
}
impl<R> Scanner<R>
where
    R: Read,
{
    pub fn new(inner: R) -> Scanner<R> {
        let reader = BufReader::new(inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    pub fn with_capacity(capacity: usize, inner: R) -> Scanner<R> {
        let reader = BufReader::with_capacity(capacity, inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    pub fn read_line(&mut self) -> BoxResult<String> {
        self.reader.read_line(&mut self.buffer)?;
        let cloned = self.buffer.trim().to_string();
        self.buffer.clear();
        Ok(cloned)
    }
    pub fn read<T>(&mut self) -> BoxResult<T>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed = self.buffer.trim().parse()?;
        self.buffer.clear();
        Ok(parsed)
    }
    pub fn read_two<T, U>(&mut self) -> BoxResult<(T, U)>
    where
        T: FromStr,
        T: Copy,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
        U: FromStr,
        U: Copy,
        U::Err: std::fmt::Debug,
        U::Err: std::error::Error,
        U::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let (a, b) = {
            let params = self.buffer.trim().split_whitespace().collect::<Vec<_>>();
            let a = params[0].parse()?;
            let b = params[1].parse()?;
            (a, b)
        };
        self.buffer.clear();
        Ok((a, b))
    }
    pub fn read_three<T>(&mut self) -> BoxResult<(T, T, T)>
    where
        T: FromStr,
        T: Copy,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        let nums = self.read_vector()?;
        Ok((nums[0], nums[1], nums[2]))
    }
    pub fn read_vector<T>(&mut self) -> BoxResult<Vec<T>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed_vec = self
            .buffer
            .trim()
            .split_whitespace()
            .map(|s| s.parse())
            .collect::<Result<Vec<_>, _>>()?;
        self.buffer.clear();
        Ok(parsed_vec)
    }
    pub fn read_matrix<T>(&mut self, lines: usize) -> BoxResult<Vec<Vec<T>>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        let mut parsed_matrix = vec![];
        for _ in 0..lines {
            self.reader.read_line(&mut self.buffer)?;
            parsed_matrix.push(
                self.buffer
                    .trim()
                    .split_whitespace()
                    .map(|s| s.parse())
                    .collect::<Result<Vec<_>, _>>()?,
            );
            self.buffer.clear();
        }
        Ok(parsed_matrix)
    }
    pub fn read_chars(&mut self) -> BoxResult<Vec<char>> {
        self.reader.read_line(&mut self.buffer)?;
        let chars = self.buffer.trim().chars().collect::<Vec<_>>();
        self.buffer.clear();
        Ok(chars)
    }
}