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: Time Limit Exceeded)

mod reader {
    use std;
    use std::io::prelude::*;
    macro_rules! read_line((  ) => {
                           {
                           let mut input = String :: new (  ) ; std :: io ::
                           stdin (  ) . read_line ( & mut input ) . unwrap (
                           ) ; input } } ;);
    pub fn read_to_vec<T: std::str::FromStr>() -> Vec<T> {
        read_line!().split_whitespace().map(|e|
                                                e.parse().ok().unwrap()).collect()
    }
}
use reader::*;
#[macro_use]
mod misc {
    #![allow(unused_imports)]
    use std;
    #[macro_export]
    macro_rules! bind_from_vec((
                               $ ( $ variable : ident ) , + = $ vector : expr
                               ) => {
                               let mut v = $ vector . clone (  ) . into_iter (
                                ) ; $ (
                               let $ variable = v . next (  ) . unwrap (  ) ;
                               ) + } ;);
}
use std::collections::{HashMap, HashSet};
use std::io::prelude::*;
fn read_two<T: std::str::FromStr>(stdin: &mut std::io::StdinLock,
                                  buf: &mut String) -> (T, T) {
    buf.clear();
    stdin.read_line(buf).ok();
    let mut iter = buf.split_whitespace().map(|e| e.parse().ok().unwrap());
    (iter.next().unwrap(), iter.next().unwrap())
}
fn main() {
    bind_from_vec!(n , k , l = read_to_vec :: < usize > (  ));
    let mut roads = HashMap::new();
    let mut railways = HashMap::new();
    {
        let stdin = std::io::stdin();
        let mut locked_stdin = stdin.lock();
        let mut buf = String::new();
        for _ in 0..k {
            let (mut p, mut q): (usize, usize) =
                read_two(&mut locked_stdin, &mut buf);
            p -= 1;
            q -= 1;
            (*roads.entry(p).or_insert(Vec::new())).push(q);
            (*roads.entry(q).or_insert(Vec::new())).push(p);
        }
        for _ in 0..l {
            let (mut r, mut s): (usize, usize) =
                read_two(&mut locked_stdin, &mut buf);
            r -= 1;
            s -= 1;
            (*railways.entry(r).or_insert(Vec::new())).push(s);
            (*railways.entry(s).or_insert(Vec::new())).push(r);
        }
    }
    let mut todo = Vec::new();
    let mut which_connected_by_roads = Vec::new();
    let mut connected_sets_by_roads = Vec::new();
    connected_sets_by_roads.push(HashSet::new());
    'cities:
        for city in 0..n {
            for (i, connected) in connected_sets_by_roads.iter().enumerate() {
                if connected.contains(&city) {
                    which_connected_by_roads.push(i);
                    continue 'cities ;
                }
            }
            let mut found = HashSet::new();
            which_connected_by_roads.push(connected_sets_by_roads.len());
            found.insert(city);
            todo.push(city);
            'dfs:
                loop  {
                    match todo.pop() {
                        Some(visit) => {
                            if let Some(connected_cities) = roads.get(&visit)
                                   {
                                for &c in connected_cities.iter() {
                                    if !found.contains(&c) {
                                        found.insert(c);
                                        todo.push(c);
                                    }
                                }
                            }
                        }
                        None => { break 'dfs ; }
                    }
                }
            connected_sets_by_roads.push(found);
            todo.clear();
        }
    let mut which_connected_by_railways = Vec::new();
    let mut connected_sets_by_railways = Vec::new();
    connected_sets_by_railways.push(HashSet::new());
    'cities:
        for city in 0..n {
            for (i, connected) in
                connected_sets_by_railways.iter().enumerate() {
                if connected.contains(&city) {
                    which_connected_by_railways.push(i);
                    continue 'cities ;
                }
            }
            let mut found = HashSet::new();
            which_connected_by_railways.push(connected_sets_by_railways.len());
            found.insert(city);
            todo.push(city);
            'dfs:
                loop  {
                    match todo.pop() {
                        Some(visit) => {
                            if let Some(connected_cities) =
                                   railways.get(&visit) {
                                for &c in connected_cities.iter() {
                                    if !found.contains(&c) {
                                        found.insert(c);
                                        todo.push(c);
                                    }
                                }
                            }
                        }
                        None => { break 'dfs ; }
                    }
                }
            connected_sets_by_railways.push(found);
            todo.clear();
        }
    for city in 0..n {
        print!("{} " , (
               connected_sets_by_roads [ which_connected_by_roads [ city ] ] .
               intersection (
               & connected_sets_by_railways [
               which_connected_by_railways [ city ] ] ) ) . count (  ));
    }
    println!("");
}