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)

extern crate core;

use std::collections::HashMap;
use std::io::{self, Read};

#[macro_export]
macro_rules! input {
  ($s:expr=>$($t:tt)*) => {
    let mut lines=$s.split("\n");
    $(
        line_parse!(lines,$t);
    )*
  };
}

macro_rules! line_parse {
  ($lines:expr,($($name:ident:$t:tt)*)) => {
    let mut line=$lines.next().unwrap().split_whitespace();
    $(value_def!(line,$name,$t);)*
  };

  //複数行
  ($lines:expr,{$n:expr;$name:ident:$t:tt}) => {
    values_def!($lines,$n,$name,$t);
  };
}

macro_rules! value_def {
    ($line:expr, $name:ident, $t:tt) => {
        let $name = value!($line, $t);
    };
}

macro_rules! values_def {
    ($lines:expr, $n:expr, $name:ident, $t:tt) => {
        let $name = {
            let mut vec = Vec::new();
            for i in 0..$n {
                let mut next = $lines.next().unwrap().split_whitespace();
                vec.push(value!(next, $t));
            }
            vec
        };
    };
}

macro_rules! value {
  //配列
  ($line:expr,[$t:tt]) => {
    $line.map(|x|{
      let mut iter=::std::iter::once(x);
      value!(iter,$t)
    }).collect::<Vec<_>>()
  };
  //タプル
  ($line:expr,($($t:tt),*)) => {
    ($(value!($line,$t),)*)
  };
  //文字列
  ($line:expr,#) => {
    $line.next().unwrap()
  };
  //インデックス(-1)
  ($line:expr,@) => {
    $line.next().unwrap().parse::<usize>().unwrap()-1
  };
  //単一値
  ($line:expr,$t:ty) => {
    $line.next().unwrap().parse::<$t>().unwrap()
  };
}

fn main() {
    let mut input = String::new();
    io::stdin().read_to_string(&mut input).unwrap();
    let output = solve(input.trim().to_string());
    println!("{}", output);
}

fn solve(input: String) -> String {
    input!(input=>(n:usize k:usize l:usize){k;k_list:(@,@)}{l;l_list:(@,@)});
    let mut k_uf = UnionFind::new(n);
    for (a, b) in k_list {
        k_uf.unite(a, b);
    }
    let mut l_uf = UnionFind::new(n);
    for (a, b) in l_list {
        l_uf.unite(a, b);
    }
    let mut count_map = HashMap::new();
    for i in 0..n {
        map_add(&mut count_map, (k_uf.find(i), l_uf.find(i)), 1);
    }
    let mut result = Vec::with_capacity(n);
    for i in 0..n {
        result.push(count_map[&(k_uf.find(i), l_uf.find(i))].to_string());
    }
    result.join(" ").to_string()
}

pub fn map_add(map: &mut HashMap<(usize, usize), i64>, key: (usize, usize), add: i64) {
    let v = match map.get(&key) {
        Some(v) => *v + add,
        None => add,
    };
    map.insert(key, v);
}

#[derive(PartialEq, Debug, Clone)]
pub struct UnionFindNode {
    pub par: usize,
    pub rank: usize,
}

#[derive(PartialEq, Debug, Clone)]
pub struct UnionFind(pub Vec<UnionFindNode>);

impl UnionFind {
    //初期化
    pub fn new(size: usize) -> UnionFind {
        let mut vec = Vec::new();
        for i in 0..size {
            vec.push(UnionFindNode { par: i, rank: 0 });
        }

        UnionFind(vec)
    }

    //根を求める
    pub fn find(&mut self, x: usize) -> usize {
        if self.0[x].par == x {
            x
        } else {
            let par = self.0[x].par;
            let v = self.find(par);
            self.0[x].par = v;
            v
        }
    }

    //xとyの集合を併合
    pub fn unite(&mut self, x: usize, y: usize) {
        let x = self.find(x);
        let y = self.find(y);
        if x == y {
            return;
        }

        if self.0[x].rank < self.0[y].rank {
            self.0[x].par = y;
        } else {
            self.0[y].par = x;
            if self.0[x].rank == self.0[y].rank {
                self.0[x].rank += 1;
            }
        }
    }

    //xとyが同じ集合に属するか
    pub fn same(&mut self, x: usize, y: usize) -> bool {
        self.find(x) == self.find(y)
    }
}

macro_rules! tests {
    ($($name:ident: $input:expr=>$output:expr,)*) => {
        mod tests {
            $(
                #[test]
                fn $name() {
                    assert_eq!($output.trim().to_string(),super::solve($input.trim().to_string()));
                }
            )*
        }
    }
}

tests! {
    test1: "4 3 1\n1 2\n2 3\n3 4\n2 3" => "1 2 2 1",
    test2: "4 2 2\n1 2\n2 3\n1 4\n2 3" => "1 2 2 1",
    test3: "7 4 4\n1 2\n2 3\n2 5\n6 7\n3 5\n4 5\n3 4\n6 7" => "1 1 2 1 2 2 2",
}