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 Ruby (2.3.3) (judge verdict: Accepted)

def inp() a=gets.chomp.split(" ").map(&:to_i)end 
def inpf() a=gets.chomp.split(" ").map(&:to_f)end
def inps() a=gets.chomp.split(" ")end  
def copy(a) Marshal.load(Marshal.dump(a)) end
def kaizyo(n)(n < 2)? 1 : (2..n).inject(:*) end
def scount(a) b = na(a.max+1); a.each{|n|b[n]+=1};return b end
def na(n=0,d=0) Array.new(n,d)end
def na2(n,m,d=0) Array.new(n){Array.new(m,d)}end
def na3(n,m,l,d=0) Array.new(n){Array.new(m){Array.new(l,d)}}end
class Uf
def initialize(n)
  @r = na(n+1)
  @a = (0...n).to_a
end
def uf(x)
  return x if (@a[x] == x)
  @a[x] = uf(@a[x])
end
def add(x,p)
  root  = uf(x)
  connect  = uf(p)
  return if root == connect
  if @r[root] > @r[connect]
    @a[connect] = root
  elsif @r[root] == @r[connect]
    @a[connect] = root
    @r[root] += 1
  else
    @a[root] = connect
  end
end
def ufj(x,p)
   return uf(x) == uf(p) 
end
end
h = {}
n,k,l = inp
a = Uf.new(n+1)
b = Uf.new(n+1)
(k).times do |i|
  d = inp
  a.add(d[0],d[1])
end
(l).times do |i|
  d = inp
  b.add(d[0],d[1])
end
(1..n).each do |i|
  aa = a.uf(i)
  bb = b.uf(i)
  h[aa+n*bb] = 0 if(h[aa+n*bb] == nil)
  h[aa+n*bb] += 1 
end
(1..n-1).each do |i|
  aa = a.uf(i)
  bb = b.uf(i)
  print "#{h[aa+n*bb]} " 
end
aa = a.uf(n)
bb = b.uf(n)
puts h[aa+n*bb]
=begin
max = c if max < c 
=end