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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Control.Monad
import qualified Data.ByteString.Char8 as B
import qualified Data.IntSet as S
import qualified Data.Array.IArray as A

readInt :: B.ByteString -> Int
readInt = maybe undefined fst . B.readInt

main = do
  [n,k,l] <- map read . words <$> getLine
  esq <- readUndirectedEdge <$> replicateM k B.getLine
  esr <- readUndirectedEdge <$> replicateM l B.getLine
  putStrLn $ unwords $ map show (connectivity n esq esr)

connectivity n esq esr = zipWith (\vsq vsr -> S.size (S.intersection vsq vsr)) vsq vsr
  where
    vsq = map (bfs gq) [1..n]
    vsr = map (bfs gr) [1..n]
    gq = buildG (1,n) esq
    gr = buildG (1,n) esr


--type Height = Int
type Width = Int
type Index = Int
type Bound = (Vertex, Vertex)

type Vertex = Int
type Vertexes = S.IntSet
type Edge = (Vertex, Vertex)
type Graph = A.Array Vertex Vertexes

buildG :: Bound -> [Edge] -> Graph
buildG = A.accumArray (flip S.insert) S.empty

from :: Graph -> Vertex -> Vertexes
from = (A.!)

readUndirectedEdge = concatMap (constructTwoWay . map readInt . B.words)

constructTwoWay :: [Int] -> [Edge]
constructTwoWay [s, t] = [(s, t), (t, s)]
constructTwoWay _ = undefined

bfs :: Graph -> Vertex -> Vertexes
bfs g v = go (S.singleton v) (S.singleton v)
  where
    go acc border
      | S.null border = acc
      | otherwise = go (S.union acc next) next
        where
          next = S.difference (transMap g border) acc

reachable :: Graph -> Vertex -> Vertex -> Bool
reachable g v w = S.member w (bfs g v)

transMap :: Graph -> Vertexes -> Vertexes
transMap g = S.unions . map (from g) . S.elems