Problem:
Score : 400 points

Problem Statement

An SNS has N users - User 1, User 2, \cdots, User N.

Between these N users, there are some relationships - M friendships and K blockships.

For each i = 1, 2, \cdots, M, there is a bidirectional friendship between User A_i and User B_i.

For each i = 1, 2, \cdots, K, there is a bidirectional blockship between User C_i and User D_i.

We define User a to be a friend candidate for User b when all of the following four conditions are satisfied:

a \neq b.

There is not a friendship between User a and User b.

There is not a blockship between User a and User b.

There exists a sequence c_0, c_1, c_2, \cdots, c_L consisting of integers between 1 and N (inclusive) such that c_0 = a, c_L = b, and there is a friendship between User c_i and c_{i+1} for each i = 0, 1, \cdots, L - 1.

For each user i = 1, 2, ... N, how many friend candidates does it have?

Constraints

All values in input are integers.

2 ≤ N ≤ 10^5

0 \leq M \leq 10^5

0 \leq K \leq 10^5

1 \leq A_i, B_i \leq N

A_i \neq B_i

1 \leq C_i, D_i \leq N

C_i \neq D_i

(A_i, B_i) \neq (A_j, B_j) (i \neq j)

(A_i, B_i) \neq (B_j, A_j)

(C_i, D_i) \neq (C_j, D_j) (i \neq j)

(C_i, D_i) \neq (D_j, C_j)

(A_i, B_i) \neq (C_j, D_j)

(A_i, B_i) \neq (D_j, C_j)

Input

Input is given from Standard Input in the following format:

N M K
A_1 B_1
\vdots
A_M B_M
C_1 D_1
\vdots
C_K D_K

Output

Print the answers in order, with space in between.

Sample Input 1

4 4 1
2 1
1 3
3 2
3 4
4 1

Sample Output 1

0 1 0 1

There is a friendship between User 2 and 3, and between 3 and 4. Also, there is no friendship or blockship between User 2 and 4. Thus, User 4 is a friend candidate for User 2.

However, neither User 1 or 3 is a friend candidate for User 2, so User 2 has one friend candidate.

Sample Input 2

5 10 0
1 2
1 3
1 4
1 5
3 2
2 4
2 5
4 3
5 3
4 5

Sample Output 2

0 0 0 0 0

Everyone is a friend of everyone else and has no friend candidate.

Sample Input 3

10 9 3
10 1
6 7
8 2
2 5
8 4
7 3
10 9
6 4
5 8
2 6
7 5
3 1

Sample Output 3

1 3 5 4 3 3 3 3 1 0

Solution in Haskell (GHC 8.8.3) (judge verdict: Accepted)

import qualified Data.Text as T
import qualified Data.Text.IO as T
import qualified Data.Text.Read as T
import Data.IntMap.Strict (IntMap)
import qualified Data.IntMap.Strict as IMS
import Data.Bool (bool)
import Data.Tuple (swap)
import qualified Data.Vector.Unboxed as VU
import Data.List (intercalate)

main :: IO ()
main = do
  [n, m, k] <- map unsafeTextToInt . T.words <$> T.getLine :: IO [Int]
  abs <- sequence . replicate m $ unsafeListToPair . map (pred . unsafeTextToInt) . T.words <$> T.getLine :: IO [(Int, Int)]
  let
    (u, v) = foldl step (IMS.empty, IMS.empty) abs :: (IntMap Int, IntMap Int)
      where
        step uv (i, j) = fst $ unite i j uv
    v0 = VU.generate n (\i -> IMS.findWithDefault 0 (snd $ root i u) v) :: VU.Vector Int
    v1 = VU.accum (const . pred) v0 . concatMap (\(i, j) -> [(i, ()), (j, ())]) $ abs :: VU.Vector Int
  cds <- sequence . replicate k $ unsafeListToPair . map (pred . unsafeTextToInt) . T.words <$> T.getLine :: IO [(Int, Int)]
  let
    v2 = VU.accum (const . pred) v1 . concatMap (\(i, j) -> bool [] [(i, ()), (j, ())] (snd $ isSame i j u)) $ cds :: VU.Vector Int
  putStrLn . intercalate " " . map show . VU.toList $ v2

type UF = IntMap Int

parent :: Int -> UF -> Maybe Int
parent = IMS.lookup

root :: Int -> UF -> (UF, Int)
root i u = maybe (u, i) (\j -> let (u', j') = root j u in (bool (IMS.insert i j' u') u (j' == j), j')) (parent i u)

unite :: Int -> Int -> (UF, IntMap Int) -> ((UF, IntMap Int), ())
unite i j (u, v) | i' == j'  = ((u'', v), ())
                 | otherwise = ((IMS.insert j' i' u'', IMS.alter (Just . succ . ((IMS.findWithDefault 0 j' v) +) . maybe 0 id) i' v), ())
  where
    (u', i') = root i u
    (u'', j') = root j u'

isSame :: Int -> Int -> UF -> (UF, Bool)
isSame i j u = (u'', i' == j')
  where
    (u', i') = root i u
    (u'', j') = root j u'

unsafeListToPair :: [Int] -> (Int, Int)
unsafeListToPair [x, y] = (x, y)
{-# INLINE unsafeListToPair #-}

unsafeTextToInt :: T.Text -> Int
unsafeTextToInt s = case T.signed T.decimal s of
  Right (n, _) -> n
{-# INLINE unsafeTextToInt #-}