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 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE ScopedTypeVariables #-}

import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import Control.Monad

-- Union-Find
type Parent = VUM.IOVector Int

makeUF :: Int -> IO Parent
makeUF n = do
    par <- VU.unsafeThaw $ VU.generate n id
    return par

root :: Int -> Parent -> IO Int
root x par = do
    r <- VUM.read par x
    if x == r
        then return x
        else do
            newr <- root r par
            VUM.write par x newr
            return newr

same :: Int -> Int -> Parent -> IO Bool
same x y par = do
    rx <- root x par
    ry <- root y par
    return $ rx == ry

unite :: Int -> Int -> Parent -> IO ()
unite x y par = do
    x' <- root x par
    y' <- root y par
    when (x' /= y') $ VUM.write par x' y'

main = do
    [n,m,k] <- map read . words <$> getLine :: IO [Int]
    uf <- makeUF (n+1)
    (fre :: VUM.IOVector Int) <- VUM.replicate (n+1) 0
    (blo :: VUM.IOVector Int) <- VUM.replicate (n+1) 0
    (rt:: VUM.IOVector Int) <- VUM.replicate (n+1) 0
    replicateM_ m $ do
        [a,b] <- map read . words <$> getLine :: IO [Int]
        unite a b uf
        VUM.modify fre (+1) a
        VUM.modify fre (+1) b
    replicateM_ k $ do
        [c,d] <- map read . words <$> getLine :: IO [Int]
        branch <- same c d uf
        when branch $ do
            VUM.modify blo (+1) c
            VUM.modify blo (+1) d
    forM_ [1..n] $ \i -> do
        r <- root i uf
        VUM.modify rt (+1) r
    forM_ [1..n] $ \i -> do
        r <- root i uf
        vs <- VUM.read rt r
        f <- VUM.read fre i
        b <- VUM.read blo i
        putStr $ show (vs - f - b - 1)
        putStr " "
    putStrLn ""