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)

import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as UM
import qualified Data.ByteString.Char8 as C
import Data.List
import Control.Monad

r' :: IO [Int]
r'  =   unfoldr    (C.readInt . C.dropWhile (==' ')) <$> C.getLine


type UF = (Parent,Rank,Size)
type Parent = UM.IOVector Int
type Rank   = UM.IOVector Int
type Size   = UM.IOVector Int

makeset :: Int -> IO UF
makeset n = do
    par <- U.thaw (U.generate n id)
    rnk <- UM.replicate n 0
    siz <- UM.replicate n 1
    return (par,rnk,siz)

root :: UF -> Int -> IO Int
root uf@(par,rnk,_) n = do
    x <- UM.read par n
    if x == n then return x else do
        nr <- root uf x
        UM.write par n nr
        UM.write rnk n 1
        return nr

same :: UF -> Int -> Int -> IO Bool
same uf x y = do
    rx <- root uf x
    ry <- root uf y
    return (rx == ry)

size :: UF -> Int -> IO Int
size uf@(par,rnk,siz) x = do
    r <- root uf x
    UM.read siz r

unite :: UF -> Int -> Int -> IO ()
unite uf@(par,rnk,siz) x y = do
    b <- same uf x y
    when (not b) $ do
        tx <- root uf x
        ty <- root uf y        
        rx <- UM.read rnk tx
        ry <- UM.read rnk ty
        sx <- size uf tx
        sy <- size uf ty
        if rx < ry then UM.write par tx ty >> UM.modify siz (+sx) ty
        else UM.write par ty tx >> when (rx == ry) (UM.modify rnk succ tx) >> UM.modify siz (+sy) tx


main :: IO ()
main = do
    [n,m,k] <- r'

    uf <- makeset n
    cnt <- UM.replicate n 0

    replicateM_ m $ do
        [a,b] <- map pred <$> r'
        unite uf a b
        UM.modify cnt succ a
        UM.modify cnt succ b
    replicateM_ k $ do
        [c,d] <- map pred <$> r'
        b <- same uf c d
        when b $ do
            UM.modify cnt succ c
            UM.modify cnt succ d

    putStrLn =<< unwords <$> mapM (\i -> do
        s <- size uf i
        c <- UM.read cnt i
        return $ show (s-c-1)
        ) [0..n-1]