Problem:
Score : 400 points

Problem Statement

We have N balls. The i-th ball has an integer A_i written on it.

For each k=1, 2, ..., N, solve the following problem and print the answer.

Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.

Constraints

3 \leq N \leq 2 \times 10^5

1 \leq A_i \leq N

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

For each k=1,2,...,N, print a line containing the answer.

Sample Input 1

5
1 1 2 1 2

Sample Output 1

2
2
3
2
3

Consider the case k=1 for example. The numbers written on the remaining balls are 1,2,1,2.

From these balls, there are two ways to choose two distinct balls so that the integers written on them are equal.

Thus, the answer for k=1 is 2.

Sample Input 2

4
1 2 3 4

Sample Output 2

0
0
0
0

No two balls have equal numbers written on them.

Sample Input 3

5
3 3 3 3 3

Sample Output 3

6
6
6
6
6

Any two balls have equal numbers written on them.

Sample Input 4

8
1 2 1 4 2 1 4 1

Sample Output 4

5
7
5
7
7
5
7
5

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import           Control.Monad
import           Control.Monad.ST
import qualified Data.Array                    as A
import qualified Data.Array.ST                 as ST
import qualified Data.Array.Unboxed            as AU
import qualified Data.ByteString.Char8         as BS
import           Data.Char
import qualified Data.Foldable                 as DF
import           Data.Int
import qualified Data.IntMap                   as IM
import           Data.List
import qualified Data.Map                      as M
import           Data.Maybe
import           Data.Ord
import qualified Data.Set                      as S
import qualified Data.Sequence                 as SQ
import           Data.Time
import qualified Data.Vector                   as V
import qualified Data.Vector.Mutable           as VM
import qualified Data.Vector.Unboxed           as VU
import qualified Data.Vector.Unboxed.Mutable   as VUM

readInt = map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine
readInts n = replicateM n readInt
readString = map BS.unpack . BS.words <$> BS.getLine
readStrings n = replicateM n <$> readString
toPair [x, y] = (x, y)

main = do
  [n] <- readInt
  a   <- readInt
  mapM_ print $ solve a

f a = (sum a', M.fromList a'')
 where
  a' = map (\x -> g $ length x) $ group $ sort a
  a'' :: [(Int, Int)]
  a'' = map (\x -> (head x, length x)) $ group $ sort a

g :: Int -> Int
g x | x < 2     = 0
    | otherwise = x * (x - 1) `div` 2

solve :: [Int] -> [Int]
solve a = map (\x -> m - g (a' M.! x) + g (a' M.! x - 1)) a
  where (m, a') = f a