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 qualified Data.Vector.Unboxed as VU
import qualified Data.ByteString.Char8 as B
import qualified Data.Map.Strict as Map

readInt :: B.ByteString -> Maybe (Int,B.ByteString)
readInt xs = do
    (x,ys) <- B.readInt xs
    return (x,B.tail ys)

analyze :: Map.Map Int Int -> [Int] -> Map.Map Int Int
analyze xx []     = xx
analyze xx (x:xs) = case Map.lookup x xx of
    Just y -> analyze (Map.update (\x -> Just (x+1)) x xx) xs
    Nothing -> analyze (Map.insert x 1 xx) xs

fun :: Int -> VU.Vector Int -> Map.Map Int Int -> Int -> Int
fun sums yy xx m = case Map.lookup (yy VU.! m) xx of
    Just z -> -z + 1 + sums
    Nothing -> sums

main :: IO ()
main = do
    n <- readLn
    as <- VU.unfoldrN n readInt <$> B.getLine
    let bs = VU.toList as
    let cs = analyze Map.empty bs
    let sums = Map.foldl' (\a b -> a + ((b*(b-1)) `div` 2)) 0 cs
    let ans = map (fun sums as cs) [0..n-1]
    mapM_ print ans