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)

{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE LambdaCase #-}
module Main where

import           Data.List
import           Control.Monad
import           Debug.Trace
import qualified Data.ByteString.Char8         as BC
import           Data.Maybe                     ( fromJust )
import qualified Data.Set                      as S
import qualified Data.IntMap.Strict            as IM
import qualified Data.IntMap.Lazy            as IML
import qualified Data.Map.Strict               as M
import           Data.Char
import qualified Data.Array.IArray as A
import qualified Data.Array.Unboxed as UA
import Data.Bits
import Control.Monad.State.Strict
import qualified Data.Array.ST as STA
import qualified Data.Array.MArray as MA
import Control.Monad.ST

modN = 1000000007


readTuple2 :: IO (Int, Int)
readTuple2 = do
    [a, b] <- map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine
    return (a, b)

readTuple3 :: IO (Int, Int, Int)
readTuple3 = do
    [a, b, c] <- map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine
    return (a, b, c)

readInt :: IO Int
readInt = fst . fromJust . BC.readInt <$> BC.getLine

readInts :: IO [Int]
readInts = map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine

split :: (a -> Bool) -> [a] -> [[a]]
split f [] = []
split f as =
    let (fo, la) = span f as
        las      = case la of
            [] -> []
            xs -> split f $ tail xs
    in  case fo of
            [] -> las
            xs -> xs : las

pow :: Int -> Int -> Int -> Int
pow base 1 modNum = base `mod` modNum
pow base time modNum
    | odd time = let 
        a = pow base (time `div` 2) modNum `mod` modNum
        in
        a * a * base `mod` modNum
    | otherwise = let
        a = pow base (time `div` 2) modNum `mod` modNum
        in
        a * a `mod` modNum

combi :: Integral a => a -> a -> a
combi n k
    | k > n = 0
    | n == k = 1
    | k > (n - k) = combi n (n - k)
    | otherwise = product [n, (n - 1)..(n - k + 1)] `div` product [1..k]

solve :: Int -> [Int] -> [Int]
solve n as = let
    arr = M.fromList $ zip [1..] as
    numMap =  foldr (M.alter $ \case
                        Nothing -> Just 1
                        Just x -> Just $ x + 1
                    ) M.empty as
    (combiMap, total) = foldl' (\(b, tot) a -> case M.lookup a numMap of
                                    Nothing  -> (b, tot)
                                    Just x -> let ansx = combi x 2
                                        in
                                        (M.insert a ansx b, tot + ansx)
                    ) (M.empty, 0) [1..n]
    ans x = let
        num = arr M.! x
        counter = numMap M.! num
        combiNum = combiMap M.! num
        in
            total - combiNum + combi (counter - 1) 2
    in
    ans <$> [1..n]


main :: IO ()
main = do
    n <- readInt
    as <- readInts
    forM_ (solve n as) print