Problem:
Score : 700 points

Problem Statement

Snuke loves constructing integer sequences.

There are N piles of stones, numbered 1 through N.
The pile numbered i consists of a_i stones.

Snuke will construct an integer sequence s of length Σa_i, as follows:

Among the piles with the largest number of stones remaining, let x be the index of the pile with the smallest index. Append x to the end of s.

Select a pile with one or more stones remaining, and remove a stone from that pile.

If there is a pile with one or more stones remaining, go back to step 1. Otherwise, terminate the process.

We are interested in the lexicographically smallest sequence that can be constructed. For each of the integers 1,2,3,...,N, how many times does it occur in the lexicographically smallest sequence?

Constraints

1 ≤ N ≤ 10^{5}

1 ≤ a_i ≤ 10^{9}

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_{N}

Output

Print N lines. The i-th line should contain the number of the occurrences of the integer i in the lexicographically smallest sequence that can be constructed.

Sample Input 1

2
1 2

Sample Output 1

2
1

The lexicographically smallest sequence is constructed as follows:

Since the pile with the largest number of stones remaining is pile 2, append 2 to the end of s. Then, remove a stone from pile 2.

Since the piles with the largest number of stones remaining are pile 1 and 2, append 1 to the end of s (we take the smallest index). Then, remove a stone from pile 2.

Since the pile with the largest number of stones remaining is pile 1, append 1 to the end of s. Then, remove a stone from pile 1.

The resulting sequence is (2,1,1). In this sequence, 1 occurs twice, and 2 occurs once.

Sample Input 2

10
1 2 1 3 2 4 2 5 8 1

Sample Output 2

10
7
0
4
0
3
0
2
3
0

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

{-# LANGUAGE RecordWildCards #-}
-- import Data.ByteString.Char8 as BC (getLine, words, readInt)
-- import Prelude hiding (getLine, words)
import Data.List hiding (words)
import Data.Function (on)
import qualified Data.Map.Strict as M
import Data.Maybe (fromJust)
import Control.Monad
import Control.Arrow

main = do
    n <- readLn
    xs <- map read . words <$> getLine
    mapM_ print . fill n . solve . groupMnts $ xs
    where
        fill n xs = let filler = M.fromAscList . zip [1..n] $ repeat 0
                        filled = (M.fromAscList xs) `M.union` filler
                        in M.elems filled

type Stones = Int
type Index = Int

sample = [1,2,1,3,2,4,2,5,8,1] :: [Stones]
sample2 = [1,2]

data Group = Group { _leftMost :: Index, _stones :: Stones, _mnts :: Int }
           deriving (Show)

groupMnts :: [Stones] -> [Group]
groupMnts = joinMountains . groupByStones . attachIndex
    where
        attachIndex = flip zip [1..]
        groupByStones
            = groupBy ((==) `on` fst) . sortBy (compare `on` first negate)
        joinMountains
            = map (\ xs@((s,i):_)  -> Group i s (length xs))

mergeGroups :: Group -> Group -> Group
mergeGroups (Group i s m) (Group i' s' m')
    = if s == s'
         then Group (min i i') s (m+m')
         else error "cannot merge and I was too lazy to use Maybe"

solve :: [Group] -> [(Int,Int)]
solve = join . consume
    -- fixme
    where
        join = foldl' f []
        f [] n = [n]
        f acc@((i,n):r) x@(i',n') = if i == i' then (i,n+n'):r else x:acc
        consume [] = []
        consume [Group{..}] = [ (_leftMost, _stones * _mnts) ]
        consume (g0:g1:rest) =
            (_leftMost g0, (_stones g0 - _stones g1)* _mnts g0)
                : consume (mergeGroups g0{_stones=_stones g1} g1:rest)