Problem:
Merge Sort

Write a program of a Merge Sort algorithm implemented by the following pseudocode. You should also report the number of comparisons in the Merge function.

Merge(A, left, mid, right)
n1 = mid - left;
n2 = right - mid;
create array L[0...n1], R[0...n2]
for i = 0 to n1-1
do L[i] = A[left + i]
for i = 0 to n2-1
do R[i] = A[mid + i]
L[n1] = SENTINEL
R[n2] = SENTINEL
i = 0;
j = 0;
for k = left to right-1
if L[i] <= R[j]
then A[k] = L[i]
i = i + 1
else A[k] = R[j]
j = j + 1

Merge-Sort(A, left, right){
if left+1 < right
then mid = (left + right)/2;
call Merge-Sort(A, left, mid)
call Merge-Sort(A, mid, right)
call Merge(A, left, mid, right)

Input

In the first line n is given. In the second line, n integers are given.

Output

In the first line, print the sequence S. Two consequtive elements should be separated by a space character.

In the second line, print the number of comparisons.

Constraints

n ≤ 500000

0 ≤ an element in S ≤ 109

Sample Input 1

10
8 5 9 2 6 3 7 1 10 4

Sample Output 1

1 2 3 4 5 6 7 8 9 10
34

Notes

Solution in Haskell (judge verdict: Memory Limit Exceeded)

import Control.Applicative
import Control.Monad.State

main = do
    n <- getLine
    list <- map read.words<$>getLine :: IO [Int]
    let (list', cnt) = runState (mergeSort list) 0
    putStrLn $ unwords.map show $ list'
    print cnt

merge :: (Ord a) => [a] -> [a] -> State Int [a]
merge xs [] = modify (+ length xs) >> return xs
merge [] ys = modify (+ length ys) >> return ys
merge (x:xs) (y:ys)
  | x <= y  = modify succ >> merge xs (y:ys) >>= \xs' -> return (x:xs')
  | otherwise = modify succ >> merge (x:xs) ys >>= \ys' -> return (y:ys')

mergeSort :: (Ord a) => [a] -> State Int [a]
mergeSort [] = return []
mergeSort [x] = return [x]
mergeSort xs = do
    let n = length xs
        (left, right) = splitAt (n `div` 2) xs
    sortedLeft <- mergeSort left
    sortedRight <- mergeSort right
    merge sortedLeft sortedRight