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 Ruby (judge verdict: Accepted)

n = gets.to_i
sAry = gets.split.map(&:to_i)

INF = 10 ** 9 + 5
$nComp = 0

def merge(aAry, left, mid, right)
    # puts "aAry = " + aAry.to_s + ", left = " + left.to_s + ", mid = " +  mid.to_s + ", right = " + right.to_s
    n1 = mid - left
    n2 = right - mid
    # lAry = aAry[left, n1 - 1]
    # rAry = aAry[mid, n2 - 1]
    lAry = aAry[left, n1]
    rAry = aAry[mid, n2]
    lAry[n1] = INF
    rAry[n2] = INF
    # puts "lAry = " + lAry.to_s
    # puts "rAry = " + rAry.to_s
    i = 0
    j = 0
    (left..(right - 1)).each do |k|
        # puts "k = " + k.to_s
        if lAry[i] <= rAry[j] then
            aAry[k] = lAry[i]
            i += 1
        else
            aAry[k] = rAry[j]
            j += 1
        end
        $nComp += 1
    end
end

def mergeSort(aAry, left, right)
    if left + 1 < right then
        mid = (left + right) / 2
        mergeSort(aAry, left, mid)
        mergeSort(aAry, mid, right)
        merge(aAry, left, mid, right)
    end
end

mergeSort(sAry, 0, n)

puts sAry.join(' ')
puts $nComp