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)

INFTY = Float::INFINITY
$count = 0

def merge(a, left, mid, right)
    n1 = mid - left;
    n2 = right - mid;
    # l[0...n1], r[0...n2] ?????????
    l = (0...n1).to_a
    r = (0...n2).to_a
    (0...n1).each do |i|
        l[i] = a[left + i]
    end
    (0...n2).each do |i|
        r[i] = a[mid + i]
    end
    l[n1] = INFTY
    r[n2] = INFTY
    i = 0
    j = 0
    # for k = left to right-1
    for k in (left...right)
        $count += 1
        if l[i] <= r[j]
            a[k] = l[i]
            i = i + 1
        else
            a[k] = r[j]
            j = j + 1
        end
    end
end

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

n = gets.to_i
a = gets.split(/ /).map(&:to_i)
puts mergeSort(a, 0, n).join(" "), $count
__END__
?????? 1
10
8 5 9 2 6 3 7 1 10 4
merge(a, left, mid, right)
n1 = mid - left;
n2 = right - mid;
l[0...n1], r[0...n2] ?????????
for i = 0 to n1-1
    l[i] = a[left + i]
    for i = 0 to n2-1
        r[i] = a[mid + i]
        l[n1] = INFTY
        r[n2] = INFTY
        i = 0
        j = 0
        for k = left to right-1
            if l[i] <= r[j]
                a[k] = l[i]
                i = i + 1
            else
                a[k] = r[j]
                j = j + 1

                mergeSort(a, left, right)
                if left+1 < right
                    mid = (left + right)/2;
                    mergeSort(a, left, mid)
                    mergeSort(a, mid, right)
                    merge(a, left, mid, right)