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 Python (judge verdict: Accepted)

def merge_sort(A):
    if len(A) <= 1:
        return A, 0
    mid = len(A) // 2
    left, lcount = merge_sort(A[:mid])
    right, rcount = merge_sort(A[mid:])
    merged, count = merge(left, right)
    return merged, lcount + rcount + count

def merge(left, right):
    lpos = 0
    rpos = 0
    #lcount = 0
    #rcount = 0
    merged = []
    while lpos < len(left) and rpos < len(right):
        if left[lpos] <= right[rpos]:
            merged.append(left[lpos])
            lpos += 1
            #lcount += 1
        else:
            merged.append(right[rpos])
            rpos += 1
            #rcount += 1
    
    if left[lpos:]:
        merged.extend(left[lpos:])
        #lcount += len(left[lpos:])
    if right[rpos:]:
        merged.extend(right[rpos:])
        #rcount += len(right[rpos:])
    
    #print merged
    #return merged, lcount + rcount
    return merged, len(merged)

if __name__ == '__main__':
    n = int(raw_input())
    A = map(long, raw_input().split())
    
    sorted, count = merge_sort(A)
    print ' '.join(str(x) for x in sorted)
    print count