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 Python3 (judge verdict: Time Limit Exceeded)

def merge(A, left, mid, right):
    n1 = mid - left
    n2 = right - mid
    
    L = [0 for i in range(n1+1)]
    R = [0 for i in range(n2+1)]

    for i in range(n1):
        L[i] = A[left + i]
        
    for i in range(n2):
        R[i] = A[mid + i]
    
    L[n1]=1000000001
    R[n2]=1000000001

    cnt1 = 0
    cnt2 = 0
    
    for k in range(left, right):
        if L[cnt1] <= R[cnt2]:
            A[k] = L[cnt1]
            cnt1 += 1
        else:
            A[k] = R[cnt2]
            cnt2 +=  1
    
    global cnt
    cnt += cnt1 + cnt2
    
    
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)
        

n = int(input().rstrip())
A = list(map(int,input().split(" ")))
cnt = 0
mergeSort(A, 0 , len(A))
print(" ".join(list(map(str,A))))
print(str(cnt))