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]*(n1+1)
    R=[0]*(n2+1)
    for i in range(n1):
        L[i]=A[left+i]
    for i in range(n2):
        R[i]=A[mid+i]
    L[n1]=float("inf")
    R[n2]=float("inf")
    i=0
    j=0
    global cnt
    cnt += (right-left)
    for k in range(left,right):
#        cnt+=1
        if L[i]<=R[j]:
            A[k]=L[i]
            i=i+1
        else:
            A[k]=R[j]
            j=j+1

def mergeSort(A,left,right):
    if left+2<right:
        mid=(left+right)//2
        mergeSort(A,left,mid)
        mergeSort(A,mid,right)
        merge(A,left,mid,right)
    elif left+1<right:
        mid =left+1
        merge(A,left,mid,right)

n=int(input())
S=list(input().split())
for i in range(n):
    S[i]=int(S[i])
cnt=0
mergeSort(S,0,n)
for i in range(n):
    if i==n-1:
        print(S[i])
    else:
        print(S[i],end=" ")
print(cnt)