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: Accepted)

cnt = 0
INFTY=10**10
def merge_sort(a,left,right):
	if left+1<right:
		mid=(left+right)//2
		merge_sort(a,left,mid)
		merge_sort(a,mid,right)
		merge(a,left,mid,right)

def merge(a,left,mid,right):
	L=a[left:mid]
	R=a[mid:right]
	L.append(INFTY)
	R.append(INFTY)
	global cnt
	i=0
	j=0
	for k in range(left,right):
		cnt+=1
		if L[i] <= R[j]:
			a[k]=L[i]
			i+=1
		else:
			a[k]=R[j]
			j+=1
			
	
n=int(input())
cnt=0
a=list(map(int,input().split()))
merge_sort(a,0,len(a))
print(*a)
print(cnt)