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)

#ALDS1_5-B Merge Sort
from collections import deque

def merge(A,B):
    ans = deque()
    count = 0
    while(True):
        if len(A)==0 and len(B) == 0:
            break
        elif len(A) == 0:
            ans.append(B.popleft())
        elif len(B) == 0:
            ans.append(A.popleft())
        elif A[0] > B[0]:
            ans.append(B.popleft())
        else:
            ans.append(A.popleft())
        count+=1
    return (ans.copy(),count)

n = int(input())
S = [int(i) for i in input().split()]
div = deque([S])
mer = deque()
count = 0
while(len(div)>0):
    d = div.pop()
    if(len(d)>2):
        mid = len(d)//2
        div.appendleft(d[:mid])
        div.appendleft(d[mid:])
    elif(len(d)==2):
        if d[0] > d[1]:
            mer.appendleft(d[::-1])
        else:
            mer.appendleft(d)
        count+=2
    else:
        mer.appendleft(d)
        
while(len(mer)>1):
    A = deque(mer.popleft())
    B = deque(mer.popleft())
    ret = merge(A,B)
    mer.append(ret[0])
    count+=ret[1]
    
ans = ""
for i in ret[0]:
    ans += str(i) + " "
print(ans[:-1])
print(count)