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)

import sys, math
input = sys.stdin.readline

MAX = 2e9

def merge(A, left, mid, right):
    n1 = mid - left
    n2 = right - mid
    L = A[left:mid]
    L.append(MAX)
    R = A[mid:right]
    R.append(MAX)
    merged = []
    index_L = 0
    index_R = 0
    comp_cnt = 0
    for _ in range(n1+n2):
        cand_L = L[index_L]
        cand_R = R[index_R]
        comp_cnt += 1
        if (cand_L < cand_R):
            merged.append(cand_L)
            index_L += 1
        else:
            merged.append(cand_R)
            index_R += 1
    A[left:right] = merged
    return comp_cnt
        
def merge_sort(A, left, right):
    comp_cnt = 0
    if (left + 1 < right):
        # Devide
        mid = (left + right) // 2
        # Solve
        _, cnt = merge_sort(A, left, mid)
        comp_cnt += cnt
        _, cnt = merge_sort(A, mid, right)
        comp_cnt += cnt
        # Conquer
        comp_cnt += merge(A, left, mid, right)
    return A, comp_cnt

def main():
    N = int(input())
    S = list(map(int, input().split()))
    left = 0
    right = len(S)
    merged, cnt = merge_sort(S, left, right)
    print(" ".join([str(x) for x in merged]))
    print(cnt)

if __name__ == "__main__":
    main()