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 Python (judge verdict: Accepted)

def merge(left, mid, right):
    L = S[left:mid]
    R = S[mid:right]
    lp, rp, xp = 0, 0, 0
    a, b = L[0], R[0]
    c = right - left
    x = [0] * c
    flg = True
    while flg:
        while flg and a <= b:
            x[xp] = a
            lp += 1
            xp += 1
            try:
                a = L[lp]
            except:
                for e in R[rp:]:
                    x[xp] = e
                    xp += 1
                flg = False
        while flg and a >= b:
            x[xp] = b
            rp += 1
            xp += 1
            try:
                b = R[rp]
            except:
                for e in L[lp:]:
                    x[xp] = e
                    xp += 1
                flg = False
    S[left:right] = x
    return c

def mergesort(left, right):
    c = 0
    if left + 1 < right:
        mid = (left + right)/2
        c += mergesort(left, mid)
        c += mergesort(mid, right)
        c += merge(left, mid, right)
    return c

global S
n = int(raw_input())
S = map(int, raw_input().split())

c = mergesort(0, n)
print " ".join(map(str,S))
print c