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)


Notes

Constraints

* n ≤ 500000
* 0 ≤ an element in S ≤ 109

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.

Example

Input

10
8 5 9 2 6 3 7 1 10 4


Output

1 2 3 4 5 6 7 8 9 10
34
num = 0
def marge_sort(array):
    global num
    if len(array) < 2: return array
    
    mid = len(array) // 2
    left = marge_sort(array[:mid])
    right = marge_sort(array[mid:])
    
    len_l, len_r = len(left), len(right)
    left += [float("inf")]
    right += [float("inf")]
    
    marray = [0] * (len_l + len_r)
    
    l, r = 0, 0
    for i in range(len_l + len_r):
        num += 1
        if left[l] <= right[r]:
            marray[i] = left[l]
            l += 1
        else:
            marray[i] = right[r]
            r += 1
        
    return marray

n = int(input())
a = list(map(int, input().split()))

print(" ".join(map(str, marge_sort(a))))
print(num)
