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
import sys,collections
n = int(sys.stdin.readline())
a = list(map(int,sys.stdin.readline().split()))
c = 0
def merge(a,left,mid,right):
  n1 = mid - left
  n2 = right - mid
  L = a[left:mid]
  R = a[mid:right]
  L.append(float("inf"))
  R.append(float("inf"))
  i = 0
  j = 0
  for k in range(left,right):
    global c
    c += 1
    if L[i] <= R[j]:
      a[k] = L[i]
      i += 1
    else:
      a[k] = R[j]
      j += 1

def mergeSort(a,left,right):
  if 1 < right - left:
    mid = (left+right)//2
    mergeSort(a,left,mid)
    mergeSort(a,mid,right)
    merge(a,left,mid,right)

mergeSort(a,0,n)
print(" ".join(map(str,a)))
print(c)
