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
def g(A,l,m,r):
 global c
 L,R=A[l:m]+[1e9],A[m:r]+[1e9]
 i=j=0
 for k in range(l,r):
  if L[i]<R[j]:A[k]=L[i];i+=1
  else:A[k]=R[j];j+=1
  c+=1
def s(A,l,r):
 if l+1<r:
  m=(l+r)//2
  s(A,l,m);s(A,m,r)
  g(A,l,m,r)
c=0
n=int(input())
A=list(map(int,input().split()))
s(A,0,n)
print(*A)
print(c)
