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
count=0
def mg(S,left,right,mid):
    global count
    L=[]
    L=S[left:mid]
    L.append(9999999999)
    R=[]
    R=S[mid:right]
    R.append(9999999999)
    r=0
    l=0
    for i in range(left,right):
        count=count+1
        if L[l]<=R[r]:
            S[i]=L[l]
            l=l+1
        else:
            S[i]=R[r]
            r=r+1
def ms(S,left,right):
    if right>left+1:
        mid=(right+left)//2
        ms(S,left,mid)
        ms(S,mid,right)
        mg(S,left,right,mid)
n=int(input())
S=[]
S=input().split()
S=[int(u) for u in S]
ms(S,0,n)
for i in range(0,n-1):
    print(S[i],end=" ")
print(S[n-1])
print(count)
