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
cnt = 0
def merge(S,left,right,mid):
    a = mid - left
    b = right - mid
    L = S[left:left+a]+[float("inf")]
    R = S[mid:mid+b]+[float("inf")]
    j = 0
    k = 0
    for i in range(left,right):
        global cnt
        cnt+=1
        if L[j] <= R[k]:
            S[i] = L[j]
            j += 1
        else:
            S[i] = R[k]
            k += 1
            
def mergeSort(S,left,right):
    if left+1<right:
        mid = (int)((left+right)/2)
        mergeSort(S,left,mid)
        mergeSort(S,mid,right)
        merge(S,left,right,mid)
        
n = int(input())
S = list(map(int, input().split()))
mergeSort(S,0,n)
print(*S)
print(cnt)
