p02272 Merge Sort
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
```python
count = 0

def merge(a, left, mid, right):
    global count

    l = a[left:mid]
    r = a[mid:right]
    l.append(10**9+1)
    r.append(10**9+1)

    i = 0
    j = 0
    for k in range(left, right):
        count += 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 left + 1 < right:
        mid = (left + right) // 2
        mergeSort(a, left, mid)
        mergeSort(a, mid, right)
        merge(a, left, mid, right)


if __name__ == '__main__':
    n = int(input())
    a = [int(x) for x in input().split()]

    mergeSort(a, 0, n)

    print(*a)
    print(count)

```