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 merge(A, left, mid, right):
	global count

	L = A[left:mid] + [1000000001]
	R = A[mid:right] + [1000000001]

	i = j = 0
	for k in range(left, right):
		if L[i] <= R[j]:
			A[k] = L[i]
			i += 1
		else:
			A[k] = R[j]
			j += 1
	count += right - left

def m_Sort(A, left, right):
	if left + 1 < right:
		mid = (left + right) // 2
		m_Sort(A, left, mid)
		m_Sort(A, mid, right)
		merge(A, left, mid, right)

if __name__ == '__main__':
	n = int(input())
	A = list(map(int, input().split()))
	count = 0
	m_Sort(A, 0, n)
	print(*A)
print(count)

