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
#include <queue>
#include <cstdio>
using namespace std;
int n, c, v, dp[500007];
int main() {
	scanf("%d",&n); dp[n]=1;
	for(int i=(n+2)/2;i>1;i--) dp[i]=dp[2*i-1]+2*dp[2*i]+dp[2*i+1];
	for(int i=2;i<=n;i++) c+=dp[i]*i;
	priority_queue<int> que;
	for(int i=0;i<n;i++) scanf("%d", &v), que.push(-v);
	for(int i=0;i<n;i++) {
		if(i) printf(" ");
		printf("%d", -que.top()); que.pop();
	}
	printf("\n%d\n", c);
	return 0;
}