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 <cstdio>
#define MAX 1145140
#define INF 1145141919
using namespace std;
int n;
int A[MAX];
int L[MAX / 2], R[MAX / 2];
int cnt;
void merge(int left,int right,int mid) {
	int n1 = mid - left;
	int n2 = right - mid;
	int i;
	for (i = 0; i < n1; i++) {
		L[i] = A[left + i];
	}
	L[n1] = INF;
	for (i = 0; i < n2; i++) {
		R[i] = A[mid + i];
	}
	R[n2] = INF;
	int j = 0, k = 0;
	for (i = left; i < right; i++) {
		cnt++;
		if (L[j] < R[k]) {
			A[i] = L[j];
			j++;
		}
		else {
			A[i] = R[k];
			k++;
		}
	}

}
void mergeSort(int left,int right) {
	if (left + 1 < right) {
		int mid = (left + right) / 2;
		mergeSort(mid,right);
		mergeSort(left,mid);
		merge(left,right,mid);
	}
}
int main() {
	int i;
	scanf("%d", &n);
	for (i = 0; i < n; i++) {
		scanf("%d",&A[i]);
	}
	mergeSort(0,n);
	for (i = 0; i < n; i++) {
		if (i)printf(" ");
		printf("%d", A[i]);
	}
	printf("\n%d\n", cnt);
}
