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 <iostream>

using namespace std;

#define MAX 500000
#define SENTINEL 2e9

int L[MAX / 2 + 2], R[MAX / 2 + 2];
int cnt;

void merge(int A[], int left, int mid, int right) {
	int n1 = mid - left;
	int n2 = right - mid;
	for (int i = 0; i < n1; ++i) L[i] = A[left + i];
	for (int i = 0; i < n2; ++i) R[i] = A[mid + i];
	L[n1] = R[n2] = SENTINEL;
	int i = 0, j = 0;
	for (int k = left; k < right; ++k) {
		cnt++;
		if (L[i] <= R[j]) A[k] = L[i++];
		else A[k] = R[j++];
	}
}

void mergeSort(int A[], int left, int right) {
	if (left < right - 1) {
		int mid = (left + right) / 2;
		mergeSort(A, left, mid);
		mergeSort(A, mid, right);
		merge(A, left, mid, right);
	}
}

int main() {
	int n; cin >> n;
	int A[MAX];
	for (int i = 0; i < n; ++i) cin >> A[i];
	mergeSort(A, 0, n);
	for (int i = 0; i < n; ++i) {
		if (i) cout << " ";
		cout << A[i];
	}
	cout << endl << cnt << endl;

	return 0;
}
