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
import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {

	public static void main(String[] args) throws Exception{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

//		Scanner s = new Scanner(System.in);
		int arrayCnt = Integer.parseInt(br.readLine());
		int[] array = new int[arrayCnt];
		String[] tmpArray = br.readLine().split(" ");
		for(int i=0 ; i<array.length ; i++) {
			array[i] = new Integer(tmpArray[i]).intValue();
		}

		int cc = sort(array, 0, array.length-1);
		StringBuilder sb = new StringBuilder();
		for(int i=0 ; i<array.length ; i++) {
			sb.append(array[i]).append(" ");
		}
		System.out.println(sb.toString().trim());
		System.out.println(cc);
	}

	public static int sort(int[] array, int start, int end) {
		int c = 0;
		if(start < end){
			int mid = (start+end)/2;
			c += sort(array, start, mid);
			c += sort(array, mid+1, end);
			c += merge(array, start, end);
		}
		return c;
	}

	public static int merge(int[] array, int start, int end) {
		int cnt = 0;
		int mid = (start+end) / 2;
		int[] left = new int[mid-start+2];
		int[] right = new int[end-mid+1];
		for(int i=0 ; i<left.length-1 ; i++) {
			left[i] = array[start+i];
		}
		for(int j=0 ; j<right.length-1 ; j++) {
			right[j] = array[mid+j+1];
		}
		int l = 0;
		int n = 0;
		left[mid-start+1] = Integer.MAX_VALUE;
		right[end-mid] = Integer.MAX_VALUE;
		for(int k=0 ; k<left.length+right.length-2 ; k++) {
			if(left[l] > right[n]) {
				array[start] = right[n];
				n++;
			}else{
				array[start] = left[l];
				l++;
			}
			cnt++;
			start++;
		}
		return cnt;
	}
}