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.util.*;

public class Main {
    static int count = 0;
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
		    arr[i] = sc.nextInt();
		}
		mergeSort(arr, 0, n);
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < n; i++) {
		    if (i > 0) {
		        sb.append(" ");
		    }
		    sb.append(arr[i]);
		}
		System.out.println(sb);
		System.out.println(count);
	}
	
	static void mergeSort(int[] arr, int left, int right) {
	    if (left + 1 < right) {
	        int mid = (left + right) / 2;
	        mergeSort(arr, left, mid);
	        mergeSort(arr, mid, right);
	        merge(arr, left, mid, right);
	    }
	}
	
	static void merge(int[] arr, int left, int mid, int right) {
	    int n1 = mid - left;
	    int n2 = right - mid;
	    int[] lArr = new int[n1 + 1];
	    int[] rArr = new int[n2 + 1];
	    for (int i = 0; i < n1; i++) {
	        lArr[i] = arr[left + i];
	    }
	    for (int i = 0; i < n2; i++) {
	        rArr[i] = arr[mid + i];
	    }
	    lArr[n1] = Integer.MAX_VALUE;
	    rArr[n2] = Integer.MAX_VALUE;
	    int lIdx = 0;
	    int rIdx = 0;
	    for (int i = left; i < right; i++) {
	        if (lArr[lIdx] <= rArr[rIdx]) {
	            arr[i] = lArr[lIdx];
	            lIdx++;
	        } else {
	            arr[i] = rArr[rIdx];
	            rIdx++;
	        }
	        count++;
	    }
	}
}

