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(); //数列Sの長さ
        int[] s = new int[n]; //数列S
        for (int i=0; i<n; i++) {
            s[i] = sc.nextInt();
        }
        //マージソート
        mergeSort(s,0,n); //配列、０、配列の長さ
        //出力
        System.out.print(s[0]);
        for (int i=1; i<n; i++) {
            System.out.print(" " + s[i]);
        }
        System.out.println();
        System.out.println(count);
    }
    /**
     * マージソート
     */
    static void mergeSort(int[] s, int left, int right) {
        if(left+1 < right) {
            int mid = (left+right)/2;
            mergeSort(s, left, mid); //先頭から中間まで
            mergeSort(s, mid, right); //中間から末尾まで
            merge(s,left,mid,right); //二つの配列を結合する
        }
    }
    /**
     * マージ
     */
    static void merge(int[] s, int left, int mid, int right) {
        int n1 = mid-left;
        int n2 = right-mid;
        int[] a = new int[n1+1];
        int[] b = new int[n2+1];
        for(int i=0; i<n1; i++) a[i] = s[left+i];
        for(int i=0; i<n2; i++) b[i] = s[mid+i];
        a[n1] = Integer.MAX_VALUE;
        b[n2] = Integer.MAX_VALUE;
        int i=0, j=0;
        for (int k=left; k<right; k++) {
            count++;
            if(a[i]<=b[j]) {
                s[k] = a[i];
                i++;
            } else {
                s[k] = b[j];
                j++;
            }
        }
    }
}

