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.*;

class Main{
    static int count = 0;
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int[] S = new int[n];
        for(int i = 0;i < n;i++){
            S[i] = sc.nextInt();
        }

        mergeSort(S);

        for(int i = 0;i < n;i++){
            if(i != 0)  System.out.print(" ");
            System.out.print(S[i]);
        }
        System.out.println();
        System.out.println(count);
    }

    /* 2つの配列LとRを併合してAを作成 */
    static void merge(int[] L,int [] R,int[] A){
        int i = 0,j = 0;    //カウンタ
        while(i < L.length || j < R.length){
            if(j >= R.length || (i < L.length && L[i] < R[j])){
                A[i + j] = L[i];
                count++;
                i++;
            }
            else{
                A[i + j] = R[j];
                count++;
                j++;
            }
        }
    }

    /* データのソート */
    static void mergeSort(int[] A){
        if(A.length > 1){
            int m = A.length / 2;
            int n = A.length - m;
            int[] L = new int[m];
            int[] R = new int[n];
            for(int i = 0;i < m;i++)    L[i] = A[i];
            for(int i = 0;i < n;i++)    R[i] = A[m + i];
            mergeSort(L);
            mergeSort(R);
            merge(L,R,A);
        }
    }
}
