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.InputStreamReader;
import java.io.IOException;
import java.io.BufferedReader;
import java.lang.Integer ;

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

        int n = Integer.parseInt(br.readLine());
        String[] input = br.readLine().split(" " , n);
        int[] A = new int[n];
        
        for(int i = 0; i < n; i++){
            A[i] = Integer.parseInt(input[i]);
        }
        int count=mergeSort(A,0,n);
        printArray(A);
        System.out.println(count);
    }

    static void printArray(int[] A){
        StringBuilder sb = new StringBuilder();
        for(int k : A){
            sb.append(k + " ");
        }
        System.out.println(sb.toString().substring(0 , sb.length() - 1));
    }

    static int mergeSort(int[] A, int left, int right){
        int count=0;
        if(left+1<right){
            int mid = (left+right)/2;
            count+=mergeSort(A, left, mid);
            count+=mergeSort(A, mid, right);
            count+=merge(A, left, mid, right);
        }
        return count;
    }

    static int merge(int[] A, int left, int mid, int right){
        int count=0; //comparisons
        int n1=mid-left, n2=right-mid;
        int[] L=new int[n1+1], R=new int[n2+1];
        System.arraycopy(A, left, L, 0, n1);
        System.arraycopy(A, mid, R, 0, n2);
        L[n1]=Integer.MAX_VALUE;
        R[n2]=Integer.MAX_VALUE;
        int i=0, j=0;
        for(int k=left; k<right; k++){
            count++;
            if(L[i]<=R[j]){
                A[k]=L[i];
                i++;
            }else{
                A[k]=R[j];
                j++;
            }
        }
        return count;
    }
}

