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.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;

/**
 *
 * @author baito
 */
public class Main {

    /**
     * @param args the command line arguments
     * @throws java.io.FileNotFoundException
     */
    static int count = 0;
    public static void main(String[] args) throws Exception {
        // TODO code application logic here

        ContestScanner sc = new ContestScanner();
        int n = sc.nextInt();
        int A[] = new int[n];
        for (int i = 0; i < n; i++) {
            A[i] = sc.nextInt();
        }
        mergeSort(A, 0, n);
        StringBuilder sb = new StringBuilder();
        sb.append(A[0]);
        for (int i = 1; i < n; i++) {
            sb.append(' ').append(A[i]);
        }
        System.out.println(sb);
        System.out.println(count);
       
    }
    //??????not include
    public static void mergeSort (int[] A , int l , int r ) {
        if(l + 1 < r){
            int mid = (l + r)/2;
            mergeSort(A, l, mid);
            mergeSort(A, mid,r);
            merge(A,l,mid,r);
            
        }
        
    }
    public static void merge (int[] A , int l , int m , int r) {
        int n1  = m - l + 1;
        int n2 =  r - m + 1;
        int L[] = new int[n1];
        int R[] = new int[n2];
        System.arraycopy(A, l, L, 0, n1-1);
        L[n1-1] = Integer.MAX_VALUE;
        System.arraycopy(A, m, R, 0, n2-1);
        R[n2-1] = Integer.MAX_VALUE;
        for (int i = l, j= 0 , k= 0; i < r; i++) {
            count++;
            if(L[j] >= R[k]){
                A[i] = R[k++];
            } else {
                A[i] = L[j++];
            }
            
            
        }
        
        
    }
    
    
    
}

//????????????????????????
class ContestScanner {
    
    private final BufferedReader reader;
    private String[] line;
    private int idx;
    
    public ContestScanner() throws FileNotFoundException {
        reader = new BufferedReader(new InputStreamReader(System.in));
    }
    
    public ContestScanner(String filename) throws FileNotFoundException {
        reader = new BufferedReader(new InputStreamReader(new FileInputStream(filename)));
    }
    //???????????? 

    public String readLine() throws Exception {
        return reader.readLine();
    }
    
    public String nextToken() throws IOException {
        if (line == null || line.length <= idx) {
            line = reader.readLine().trim().split(" ");
            idx = 0;
        }
        return line[idx++];
    }
    
    public long nextLong() throws IOException, NumberFormatException {
        return Long.parseLong(nextToken());
    }
    
    public int nextInt() throws NumberFormatException, IOException {
        return (int) nextLong();
    }
    
    public double nextDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(nextToken());
    }
}