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.*;
import java.io.*;

public class Main {
    int count = 0;
    
    public static void main(String[] args) {
        Main main = new Main();
        main.solv();
    }
    
    private void solv() {
        Scanner input = new Scanner(System.in);
        
        int n = input.nextInt();
        int[] S = new int[n];
        for (int i = 0; i < n; i++) S[i] = input.nextInt();
        
        count = 0;
        mergeSort(S, 0, S.length);
        print(S);
        System.out.println(count);
    }
    
    private void merge(int[] A, int left, int mid, int right) {
        int n1 = mid - left;
        int n2 = right - mid;
        int[] L = new int[n1+1], R = new int[n2+1];
        
        for (int i = 0; i < n1; i++) {
            L[i] = A[left + i];
        }
        for (int i = 0; i < n2; i++) {
            R[i] = A[mid + i];
        }
        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++];
            } else {
                A[k] = R[j++];
            }
        }
    }
    private void mergeSort(int[] A, int left, int right) {
        if (left + 1 < right) {
            int mid = (left + right) / 2;
            mergeSort(A, left, mid);
            mergeSort(A, mid, right);
            merge(A, left, mid, right);
        }
    }
    
    private void print(Object[] xs) {
        StringBuilder sb = new StringBuilder();
        for (Object x : xs) sb.append(x.toString()).append(' ');
        System.out.println(sb.toString().trim());
    }
    
    private void print(int[] xs) {
        StringBuilder sb = new StringBuilder();
        for (int x : xs) sb.append(x).append(' ');
        System.out.println(sb.toString().trim());
    }
    
    private static class Scanner {
        BufferedReader r;
        StreamTokenizer st;
        
        public Scanner(InputStream in) {
            r = new BufferedReader(new InputStreamReader(in));
            st = new StreamTokenizer(r);
        }
        
        public String next() {
            nextToken();
            return st.sval;
        }
        
        public Integer nextInt() {
            nextToken();
            return (int)st.nval;
        }
        
        private int nextToken() {
            int token = st.TT_EOF;
            try {
                token = st.nextToken();
            } catch (IOException e) {
            }
            return token;
        }
    }
}