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.*;

class Main {
        public static long[] A;
        public static int count;
        public static void main(String args[]) {
                count = 0;
                new Thread(null, ()->{
                        Scanner sc = new Scanner(System.in);
                        int N = sc.nextInt();
                        A = new long[N];
                        for (int i = 0; i < N; i++) {
                                A[i] = sc.nextLong();
                        }
                        mergeSort(0, N);
                        for (int i = 0; i < N; i++) {
                                System.out.print(A[i]);
                                System.out.print(i != N-1 ? " ":"\n");
                        }
                        System.out.println(count);
                }, "", 1<<24).start();
        }
        public static void merge(int left, int mid, int right) {
                int n1 = mid - left;
                int n2 = right - mid;
                long[] L = new long[n1 + 1];
                long[] R = new long[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] = 1000000001L;
                R[n2] = 1000000001L;
                int i = 0;
                int 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++;
                        }
                }
        }
        public static void mergeSort(int left, int right) {
                if (left + 1 < right) {
                        int mid = (left + right) / 2;
                        mergeSort(left, mid);
                        mergeSort(mid, right);
                        merge(left, mid, right);
                }
        }
        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 int nextInt() {
                        nextToken();
                        return (int)st.nval;
                }

                public long nextLong() {
                        nextToken();
                        return (long)st.nval;
                }

                private int nextToken() {
                        int token = st.TT_EOF;
                        try {
                                token = st.nextToken();
                        } catch (IOException e) {
                        }
                        return token;
                }
        }
}