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.InputStreamReader;
import java.util.stream.Stream;

public class Main {
    static final int MAX = 1000000001;
    static int count = 0;

    public static void main(String[] args) throws Exception {
        // Here your code !
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        int[] S = Stream.of(br.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
        int[] R = mergeSort(S, 0, n-1);
        
        StringBuilder sb = new StringBuilder();
        sb.append(R[0]);
        for(int i = 1; i < R.length - 1; i++) {
            sb.append(" ");
            sb.append(R[i]);
        }
        System.out.println(sb.toString());
        System.out.println(count);
    }

    public static int[] mergeSort(int[] s, int left, int right) {
        if(left == right) {
            int[] ret = new int[2];
            ret[0] = s[left];
            ret[1] = MAX;
            return ret;
        } else {
            int mid = left + (right - left) / 2;
            int[] l = mergeSort(s, left, mid);
            int[] r = mergeSort(s, mid+1, right);
            return merge(l, r);
        }
    }

    public static int[] merge(int[] left, int[] right) {
        int[] r = new int[(left.length-1) + (right.length-1) + 1];
        int ri = 0;
        int li = 0;
        for(int i = 0; i < r.length - 1; i++) {
            if(left[li] <= right[ri]) {
                r[i] = left[li];
                li++;
            } else {
                r[i] = right[ri];
                ri++;
            }
            count++;
        }
        r[r.length - 1] = MAX;

        return r;
    }
}