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;

class Main {
    static int compare = 0;

    static void merge(int[] A, int left, int mid, int right){
        int l1 = mid-left;
        int l2 = right-mid;

        int[] L = new int[l1+1];
        int[] R = new int[l2+1];

        for(int i = 0; i < l1; i++)
            L[i] = A[left + i];

        for(int i = 0; i < l2; i++)
            R[i] = A[mid + i];

        L[l1] = R[l2] = 1000000001; // Sの要素より確実に大きいInfのようなものを番兵として扱う

        int i = 0;
        int j = 0;

        for(int k = left; k < right; k++){
            compare++;

            if(L[i] <= R[j]){
                A[k] = L[i];
                i++;
            }else{
                A[k] = R[j];
                j++;
            }

        }
    }

    static 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);
        }
    }

    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(" ");
        int[] arr = new int[n];

        for (int i = 0; i < n; i++) {
            arr[i] = Integer.parseInt(input[i]);
        }

        mergeSort(arr, 0, n);

        StringBuilder sb = new StringBuilder();

        sb.append(arr[0]);

        for(int i = 1; i < n; i++){
            sb.append(" " + arr[i]);
        }

        System.out.println(sb.toString());
        System.out.println(compare);
    }
}
