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.util.stream.*;

class Main {
    public static int count = 0;
    public static void main(String[] args) {
	Scanner in = new Scanner(System.in);
	int n = in.nextInt();
	int[] S = new int[n];
	for (int i = 0; i < n; i++) {
	    S[i] = in.nextInt();
	}
	mergeSort(S, 0, n);
	System.out.println(IntStream.of(S)
			   .mapToObj(String::valueOf)
			   .collect(Collectors.joining(" ")));
	System.out.println(count);
    }

    public static void merge(int[] S, int left, int mid, int right) {
	int n1 = mid - left, n2 = right - mid;
	int[] L = new int[n1 + 1], R = new int[n2 + 1];
	for (int i = 0; i < n1; i++) {
	    L[i] = S[left + i];
	}
	for (int i = 0; i < n2; i++) {
	    R[i] = S[mid + i];
	}
	L[n1] = R[n2] = Integer.MAX_VALUE;
	int i = 0, j = 0;
	for (int k = left; k < right; k++) {
	    count++;
	    if (L[i] <= R[j]) {
		S[k] = L[i++];
	    } else {
		S[k] = R[j++];
	    }
	}
    }

    public static void mergeSort(int[] S, int left, int right) {
	if (left + 1 < right) {
	    int mid = (left + right) / 2;
	    mergeSort(S, left, mid);
	    mergeSort(S, mid, right);
	    merge(S, left, mid, right);
	}
    }
}

