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.IOException;
import java.io.InputStreamReader;

class Main{
    private static int t = 0;
    public static void main(String[] args) throws IOException{
        final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        final StringBuilder sb = new StringBuilder();
        final int n = Integer.parseInt(br.readLine());
        final String[] in = br.readLine().split(" ");
        final int[] s = new int[n];
        for(int i = 0; i<n; i++)
            s[i] = Integer.parseInt(in[i]);
        mergeSort(s, 0, n);
        sb.append(s[0]);
        for(int i = 1; i<n; i++)
            sb.append(' ').append(s[i]);
        sb.append('\n').append(t).append('\n');
        System.out.print(sb);
    }
    private static void mergeSort(int[] a, int l, int r){
        if(l+1<r){
            final int m = (l+r)>>>1;
            mergeSort(a, l, m);
            mergeSort(a, m, r);
            merge(a, l, m, r);
        }
    }
    private static void merge(int[] a, int l, int m, int r){
        final int n1 = m-l;
        final int n2 = r-m;
        final int[] L = new int[n1+1];
        final int[] R = new int[n2+1];
        System.arraycopy(a, l, L, 0, n1);
        System.arraycopy(a, m, R, 0, n2);
        L[n1] = R[n2] = Integer.MAX_VALUE;
        int i = 0, j = 0;
        for(int k = l; k<r; k++){
            if(L[i]<=R[j]) a[k] = L[i++];
            else a[k] = R[j++];
            t++;
        }
    }
}