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
#include <bits/stdc++.h>
using namespace std;

int n, a[500010];
int cnt = 0;

int L[250010], R[250010];
const int inf = 2000000000;

void merge( int  l, int m, int r ){
    int n1 = m - l;
    int n2 = r - m;
    for( int i = 0; i < n1; i++ ) L[i] = a[l + i];
    for( int i = 0; i < n2; i++ ) R[i] = a[m + i];

    L[n1] = R[n2] = inf;
    int i = 0, j = 0;
    for( int k = l; k < r; k++ ){
        cnt++;
        if( L[i] <= R[j] ){
            a[k] = L[i++];
        }
        else {
            a[k] = R[j++];
        }
    }
}

void msort( int l, int r ){
    if( l + 1 < r ){
        int m = ( l + r )/ 2;
        msort( l, m );
        msort( m, r );
        merge( l, m, r );
    }
}

int main()
{
    cin >> n;
    for( int i = 0; i < n; i++ ) cin >> a[i];

    msort( 0, n );

    for( int i = 0; i < n; i++ ) cout << ( i ? " " : "" ) << a[i];
    cout << endl << cnt << endl;

    return 0;
}

