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 <iostream>

using namespace std;

int cnt;
int A[500010], tmp[500010];

void margeSort(int l, int r) {
    if (r - l == 1) return;
    int m = (l + r) / 2;
    margeSort(l, m);
    margeSort(m, r);
    int i = 0;
    for (int il = l, ir = m; il < m || ir < r; cnt++)
        if (il < m)
            if (ir < r)
                tmp[i++] = A[il] < A[ir] ? A[il++] : A[ir++];
            else
                tmp[i++] = A[il++];
        else
            tmp[i++] = A[ir++];
    for (int j = 0; j < i; ++j) A[l + j] = tmp[j];
}

void outputArray(int a[], int n) {
    cout << a[0];
    for (int i = 1; i < n; ++i) {
        cout << ' ' << a[i];
    }
    cout << endl;
}

int main() {
    int n;
    cin >> n;
    for (int i = 0; i < n; ++i) cin >> A[i];
    margeSort(0, n);
    outputArray(A, n);
    cout << cnt << endl;
    return 0;
}

