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 <algorithm>
#include <cstdio>

static const size_t n_max = 500000;
static int S[n_max], L[n_max], R[n_max];
static int c = 0;

void merge_sort(size_t i, size_t j) {
  if (j - i <= 1)
    return;
  size_t k = (i + j) / 2;
  merge_sort(i, k);
  merge_sort(k, j);
  std::copy(S + i, S + k, L);
  std::copy(S + k, S + j, R);
  c += j - i;
  for (size_t l = i, p = 0, q = 0;; l++) {
    if (p < k - i && q < j - k) {
      if (L[p] <= R[q])
        S[l] = L[p++];
      else
        S[l] = R[q++];
    } else if (p < k - i)
      S[l]= L[p++];
    else if (q < j - k)
      S[l] = R[q++];
    else
      break;
  }
}

int main() {
  size_t n;
  scanf("%zu", &n);
  for (size_t i = 0; i < n; i++)
    scanf("%d", S + i);
  merge_sort(0, n);
  for (size_t i = 0; i < n - 1; i++)
    printf("%d ", S[i]);
  printf("%d\n%d\n", S[n-1], c);
  return 0;
}