Problem:
Merge Sort

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)

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.

Constraints

n ≤ 500000

0 ≤ an element in S ≤ 109

Sample Input 1

10
8 5 9 2 6 3 7 1 10 4

Sample Output 1

1 2 3 4 5 6 7 8 9 10
34

Notes

Solution in C (judge verdict: Wrong Answer)

#include<stdio.h>
#define nmax 500000


void merge(int,int,int);
void mergeSort(int,int);

int A[nmax],count=0;
int main(){
  
  int n;
  int i;

  scanf("%d",&n);
  for( i = 0 ; i < n ; i++ )
    scanf("%d",&A[i]);

  mergeSort(0,n);

  for( i = 0 ; i < n-1 ; i++ )
    printf("%d ",A[i]);
  printf("%d\n",A[i]);
  printf("%d\n",count);

  return 0;
}

void merge(int left,int mid,int right)
{
  int n1 = mid - left;
  int n2 = right - mid;
  int L[n1+1],R[n2+1];
  int i,j,k;

  for( i = 0 ; i < n1 ; i++ )
    L[i] = A[left+i];
  for(i = 0 ; i < n2 ; i++ )
    R[i] = A[mid+i];
  L[n1] = 100000000;
  R[n2] = 100000000;
  i = 0;
  j = 0;
  for( k = left ; k < right ; k++ )
    {
      count++;
      if(L[i] <= R[j]){
	A[k] = L[i];
	i = i + 1;
      }
      else
	{
	  A[k] = R[j];
	  j = j + 1;
	}
    }
}

void mergeSort(int left,int right)
{
  int mid;

  if( left+1 < right )
    {
      mid = (left+right)/2;
      mergeSort(left,mid);
      mergeSort(mid,right);
      merge(left,mid,right);
    }

}