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: Accepted)

#include<stdio.h>
#define N 500000
#define M 2000000000


int L[N/2+2],R[N/2+2];
int count=0;


void merge(int A[],int l,int m,int r){
  int i,j,k;
  int n1;
  int n2;
  n1 = m - l;
  n2 = r - m;
  for(i=0;i<n1;i++){
    L[i] = A[l+i];
  }
  for(i=0;i<n2;i++){
    R[i]=A[m+i];
  }
  L[n1] = R[n2]=M;
  i = j = 0;
  for(k=l;k<r;k++){
    count++;
    if(L[i] <= R[j]){
      A[k] = L[i];
      i++;
    }
      else {
	A[k] = R[j];
	j++;
      }
  }
}


void mergesort(int A[],int l,int r){
  int m;
  if(l+1<r){
    m = (l+r)/2;
    mergesort(A,l,m);
    mergesort(A,m,r);
    merge(A,l,m,r);
  }
}


int main(){
  int i,a,b[N];
  scanf("%d",&a);
  for(i=0;i<a;i++){
    scanf("%d",&b[i]);
  }
  mergesort(b,0,a);
  for(i=0;i<a-1;i++){
    //if(i>=1) printf(" ");
    printf("%d ",b[i]);
  }
  printf("%d\n",b[a-1]);
  printf("%d",count);
  printf("\n");
  return 0;
}