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 PHP (judge verdict: Time Limit Exceeded)

<?php
    $count=0;
     
    function Merge(&$A,$left,$mid,$right){
            global $count;
            $n1 = $mid - $left;
            $n2 = $right - $mid;
            $L = array();
            $R = array();
            for($i = 0;$i < $n1;$i++){
                    array_push($L,$A[$left+$i]);
            }
            for($i = 0;$i < $n2;$i++){
                    array_push($R,$A[$mid+$i]);
            }
            array_push($L,1000000001);
            array_push($R,1000000001);
            $i = 0;
            $j = 0;
            for($k = $left;$k < $right;$k++){
                    $count++;
                    if($L[$i]<=$R[$j]){
                            $A[$k] = $L[$i];
                            $i++;
                    }else{
                            $A[$k] = $R[$j];
                            $j++;
                    }
            }
    }
 
    function Merge_Sort(&$A,$left,$right){
            if($left + 1 < $right){
                    $mid = (int)(($left + $right)/2);
                    Merge_Sort($A,$left,$mid);
                    Merge_Sort($A,$mid,$right);
                    Merge($A,$left,$mid,$right);
            }
    }
 
    $A=array();
    (int)$max=fgets(STDIN);
    $num=fgets(STDIN);
    for($i=0;$i<$max;$i++){
            if($i==0){
                    $n=strtok($num," ");
            }else{
                    $n=strtok(" ");
            }
            array_push($A,(int)$n);
    }
     
    Merge_Sort($A,0,$max);
     
    for($i=0;$i<$max;$i++){
            printf("%d",$A[$i]);
            if($i!=$max-1){
                    printf(" ");
            }else{
                    printf("\n");
            }
    }
    printf("%d",$count);
?>