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: Runtime Error)

<?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($L,500001);
			array_push($R,500001);
			$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);
?>