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: Accepted)

<?php
ini_set("memory_limit", "-1");
fscanf(STDIN, "%d", $num_count);
$target_num = array_map("intval", explode(" ", trim(fgets(STDIN))));
$count = 0;
merge_sort(0, $num_count);

echo implode(" ", $target_num), "\n";
echo $count, "\n";

function merge($left, $mid, $right) {
    global $target_num, $count;
    
    $n1 = $mid - $left;
    $L = [];
    for ($i = 0; $i < $n1; $i++) {
        $L[] = $target_num[$left+$i];
    }
    $L[$n1] = PHP_INT_MAX;

    $n2 = $right - $mid;
    $R = [];
    for ($i = 0; $i < $n2; ++$i) {
        $R[] = $target_num[$mid+$i];
    }
    $R[$n2] = PHP_INT_MAX;

    $i = 0;
    $j = 0;
    for ($k = $left; $k < $right; $k++) {
        if ($L[$i] <= $R[$j]) {
            $target_num[$k] = $L[$i];
            $i++;
        } else {
            $target_num[$k] = $R[$j];
            $j++;
        }
        ++$count;
    }
}

function merge_sort($left, $right) {
    if ($left+1 < $right) {
        $mid = floor(($left + $right)/2);
        merge_sort($left, $mid);
        merge_sort($mid, $right);
        merge($left, $mid, $right);
    }
}