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 Ruby (judge verdict: Accepted)

def merge_sort(array, left, right)
	return 0 unless left + 1 < right
	mid = (left + right) / 2
	compared_count  = merge_sort(array, left, mid)
	compared_count += merge_sort(array, mid, right)
	compared_count += merge(array, left, mid, right)
	compared_count
end

def merge(array, left, mid, right)
	left_array_size  = mid - left
	right_array_size = right - mid

	left_array  = []
	left_array_size.times { |i| left_array << array[left + i] }

	right_array = []
	right_array_size.times { |i| right_array << array[mid + i] }

	# 下記のループでの番兵をセット(最後は必ず片方がnilになるため)
	left_array  << Float::INFINITY
	right_array << Float::INFINITY

	compared_count = 0
	i = j = 0
	(left...right).each do |k|
		if left_array[i] <= right_array[j]
			array[k] = left_array[i]
			i += 1
		else
			array[k] = right_array[j]
			j += 1
		end
		compared_count += 1
	end
	compared_count
end

array_size = STDIN.gets.to_i
array = STDIN.gets.split[0...array_size].map(&:to_i)
compared_count = merge_sort(array, 0, array_size)
puts array.join(" ")
puts compared_count