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: Time Limit Exceeded)

#!/usr/bin/ruby
$c=0
$sentinel=[999999999]
def merge(a,left,mid,right)
	n1=mid-left
	n2=right-mid
	l=a[left,n1]+$sentinel
	r=a[mid,n2]+$sentinel
	i=0
	j=0
	left.step(right-1){|k|
		$c+=1
		if l[i]<=r[j]
			a[k]=l[i]
			i=i+1
		else
			a[k]=r[j]
			j=j+1
		end
	}
end

def mergesort(a,left,right)
	if left+1<right
		mid=(left+right)/2
		mergesort(a,left,mid)
		mergesort(a,mid,right)
		merge(a,left,mid,right)
	end
end

n=gets.to_i
a=gets.split.map(&:to_i)
mergesort(a,0,a.length)
puts a*' '
p $c