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)


Notes

Constraints

* n ≤ 500000
* 0 ≤ an element in S ≤ 109

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.

Example

Input

10
8 5 9 2 6 3 7 1 10 4


Output

1 2 3 4 5 6 7 8 9 10
34
cnt=0
def mer(l,r):
    global cnt
    ll=len(l)
    rr=len(r)
    md=[]
    i,j=0,0
    l.append(float('inf'))
    r.append(float('inf'))
    for k in range(ll+rr):
        cnt+=1
        if l[i]<=r[j]:
            md.append(l[i])
            i+=1
        else:
            md.append(r[j])
            j+=1
    return md
def mergesort(a):
    m=len(a)
    if m<=1:
        return a
    m=m//2
    l=mergesort(a[:m])
    r=mergesort(a[m:])
    return mer(l,r)
n=int(input())
a=list(map(int, input().split()))
b=mergesort(a)
for i in range(n-1):
    print(b[i],end=" ")
print(b[n-1])
print(cnt)
