You are given $n$ integers $w_i (i = 0, 1, ..., n-1)$ to be sorted in ascending order. You can swap two integers $w_i$ and $w_j$. Each swap operation has a cost, which is the sum of the two integers $w_i + w_j$. You can perform the operations any number of times.

Write a program which reports the minimal total cost to sort the given integers.

Constraints

* $1 \leq n \leq 1,000$
* $0 \leq w_i\leq 10^4$
* $w_i$ are all different

Input

In the first line, an integer $n$ is given. In the second line, $n$ integers $w_i (i = 0, 1, 2, ... n-1)$ separated by space characters are given.

Output

Print the minimal cost in a line.

Examples

Input

5
1 5 3 4 2


Output

7


Input

4
4 3 2 1


Output

10
def partition(A, l, r):
  p = A[r]
  j = l - 1
  for i in range(l, r):
    if A[i] <= p:
      j += 1
      A[j], A[i] = A[i], A[j]
  j += 1
  A[j], A[r] = A[r], A[j]
  return j

def quick_sort(A, l, r):
  if l < r:
    p = partition(A, l, r)
    quick_sort(A, l, p - 1)
    quick_sort(A, p + 1, r)

def minimum_cost_sort(A):
  cost = 0
  B = A[:]
  quick_sort(A, 0, len(A) - 1)
  for i in range(len(A) // 2):
    if A[i] != B[i]:
      cost += A[i] + B[i]
  return cost

N = int(input())
A = list(map(int, input().split()))
print(minimum_cost_sort(A))