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 minimum_cost_sort(A):
  cost = 0
  B = sorted(A)
  for i in range(len(B)):
    x = A.index(B[i])
    cnt = 0
    tmp = 0
    while x != i:
      y = A.index(B[x])
      A[x], A[y] = A[y], A[x]
      tmp += A[x] + A[y]
      cnt += 1
      x = y
    if cnt > 0:
      cost += tmp
      #cost += min(tmp, (B[i] + B[0]) * 2 + tmp - (B[i] - B[0]) * cnt)
  return cost

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