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
import math

n = int(input())
A = list(map(int,input().split()))

MAX = max(A)
m = min(A)
B = A.copy()
result = 0

def merge(A, left, mid, right):

  global  count

  L = A[left:mid]
  L.append(math.inf)
  R = A[mid:right]
  R.append(math.inf)
  i = 0
  j = 0

  for k in range(left,right):
    if L[i] <= R[j]:
      A[k] = L[i]
      i = i + 1
    else:
      A[k] = R[j]
      j = j + 1


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)

mergeSort(B,0,n)

T = [None] * (MAX+1)
V = [False] * n
for i in range(n):
    T[B[i]] = i

for i in range(n):
    if V[i]: continue
    cur = i
    ant = 0
    S = 0
    s = MAX
    while(1):
        V[cur] = True
        v = A[cur]
        if v < s:
            s = v
        S += v
        ant += 1

        cur = T[v]
        if V[cur]: break

    result += min(S+(ant-2)*s,S+s+(ant+1)*m)


print(result)

