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
WMAX = 10 ** 4 + 1
n = int(input())
A = list(map(int, input().split()))  #1 5 3 4 2
B = sorted(A)  #1 2 3 4 5

is_visited = [False] * n
next_idxs = {}

for i, b in enumerate(B):
  next_idxs[b] = i

m_A = min(A)

ans = 0
for i in range(n):
  if is_visited[i]:
    continue
  cur = i
  S = 0
  n2 = 0
  m = WMAX
  while True:
    is_visited[cur] = True
    S += A[cur]
    m = min(m, A[cur])
    n2 += 1
    cur = next_idxs[A[cur]]
    if is_visited[cur]:
      break
  ans += min(m*(n2-2) + S, m+S+(1+n2)*m_A)

print(ans)

