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
n = int(input())
arr = list(map(int, input().split()))
idx = {}
for i, a in enumerate(sorted(arr)):
    idx[a] = i
visit = [False]*n
Min = min(arr)
ans = 0
for i in range(n):
    if visit[i]:
        continue
    visit[i] = True
    now = idx[arr[i]]
    tmp_min = arr[i]
    tot = tmp_min
    cnt = 1
    while now != i:
        visit[now] = True
        tot += arr[now]
        cnt += 1
        if tmp_min > arr[now]:
            tmp_min = arr[now]
        now = idx[arr[now]]
    ans += min(tot + (cnt - 2)*tmp_min, tot + tmp_min + (cnt + 1)*Min)
print(ans)
