Problem:
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Minimum Cost Sort

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.

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.

Constraints

$1 \leq n \leq 1,000$

$0 \leq w_i\leq 10^4$

$w_i$ are all different

Sample Input 1

5
1 5 3 4 2

Sample Output 1

7

Sample Input 2

4
4 3 2 1

Sample Output 2

10

Solution in Python3 (judge verdict: Accepted)

n = int(input())
l = list(map(int, input().split()))
s = sorted(l)
cost = 0
for i in range(n):
    a = l.index(s[i])
    j = 0
    while a > i:
        j += 1
        b = l.index(s[a])
        cost += l[b]
        l[a], l[b] = l[b], l[a]
        a = b
    cost += min(s[i] * j, s[i] * 2 + s[0] * (j + 2))
print(cost)