Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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: Wrong Answer)

def perfect_swap():
    global n, a, b, cost
    for i in range(1, n - 1):
        for j in range(i + 1, n):
            ai, aj = a[i], a[j]
            if ai == b[j] and aj == b[i]:
                a[i], a[j] = aj, ai
                cost += ai + aj


def lowest_swap():
    global n, a, b, cost
    for i in range(n - 1):
        bi, tmp_cost, count = b[i], 0, 0
        while a[i] != bi:
            si = a.index(bi)
            bsi = b[si]
            sj = a.index(bsi)
            a[si], a[sj] = bsi, bi
            tmp_cost += bi + bsi
            count += 1
        if count > 0:
            if i > 0:
                bip = b[i - 1]
                cost += min(tmp_cost, (bi + bip) * 2 + tmp_cost - (bi - bip) * count)
            else:
                cost += tmp_cost


n, a, cost = int(input()), list(map(int, input().split())), 0
b = sorted(a)
perfect_swap()
lowest_swap()
print(cost)