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)

#最小コストソート

n = int(input())
a = list(map(int, input().split()))
b = sorted(a)
c = 0
for i in range(n-1):
    t = cnt = 0
    #本来i番目にいるべき値はaではどこにいるのか（ループの最小値）
    x = a.index(b[i])
    #もしあるべき場所にあったり、あるべき場所に帰ってきたら終了
    while x != i:
        #ループで最も小さい値を使いまわしながら整えていく
        #ループの最小値が入っている場所にいるべき値がaでは何処にいるか
        y = a.index(b[x])
        #a[x]とa[y]を入れ替えればよい
        a[x],a[y] = a[y],a[x];cnt += 1
        t += a[x] + a[y]
        x = y
    if cnt: c += min(t, (b[i]+b[0])*2 + t -(b[i]-b[0])*cnt)
print(c)
# print(a)