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
MAX = 1000
VMAX = 10000


def main():
    n = int(input())
    
    a_s = list(map(int, input().split(' ')))
    minimum = min(a_s)

    ans = 0

    t_s = [0] * (VMAX+1)
    b_s = [a for a in a_s]
    v_s = [False for _ in range(n)]
    b_s = sorted(b_s)

    for i in range(n):
        t_s[b_s[i]] = i

    for i in range(n):
        if v_s[i]:
            continue
        cur = i
        S = 0
        m = VMAX
        a_n = 0

        while True:
            v_s[cur] = True
            a_n += 1
            v = a_s[cur]
            m = min(m, v)
            S += v
            cur = t_s[v]
            if v_s[cur]:
                break
        ans += min(S + (a_n-2)*m, m+S+(a_n+1)*minimum)
    
    print(ans)


if __name__ == '__main__':
    main()

