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
def solve(n, A):
    def cycles():
        V = [False] * n
        B = sorted(A)
        T = {B[i]: i for i in range(n)}
        C = []

        for i in range(n):
            if V[i]:
                continue
            cur = i
            cycle = []
            while not V[cur]:
                V[cur] = True
                cycle.append(cur)
                cur = T[A[cur]]
            C.append(cycle)

        return C

    ans = 0
    s = min(A)

    for cycle in cycles():
        S = sum([A[i] for i in cycle])
        m = min([A[i] for i in cycle])
        an = len(cycle)
        ans += min(S + (an - 2) * m, m + S + (an + 1) * s)

    return ans


def main():
    n = int(input())
    A = [int(x) for x in input().split()]

    print(solve(n, A))


main()

