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 resolve():
    def solve(n, arr):

        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
        minV = 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, S+(an+1)*minV+m)
        return ans

    N = int(input())
    A = list(map(int, input().split()))
    ans = solve(N, A)
    print(ans)

if __name__ == '__main__':
    resolve()
