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
import sys

def minimumCostSort(A):
    B = sorted(A)
    V = [False] * len(A)
    T = [0] * 10001
    ans = 0
    s = min(A)

    for i in range(len(A)):
        T[B[i]] = i

    for i in range(len(A)):
        if V[i]:
            continue
        S = an = 0
        j = i
        m = 10000
        while True:
            V[j] = True
            an += 1
            v = A[j]
            m = min(m, v)
            S += v
            j = T[v]
            if V[j]:
                break
        ans += min(S + (an - 2) * m, m + S + (an + 1) * s)
    return ans

if __name__ == "__main__":
    lines = sys.stdin.readlines()
    A = map(int, lines[1].split())
    print minimumCostSort(A)