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
"""Minimum cost Sort."""

def min_cost_sort(A):
    """Sort list A in ascending order.
 
    And return the switching cost in sorting.
    """
    B = list(A)
    B.sort()
    cost = 0
    min_w = B[0]
    for i, b in enumerate(B):
        tmp_cost = 0
        bi = A.index(b)
        cnt = 0
        while bi != i:
            cnt += 1
            st = B[bi]
            si = A.index(st)
            tmp_cost += b + st
            A[bi], A[si] = st, b
            bi = si
        if cnt:
            dec = cnt * (b - min_w)
            inc = 2 * (min_w + b)
            if dec < inc:
                cost += tmp_cost
            else:
                cost += tmp_cost - dec + inc
    return cost


n = input()

A = list(map(int, input().split()))

ans = min_cost_sort(A)

print(ans)