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_c_sort(A, n):
    cost = 0
    for i in range(n - 1):
        min_i = i
        for j in range(i + 1, n):
            if A[min_i] > A[j]:
                min_i = j
        if min_i != i:
            cost += A[min_i]
            cost += A[i]
            A[min_i], A[i] = A[i], A[min_i]
    return cost


n = int(input())

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

cost = min_c_sort(A, n)

print(cost)