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
n = int(input())
loads = list(map(int, input().split()))
min_value = 0
for i in range(n-1):
    tmp = (i,i)
    min = 2 * 10e4 + 1
    for j in range(i,n):
        if loads[i] > loads[j]:
            sum = loads[i] + loads[j]
            if min > sum:
                tmp = (i, j)
                min = sum
    if(min < 2*10e4 + 1):
        min_value += min
    loads[tmp[0]], loads[tmp[1]] = loads[tmp[1]], loads[tmp[0]]

print(min_value)

