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

sorted_data=sorted(data)
mindata=sorted_data[0]

data_dict={}
for i in range(n):
    data_dict[data[i]]=i#key：データに含まれる要素　value:そのデータのインデックス

sorted_data_dict={}
for i in range(n):
    sorted_data_dict[sorted_data[i]]=i


swap_cost=0


for x in sorted_data:
    if(sorted_data_dict[x]!=data_dict[x]):
        tmp_cost=0
        swap_num=0

        while(sorted_data_dict[x]!=data_dict[x]):
            ind1=data_dict[x]
            ind2=data_dict[sorted_data[ind1]]
            data_dict[x]=ind2
            data_dict[sorted_data[ind1]]=ind1
            tmp_cost+=x+sorted_data[ind1]
            swap_num+=1
        if( (x+mindata)*2 < swap_num*(x-mindata) ):
            tmp_cost+=(x+mindata)*2 - swap_num*(x-mindata)
        swap_cost+=tmp_cost

print(swap_cost)
