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=input()
l=map(int,raw_input().split())
s=sorted(l)
c=0
for i in range(n):
    a=l.index(s[i])
    j=0
    while a>i:
        j+=1
        b=l.index(s[a])
        c+=l[b]
        l[a],l[b]=l[b],l[a]
        a=b
    c+=min(s[i]*j,s[i]*2+s[0]*(j+2))
print c