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
input()
w=list(map(int,input().split()))
x=min(w)
m={k:v for k,v in zip(sorted(w),w)if k!=v}
l=list(m.keys())
n=0
while l:
 a=l.pop();b=m[a];l.remove(b)
 if a==m[b]:n+=a+b
 else:
  t=[b]
  while 1:
   c=m[b];t+=[c]
   if c==a:p,q=len(t),min(t);n+=sum(t)+min((p-2)*q,q+(p+1)*x);break
   else:b=c;l.remove(c)
print(n)
