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())
a=list(map(int,input().split()))
b=sorted(a)
m=b[0]
c=0
for i in range(n):
 t=k=0
 x=a.index(b[i])
 while x>i:
  y=a.index(b[x])
  a[x],a[y]=b[x],b[i]
  k+=1
  t+=b[x]+b[i]
  x=y
 if k:c+=min(t,(b[i]+m)*2+t-(b[i]-m)*k)
print(c)
