p02278 Minimum Cost Sort
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
```python
n = int(input())
A = [int(i) for i in input().split()]
B = A.copy()
B.sort()
ans = 0
for i in B:
    ixB = B.index(i)
    counter = 0
    while(True):
        ixA = A.index(i)
        if ixA == ixB:
            break
        else:
            counter += 1
            num = B[ixA]
            ixN = A.index(num)
            A[ixA],A[ixN] = A[ixN],A[ixA]
            ans += A[ixA] + A[ixN]
    tmp = (B[0] - i)*counter + (B[0]+i)*2
    if tmp < 0:
        ans += tmp
print(ans)

```