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)
c = 0

for i in range(n-1):
    t = cnt = 0
    x = A.index(B[i])
    
    while x != i:
        y = A.index(B[x])
        A[x], A[y] = B[x], B[i]
        cnt += 1
        t += B[x] + B[i]
        x = y
    if cnt:
        c += min(t, (B[i]+B[0])*2+t-(B[i]-B[0])*cnt)
print(c)
