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
#coding:utf-8
n = int(input())
A = list(map(int, input().split()))
B = A[:]
B.sort()
C = [True for i in range(n)]
minA = min(A)

j = 0
a = []
total = 0
for i in range(n):
    circle = []
    j = i
    while C[j]:
        C[j] = False
        j = B.index(A[j])
        circle.append(A[j])
    n_c = len(circle)
    if n_c == 2:
        total += (circle[0]+circle[1])
    if n_c > 2:
        minc = min(circle)
        cirSum = sum(circle)
        total += min( cirSum + (n-2) * minc , cirSum + minc + (n+1)*minA)
    a.append(circle)
    

print(total)
