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 = [int(_) for _ in input().split()]

done = {}
for i in range(n):
    done[a[i]] = 0
# print(done)

direct = {}
a_sorted = sorted(a)
for i in range(n):
    direct[a_sorted[i]] = i
# print(direct)

group_list = []
for i in range(n):
    if done[a[i]] == 1:
        continue
    else:
        f = a[i]
        done[f] = 1
        group = [f]
        n = f
        while a[direct[n]] != f:
            n = a[direct[n]]
            done[n] = 1
            group.append(n)
        group_list.append(group)
# print(group_list)

m = a_sorted[0]
cost = 0
while len(group_list) > 0:
    group = group_list.pop()
    if len(group) == 1:
        continue
    else:
        cost += min(sum(group) + (len(group) - 2) * min(group), sum(group) + min(group) + (len(group) + 1) * m)
print(cost)
