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, a, cost = int(input()), list(map(int, input().split())), 0
b = sorted(a)
b0 = b[0]
for i in range(n - 1):
    bi, tmp_cost, count = b[i], 0, 0
    si = a.index(bi)
    while si != i:
        bsi = b[si]
        sj = a.index(bsi)
        a[si], a[sj] = bsi, bi
        tmp_cost += bi + bsi
        count += 1
        si = sj
    if count:
        cost += min(tmp_cost, (bi + b0) * 2 + tmp_cost - (bi - b0) * count)
print(cost)