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, cost = int(input()), 0
num = list(map(int, input().split()))
num_s = sorted(num)
n0 = num_s[0]

for i in range(n - 1):
    ni, tmp, cnt = num_s[i], 0, 0
    si = num.index(ni)
    while si != i:
        nsi = num_s[si]
        sj = num.index(nsi)
        num[si], num[sj] = nsi, ni
        tmp += ni + nsi
        cnt += 1
        si = sj
    if cnt:
        cost += min(tmp, (ni + n0) * 2 + tmp - (ni - n0) * cnt)
print(cost)