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
def solve(a, n):
    vmax = 10000
    ans = 0
    all_min = min(a)
    b = sorted(a)
    v = [False] * n

    t = {}
    for i in range(n):
        t[b[i]] = i
    for i in range(n):
        if v[i]:
            continue
        cur = i
        w_sum = 0
        w_min = vmax
        an = 0
        while True:
            v[cur] = True
            an += 1
            v_cur = a[cur]
            w_min = min(w_min, v_cur)
            w_sum += v_cur
            cur = t[v_cur]
            if v[cur]:
                break
        ans += min(w_sum + (an-2) * w_min, w_min + w_sum + (an+1) * all_min)

    return ans


n = int(input())
a = [int(v) for v in input().split()]

ans = solve(a, n)
print(ans)
