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())
w = list(map(int, input().split()))
s = sorted(w)

cost = 0
for i in range(n):
    # 最小の要素と最小の要素の位置に適した要素と交換していく
    now_v = s[i]
    now_idx = w.index(s[i])
    j = 0 # 交換回数
    while now_idx > i:
        j += 1
        target_v = s[now_idx]
        target_idx = w.index(target_v)
        cost += w[target_idx] # ターゲットの方だけ足していく
        w[now_idx], w[target_idx] = w[target_idx], w[now_idx]
        now_idx = target_idx
    # now_v * j: 普通の交換。
    # now_v * 2 + s[0] * (j + 2): 
    #       s[0]は最小値。
    #       最小値と現在値を交換して(コスト: now_v + s[0])、
    #       ソート完了後に(コスト: s[0] * j)
    #       最小値と現在値を元に戻すコスト(コスト: now_v + s[0])。
    #       2回以上ならこっちが少ない。
    cost += min(now_v * j, now_v * 2 + s[0] * (j + 2))
print(cost)

