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 = list(map(int, input().split()))
b = sorted(a)
c = 0
for i in range(n - 1):
    t = cnt = 0
    # 動かす数字の位置
    x = a.index(b[i])
    while x != i:
        # 動かす数字の所にあるべき数字
        y = a.index(b[x])
        # a[x], a[y] = b[x], b[i]
        a[x], a[y] = a[y], a[x]
        cnt += 1
        # t += b[x] + b[i]
        t += a[x] + a[y]
        x = y
    if cnt:
        c += min(t, (b[i] + b[0]) * 2 + t - (b[i] - b[0]) * cnt)
print(c)
