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()))
ws = sorted(w)
d = {v:i for i, v in enumerate(ws)}
checked = [False] * n
cost = 0
wmin = min(w)

for i in range(n):
    if checked[i] or d[w[i]] == i:
        continue
    # 循環群をさがす
    gcnt = 0
    gmin = gtot = w[i]
    nexti = d[w[i]]
    while nexti != i:
        checked[nexti] = True
        gcnt += 1
        gmin = min(gmin, w[nexti])
        gtot += w[nexti]
        nexti = d[w[nexti]]
    cost += gtot + min(gmin * (gcnt - 1), wmin * (gcnt + 2) + gmin)
print(cost)

