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
mp = {}
MAXN = 1010
mini =  100000
w = [0] * MAXN
done = [False] * MAXN

n = int(input())
w1 = [int(i) for i in input().split()]

for index, value in enumerate(w1):
    w[index] = value

for i in range(n):
    mp[w[i]] = 0
    mini = min(mini, w[i])

k = 0
for i in sorted(w1):
    mp[i] = k
    k += 1

ans = 0
for i in range(n):
    if done[i]: continue
    cnt = 0
    now = i
    mi = 100000
    total = 0
    while (True):
        if done[now]: break
        cnt += 1
        done[now] = True
        mi = min(mi, w[now])
        total += w[now]
        now = mp[w[now]]
    tmp = total + (cnt - 2) * mi
    tmp = min(tmp, total + mi + mini * (cnt + 1))
    ans += tmp
print(ans)

