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())
wlist = list(map(int,input().split()))
wdic = {j:i for i,j in enumerate(wlist)}
wlist.sort()
cost = 0
used = [0]*n
res = []
for i in range(n):
    storage = []
    if used[i]:
        continue # next loop
    w = wlist[i]
    minimum = w
    used[i] = 1
    a = wdic[w]
    b = wlist[a]
    storage.append(w)
    while b not in storage:
        w = b
        used[a] = 1
        a = wdic[w]
        b = wlist[a]
        storage.append(w)
        #print(w,a,b,storage)
    ls = len(storage)
    cost += (sum(storage) - minimum)
    res.append((minimum,ls))
m,l = res[0]
if l>=2:
    cost += m*(l-1)
for minimum,ls in res[1:]:
    if ls>=2:
        cost += min(2*(m+minimum)+m*(ls-1), minimum*(ls-1))
    
print(cost)
