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
# coding: utf-8

n = int(input().rstrip())
wi = [int(i) for i in input().rstrip().split()]
visited = [False for i in range(n)]
minw = min(wi)
dict = {}
for i, v in enumerate(sorted(wi)):
    dict[v] = i

ans = 0
for i in range(n):
    if visited[i]:
        continue
    cnt = 0
    now = i
    mi = 100000
    s = 0
    while True:
        if visited[now]:
            break
        cnt += 1
        visited[now] = True
        mi = min(mi, wi[now])
        s += wi[now]
        now = dict[wi[now]]
    
    tmp = s + (cnt-2)*mi
    tmp = min(tmp, s+mi+minw*(cnt+1))
    ans += tmp

print(ans)
    
