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
def solve(w_list, sort_list):
    ans = 0
    min_num = sort_list[0]
    for i in range(len(w_list)):
        x = sort_list.index(w_list[i])
        if x == i:
            continue
        sum_cost = 0
        min_loop_n = 10**4 + 1
        j = i
        loop_count = 0
        while True:
            loop_count += 1 
            sum_cost += w_list[j]
            min_loop_n = min(min_loop_n, w_list[j])
            if x == i:
                break
            w_list[x], w_list[j] = w_list[j], w_list[x]
            x = sort_list.index(w_list[j])
        ans += min(sum_cost + (loop_count-2)*min_loop_n, sum_cost + min_loop_n + (loop_count+1)*min_num)
    return ans
        
            
            
n = int(input())
w_list = list(map(int, input().split()))
sort_list = sorted(w_list)
print(solve(w_list, sort_list))
        
        
        
    
