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()))
W_2 = W[:]
sorted_W = sorted(W)
cost = 0
for i in range(n):
    if i==0:
        while W[i]!=sorted_W[i]:
            a=W.index(sorted_W[i])
            b=W.index(sorted_W[a])
            W[a],W[b]=W[b],W[a]
            W_2[a],W_2[b]=W_2[b],W_2[a]
            cost+=W[a]+W[b]
    else:
        cost1=0
        cost2=0
        while W[i]!=sorted_W[i]:
            a=W.index(sorted_W[i])
            b=W.index(sorted_W[a])
            W[a],W[b]=W[b],W[a]
            cost1+=W[a]+W[b]
        c = W_2.index(sorted_W[i])
        W_2[0],W_2[c]=W_2[c],W_2[0]
        cost2+=W_2[0]+W_2[c]
        while W_2[0]!=sorted_W[0]:
            a=W_2.index(sorted_W[0])
            b=W_2.index(sorted_W[a])
            W_2[a],W_2[b]=W_2[b],W_2[a]
            cost2+=W_2[a]+W_2[b]
        if cost1<=cost2:
            W_2=W[:]
            cost+=cost1
        else:
            W=W_2[:]
            cost+=cost2
print(cost)
