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 = [[int(i)] for i in input().split()]
for ni in range(n):
    W[ni].append(ni)
W.sort()
G = [[] for i in range(n)]
i = 0
j = 0
cnt = 0
D = []
while cnt < n:
    if W[i][0] in G[j]:
        j += 1
        while i in D:
            i += 1
    else:
        G[j].append(W[i][0])
        D.append(i)
        cnt += 1
        i = W[i][1]
group_num = j + 1
cost = 0
W_min = min([min(G[i]) for i in range(group_num)])
for gi in range(group_num):
    if len(G[gi]) > 1:
        if (min(G[gi])+W_min)*2 > (min(G[gi])-W_min)*(len(G[gi])-1):
            cost += sum(G[gi])+ (len(G[gi])-2)*min(G[gi])
        else:
            cost += sum(G[gi])-min(G[gi])+ (len(G[gi])-1)*W_min+(min(G[gi])+W_min)*2

print(cost)
