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
def MCS(A,n):
    B=sorted(A)
    B0=B[0]
    cost=0
    for i in range(n-1):
        Bi,t_cost,count=B[i],0,0
        si=A.index(Bi)
        while si!=i:
            bsi=B[si]
            sj=A.index(bsi)
            A[si],A[sj]=bsi,Bi
            t_cost+=Bi+bsi
            count+=1
            si=sj
        if count:
            cost+=min(t_cost,(Bi + B0) * 2 + t_cost - (Bi - B0) * count) 
    print(cost)
if __name__=="__main__":
    n=int(input())
    A=input().split(" ")
    for i in range(n):
        A[i]=int(A[i])
    MCS(A,n)