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
#最小コストソート
n = int(input())
A = list(map(int, input().split()))
#整列
B = sorted(A)
#サイクルに採用されたか否か
C = [0 for _ in range(n)]
CNT = 0
minA = B[0]

for i in range(n):
    #正しい位置にいるか
    if A[i] == B[i]:
        C[i] == 1
    #サイクルに採用済みか
    elif C[i] == 0:
        cyc = []
        ind = i
        #サイクル作成
        while C[ind] == 0:
            a = A[ind]
            cyc.append(a)
            C[ind] = 1
            ind = B.index(a)
        #2種のコスト計算
        mincyc = min(cyc)
        cost1 = sum(cyc) + (len(cyc) - 2) * mincyc
        cost2 = sum(cyc) + mincyc + (len(cyc) + 1) * minA
        if cost1 > cost2:
            CNT += cost2
        else:
            CNT += cost1
    else:
        pass
print(CNT)
