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
import sys

n = int(input())
a = list(map(int, input().split()))
b= sorted(a)

ans = 0
for i in range(n):
    w = 0
    cnt = 0
    x = a.index(b[i]) # b[i]: sort未済の中で最小値
    while x != i:
        y = a.index(b[x]) #位置xに来るべき数の位置
        a[x], a[y] = b[x], b[i] #b[i] -> 位置yに移動
        cnt += 1
        w += b[x] + b[i]
        x = y
    if cnt > 0: 
        ans += min(w, (b[i] + b[0]) * 2 + w - (b[i] - b[0]) * cnt) #b[0]が全体の最小値

print(ans)
