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(sys.stdin.readline())
w = list(map(int, sys.stdin.readline().split()))
c = [False]*n
u = sorted(w)
cost = 0
while False in c:
    i = c.index(False)
    c[i] = True
    i0=i
    llen=1
    lmin=w[i]
    while True:
        i = u.index(w[i])
        if c[i]: break
        c[i] = True
        llen+=1
        if lmin > w[i]: lmin = w[i]
        cost += w[i]

    if llen>1:
        cost += w[i0]+min(lmin+(llen+1)*min(w), lmin*(llen-2))

print(cost)
