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 copy
n = int(input())
a = list(map(int, input().split()))
b = copy.deepcopy(a)
b.sort()
loop = []
minp = min(a)
t = [0 for i in range(n)]
while True:
    i = t.index(0)
    j = len(loop)
    loop.append([a[i]])
    t[i] = 1
    while True:
        i = b.index(a[i])
        if t[i] == 1:
            break
        t[i] = 1
        loop[j].append(a[i])
    if sum(t) == n:
        break
    j += 1
print(loop)
cost = 0
for i in loop:
    if len(i) == 1:
        continue
    ps = sum(i)
    pl = len(i)
    pm = min(i)
    p1 = ps + (pl - 2) * pm
    p2 = ps + pm + (pl + 1) * minp
    cost += min(p1, p2)
print(cost)
