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 functools

def find_all_rings(items):
    "items: (??°???, ?????????????????????????????????)"
    l = len(items)
    check_list = [False] * l
    rings = []
    i = 0
    while i < l:
        if check_list[i] == False:
            ring = []
            first = items[i]
            ring.append(first)
            check_list[i] = True
            item_index = first[1]
            item = items[item_index]
            while item[0] != first[0]:
                ring.append(item)
                check_list[item_index] = True
                item_index = item[1]
                item = items[item_index]
            rings.append(ring)
        i += 1
    return rings

def compute_ring_cost(min_all, ring):
    l = len(ring)
    if l <= 1:
        return 0
    w = [item[0] for item in ring]
    min_ring = min(w)
    sum_ring = sum(w)
    if (l + 1) * min_all < (l - 3) * min_ring:
        return sum_ring + min_ring + (l + 1) * min_all
    else:
        return sum_ring + (l - 2) * min_ring

n = int(input())
ns = list(map(int, input().split()))
items = []
sorted_items = []
for i in range(n):
    item = (ns[i], i)
    items.append(item)
    sorted_items.append(item)

sorted_items.sort(key = lambda x : x[0])

for i in range(n):
    item = sorted_items[i]
    items_index = item[1]
    items[items_index] = (item[0], i)

rings = find_all_rings(items)
compute_ring_cost1 = functools.partial(compute_ring_cost, min(ns))
print(sum(map(compute_ring_cost1, rings)))