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
# line = "10 7 8 9"
# L = [int(x) for x in line.split()]
# n = len(L)

n = int(input())
line = input()
L = [int(x) for x in line.split()]

flags = [False] * n
loops = []

S = sorted(L)
for i, x in enumerate(L):
    k = S.index(x)
    if flags[k]:
        continue
    if i == k:
        flags[i] = True
        continue

    loop = []
    while x not in loop:
        flags[k] = True
        loop.append(x)
        x = L[k]
        k = S.index(x)
    loops.append(loop)

cost = 0
for loop in loops:
    m = min(loop)
    cost += m * (len(loop)-1) + sum(loop) - m

print(cost)