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 itertools


WAIT, PRESORT, SORTED = 0, 1, 2
cost = 0

def swap(w1, w2):
    global cost
    cost += w1[WAIT] + w2[WAIT]
    w1[PRESORT], w2[PRESORT] = w2[PRESORT], w1[PRESORT]

n = input()
w = [[wi, i, None] for i, wi in enumerate(map(int, input().split()))]
s = sorted(w)

for i, wi in enumerate (s):
    wi[SORTED] = i

for si in s:
    tmp = si
    t = []
    while tmp[SORTED] != si[PRESORT]:
        tmp = w[tmp[SORTED]]
        t += [tmp]
    
    for ti in t[::-1]:
        swap(si, ti)

print(cost)