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

flags = [False] * n
loops = []

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

    ws = []
    while S[x] not in ws:
        flags[x] = True
        ws.append(S[x])
        x = I[x]
    loops.append(ws)

cost = 0
for loop in loops:
    a = sum(loop) + (len(loop) - 2) * min(loop)
    b = sum(loop) + min(loop) + (len(loop) + 1) * min(L)
    cost += min(a, b)

print(cost)