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())
W = list(map(int, input().split()))

_W = W[:]
_W.sort()
m = _W[0]

C = [None for _ in range(_W[n - 1] + 1)]
V = [False for _ in range(_W[n - 1] + 1)]

for i in range(n):
    C[_W[i]] = W[i]

r = 0

for i in _W:
    if V[i]:
        continue
    nxt = C[i]
    V[i] = True
    if nxt == i or V[nxt]:
        continue
    sum_w = i
    min_w = i
    c = 1
    while V[nxt] is False:
        V[nxt] = True
        sum_w += nxt
        nxt = C[nxt]
        c += 1
    r += min(sum_w + (c - 2) * min_w, sum_w + min_w + (c + 1) * m)

print(r)

