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())
A = list(map(int, input().split()))
s = min(A)
def solve():
    ans = 0
    V = [False] * n
    # B = sorted(A)
    # T = {B[i]: i for i in range(n)}
	T = {B: i for i, B in enumerate(sorted(A))}
    for i in range(n):
        if V[i]:
            continue
        cur = i
        S = an = 0
        m = 10000
        while not V[cur]:
            V[cur] = True
            an += 1
            v = A[cur]
            m = min(m, v)
            S += v
            cur = T[v]
        ans += min(S + (an - 2) * m, m + S + (an + 1) * s)
    return ans
print(solve())

