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, = map(int, input().split())
C = {w: i for i, w in enumerate(W)}
W.sort()

ans = 0
S = []
used = [0]*N
for i in range(N):
    if used[i]:
        continue
    sq = []
    w = W[i]
    p = i; j = None
    while j != i:
        j = C[w]; w = W[j]
        used[j] = 1
        sq.append(w)
        p = j
    mi = min(sq); ln = len(sq)
    if ln >= 2:
        ans += sum(sq)
    S.append((mi, ln))
S.sort()
m, ln = S[0]
if ln >= 2:
    ans += (ln-2)*m
for mi, ln in S[1:]:
    if ln <= 2:
        continue
    ans += min(m+mi+ln*m, (ln-2)*mi)
print(ans)

