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 copy
INFTY=1000000000
MAX = 1000
VMAX = 100000

def solve(W,N,VMAX):
    T = [-1 for _ in range(VMAX)]
    for i in range(N):
        ans = 0
        V = [False for _ in range(N)]
        WW=copy.deepcopy(W)
        WW.sort()
        for i in range(N):
            T[WW[i]] = i
        for i in range(N):
            if V[i]:
                continue
            cur = i
            S = 0
            m = VMAX
            an = 0
            while True:
                V[cur] = True
                an += 1
                v = W[cur]
                m = min(m,v)
                S += v
                cur = T[v]
                if V[cur]:
                   break
            ans += min(S + (an - 2) * m, m + S + (an + 1) * s)
    return ans

N = int(input())
W = list(map(int,input().split()))
s = min(W)
ans = solve(W,N,VMAX)
print(ans)
