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
def solve(A,n,s):
    ans = 0

    V = [False for i in range(n)] # 値が交換済みかどうか
    B = sorted(A)
    T = [None for i in range(10001)]
    for i in range(n):
        T[B[i]] = i
    for i in range(n):
        if V[i]: continue
        cur = i #カーソル
        S = 0 #サークル内の数字の総和
        m = 10000 # VMAX
        an = 0 # サークルに含まれる数字の個数
        while True: #サークル内の処理
            V[cur] = True
            an += 1
            v = A[cur]
            m = min(m,v) #mがサークル内の最小の数字
            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())
A = [int(x) for x in input().split()]
s = min(A)

ans = solve(A,n,s)
print(ans)
