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
#!/usr/bin/env python

import sys
import math
import itertools as it
from collections import deque

sys.setrecursionlimit(10000000)

N = input()
A_ = map(int, raw_input().split())
minA = min(A_)
lst = []
for i in range(N):
    lst.append((A_[i], i))
lst.sort()

A = [0] * N
for i in range(N):
    A[lst[i][1]] = (lst[i][0], i)

flag = [False] * N

def func(pos, lst):
    if flag[pos]:
        return
    lst.append(A[pos][0])
    flag[pos] = True
    func(A[pos][1], lst)

ans = 0
for i in range(N):
    if not flag[i]:
        ret = []
        func(i, ret)
        ans += min(min(ret) * (len(ret) - 2) + sum(ret), sum(ret) + min(ret) + minA * (len(ret) + 1))

print ans
