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,mn,mx):
	ans=0
	V=[False]*n
	b=sorted(a)
	T=[0]*(mx+1)
	for i in range(n): T[b[i]]=i
	for i in range(n):
		if V[i]: continue
		cur=i
		sum=0
		cnt=0
		m=1<<30
		while True:
			V[cur]=True
			v=a[cur]
			cnt+=1
			sum+=v
			m=min(m,v)
			cur=T[v]
			if V[cur]: break
		ans+=min(sum+(cnt-2)*m,sum+m+(cnt+1)*mn)
	return ans

n=int(input())
a=list(map(int,input().split()))
mn=1<<30
mx=mn*-1
for i in range(n):
	mn=min(mn,a[i])
	mx=max(mx,a[i])
print(solve(a,n,mn,mx))

