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
#include<cstdio>
#include<algorithm>
#include<iostream>
using namespace std;
#define M 1001
#define MAX 10000

int n,A[M],s;
int B[M],T[MAX+1];
bool V[M];

int solve(){
	int ans = 0;
	int i;
	for( i=0 ; i < n; i++ ){
		B[i]=A[i];
	}
	sort(B,B+n);
	for( i = 0; i < n; i++ ) T[B[i]]=i;
	for( i = 0; i < n; i++ ){
		if(V[i]) continue;
		int cur = i;
		int S = 0;
		int m = MAX;
		int an = 0;
		while(!V[cur]){
			V[cur] = true;
			an++;
			int v = A[cur];
			m = min(m,v);
			S += v;
			cur = T[v];
		}
		ans += min(S+(an-2)*m,S+m+(an+1)*s);
	}
	return ans;
}

int main(){
	scanf("%d",&n);
	s = MAX;
	for(int i = 0; i < n; i++){
		scanf("%d",&A[i]);
		s = min(s,A[i]);
	}
	printf("%d\n",solve());
}
