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 <algorithm>
#include <cstdio>
#include <iostream>
using namespace std;

int n, w[1000], s;
int a[1000], d[10001]; //destination 

long solve(){
	long ret=0;	
	
	bool v[1000];
	for(int i=0; i<n; ++i){
		a[i]=w[i];
		v[i]=false;	
	}
	sort(a, a+n); //a[]??????w[]???????????¢?????\???
	
	//??????a[i]??????????????????????????´??????d[]?????\??????
	for(int i=0; i<n; ++i) d[a[i]]=i;
	
	for(int i=0; i<n; ++i){
		if(v[i]) continue; //??¢???????????????????????????????????????????????§???????????????????????£?????????
		
		//?????????????????¢???
		int cur=i; //?????¨??????
		int sum=0;
		int m=10000; //???????????????????????????????°????
		int an=0; //?????????????????§??????
		
		while(1){
			v[cur]=true; //?¨??????????????¨????
			an++;
			int z=w[cur];
			sum+=z;
			m=min(m, z);
			cur=d[z]; //?¬??????????
			if(v[cur]) break; //?????¨??????
		}
		
		ret += min(sum+(an-2)*m , m+sum+(an+1)*s);	
	}
	return ret;
}

int main(){
	scanf(" %d", &n);
	
	s=10000;
	for(int i=0; i<n; ++i){
		scanf(" %d", &w[i]);
		s=min(s, w[i]); //s???w[]?????????????°????????´?
	}
	
	printf("%ld\n", solve());
}