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 <bits/stdc++.h>
#define ll long long
#define INF 999999999
#define MOD 1000000007
#define rep(i,n) for(int i=0;i<n;i++)

using namespace std;

typedef pair<int,int>P;

const int MAX_N = 1000;

int w[MAX_N];
int a[MAX_N];
int pos[10001];		//?????????????????????????????????????????¢???????????????????????????
bool flag[MAX_N];	//???????????????i???????????°???????????????????????????????????????
vector<int> loop;

int main()
{
	int n,ans=0;
	cin >> n;
	rep(i,n){
		scanf("%d",&w[i]);
		a[i] = w[i];
		pos[w[i]] = i;
	}
	fill(flag,flag+n,false);
	sort(a,a+n);
	rep(i,n){
		loop.clear();
		int x = i;
		while(1){
			if(flag[x] == false){
				loop.push_back(w[x]);
				flag[x] = true;
				x = pos[a[x]];
			}else{
				break;
			}	
		}
		int suml = 0;
		int minl = INF;
		if(loop.size() >= 2){
			rep(j,loop.size()){
				suml += loop[j];
				minl = min(minl,loop[j]);
			}
			ans += min(suml+minl*(loop.size()-2),suml+minl+a[0]*(loop.size()+1));
		}
	}
	cout << ans << "\n";	
}