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<iostream>
#include<algorithm>
using namespace std;
static const int MAX = 1000;
static const int VMAX = 10000;
int n, A[MAX], s;
int B[MAX], T[VMAX+1];
int solve(){
int ans = 0;
bool V[MAX];
for(int i = 0; i < n; i++){
B[i] = A[i];
V[i] = false;
}
sort(B, B+n);
for(int i = 0; i < n; i++) T[B[i]] = i;
for(int i = 0; i < n; i++){ 
if(V[i]) continue;
int cur = i;
int S = 0;
int m = VMAX;
int an = 0;
while(1){
V[cur] = true;
an++;
int v = A[cur];
m = min(m, v);
S += v;
cur = T[v];
if(V[cur]) break;
}
ans += min(S + (an - 2) * m, m + S + (an + 1) * s);
}
return ans;
}
int main(){
cin >> n;
s = VMAX;
for(int i = 0; i < n; i++){
cin >> A[i];
s = min(s, A[i]);
}
int ans = solve();
cout << ans << endl;
return 0;
}
