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>
using namespace std;
typedef struct D {
  int c;
  vector<pair<int, int> > W;
  bool operator<(const D &a) const { return c < a.c; }
} D;
int N, W[1005], C[1005], c = 0, t, p, res = 1000000000;
map<int, int> H;
map<int, int> rH;
map<vector<pair<int, int> >, int> MC;
int main() {
  scanf("%d", &N);
  for (int i = 0; i < N; i++) scanf("%d", C + i);
  memcpy(W, C, sizeof(C));
  sort(C, C + N);
  for (int i = 0; i < N; i++) {
    H[C[i]] = i;
    rH[i] = C[i];
  }
  D tmp = {0};
  for (int i = 0; i < N; i++) tmp.W.push_back(make_pair(W[i], H[W[i]]));
  MC[tmp.W] = 0;
  priority_queue<D> Q;
  Q.push(tmp);
  for (; !Q.empty();) {
    tmp = Q.top();
    Q.pop();
    if (MC[tmp.W] != 0 && MC[tmp.W] < tmp.c) continue;
    int f = 1;
    for (int i = 0; i < tmp.W.size(); i++) {
      if (tmp.W[i].second != i) {
        f = 0;
        D ins = tmp;
        ins.c += tmp.W[i].first + tmp.W[tmp.W[i].second].first;
        swap(ins.W[i], ins.W[ins.W[i].second]);
        if (MC[ins.W] == 0 || MC[ins.W] > ins.c) {
          MC[ins.W] = ins.c;
          Q.push(ins);
        }
      }
    }
    if (f) res = min(res, tmp.c);
  }
  printf("%d\n", res);
  return 0;
}
