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;
class UnionFind {
  vector<int> v;
  vector<int> mini;

 public:
  UnionFind(const vector<int>& val) : v(val.size(), -1), mini(val) {}
  int find(int a) { return v[a] < 0 ? a : v[a] = find(v[a]); }
  bool same(int a, int b) { return find(a) == find(b); }
  void unite(int a, int b) {
    a = find(a);
    b = find(b);
    if (a == b) return;
    if (v[a] < v[b]) {
      mini[a] = min(mini[a], mini[b]);
      v[a] += v[b];
      v[b] = a;
    } else {
      mini[b] = min(mini[a], mini[b]);
      v[b] += v[a];
      v[a] = b;
    }
  }
  int get(int a) { return mini[find(a)]; }
  int size(int a) { return -v[find(a)]; }
};
int main() {
  int n;
  cin >> n;
  vector<int> w(n);
  int mini = 1e4 + 1;
  for (int i = 0; i < n; i++) {
    cin >> w[i];
    mini = min(mini, w[i]);
  }
  auto a = w;
  sort(a.begin(), a.end());
  UnionFind uf(w);
  for (int i = 0; i < n; i++) {
    int it = lower_bound(a.begin(), a.end(), w[i]) - a.begin();
    uf.unite(i, it);
  }
  int res = 0;
  vector<int> rts;
  for (int i = 0; i < n; i++) {
    res += w[i] + (uf.get(i) == w[i] ? -w[i] : uf.get(i));
    if (i == uf.find(i)) rts.push_back(i);
  }
  for (auto rt : rts) {
    if (uf.get(rt) == mini) continue;
    int dis = (uf.get(rt) - mini) * (uf.size(rt) - 1) - uf.get(rt) * 2 - mini;
    if (dis > 0) {
      res -= dis;
    }
  }
  cout << res << endl;
  return 0;
}
