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;
struct unionfind {
  vector<int> par, rank;
  unionfind(int n) {
    par.resize(n);
    rank.resize(n);
    for (int i = 0; i < n; i++) {
      par[i] = i;
      rank[i] = 1;
    }
  }
  bool same(int u, int v) { return root(u) == root(v); }
  void unite(int u, int v) {
    if (same(u, v)) return;
    u = root(u), v = root(v);
    if (rank[u] > rank[v]) swap(u, v);
    par[u] = v;
    rank[v] += rank[u];
  }
  int root(int v) {
    if (par[v] == v) return v;
    return par[v] = root(par[v]);
  }
};
void solve() {
  int N;
  cin >> N;
  vector<int> ws(N), cs(N);
  set<int> s;
  map<int, int> mp;
  for (int i = 0; i < N; i++) {
    cin >> ws[i];
    s.insert(ws[i]);
  }
  int cnt = 0;
  for (int v : s) {
    mp[v] = cnt++;
  }
  for (int i = 0; i < N; i++) {
    cs[i] = mp[ws[i]];
  }
  unionfind uf(N);
  vector<int> es[N];
  for (int i = 0; i < N; i++) {
    uf.unite(i, cs[i]);
  }
  for (int i = 0; i < N; i++) {
    es[uf.root(cs[i])].push_back(ws[cs[i]]);
  }
  int ans = 0;
  for (int i = 0; i < N; i++) {
    auto e = es[i];
    int n = e.size(), x = INT_MAX;
    if (n < 2) continue;
    for (int v : e) {
      ans += v;
      x = min(v, x);
    }
    ans += (n - 2) * x;
  }
  cout << ans << endl;
}
int main(void) {
  solve();
  return 0;
}
