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;
void fnInput(int &rnMaxSiz, vector<int> &rvnSort) {
  cin >> rnMaxSiz;
  rvnSort.resize(rnMaxSiz);
  for (int i = 0; i < rnMaxSiz; i++) cin >> rvnSort[i];
}
int fnPartition(vector<int> &rvnSort, int &nSwpCnt, int nFront, int nBack) {
  int nMid = nFront;
  for (int i = nFront; i < nBack; i++)
    if (rvnSort[i] <= rvnSort[nBack]) {
      if (rvnSort[nMid] != rvnSort[i]) nSwpCnt += rvnSort[nMid] + rvnSort[i];
      swap(rvnSort[nMid++], rvnSort[i]);
    }
  if (rvnSort[nMid] != rvnSort[nBack])
    nSwpCnt += rvnSort[nMid] + rvnSort[nBack];
  swap(rvnSort[nMid], rvnSort[nBack]);
  return nMid;
}
void fnQuickSort(vector<int> &rvnSort, int &nSwpCnt, int nFront, int nBack) {
  if (nFront < nBack) {
    int nMid = fnPartition(rvnSort, nSwpCnt, nFront, nBack);
    fnQuickSort(rvnSort, nSwpCnt, nFront, nMid - 1);
    fnQuickSort(rvnSort, nSwpCnt, nMid + 1, nBack);
  }
}
void fnResult(int nSwpCnt) { cout << nSwpCnt << endl; }
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int nMaxSiz;
  vector<int> vnSort;
  int nSwpCnt = 0;
  fnInput(nMaxSiz, vnSort);
  fnQuickSort(vnSort, nSwpCnt, 0, vnSort.size() - 1);
  fnResult(nSwpCnt);
  return 0;
}
