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 StCst {
  int m_nNo;
  int m_nInSeq;
  bool m_bDone;
  static bool AsdNo(const StCst &roLeft, const StCst &roRight) {
    return roLeft.m_nNo < roRight.m_nNo;
  }
};
void fnInput(int &rnMaxSiz, vector<StCst> &rvoSort, int &rnMinNo) {
  int nCnt = 0;
  cin >> rnMaxSiz;
  rvoSort.resize(rnMaxSiz);
  for (int i = 0; i < rnMaxSiz; i++) {
    cin >> rvoSort[i].m_nNo;
    rnMinNo = min(rnMinNo, rvoSort[i].m_nNo);
    rvoSort[i].m_nInSeq = nCnt++;
  }
}
void fnMinCostSort(vector<StCst> &rvoSort, int nMinNo, int &rnSwpCnt) {
  sort(begin(rvoSort), end(rvoSort), StCst::AsdNo);
  int nCost;
  for (int i = 0; i < rvoSort.size(); i++) {
    if (rvoSort[i].m_bDone) continue;
    int nTotal = rvoSort[i].m_nNo;
    int nCurSize = 1;
    int nCurMin = rvoSort[i].m_nNo;
    rvoSort[i].m_bDone = true;
    int j = rvoSort[i].m_nInSeq;
    while (rvoSort[j].m_nInSeq != rvoSort[i].m_nInSeq) {
      nTotal += rvoSort[j].m_nNo;
      nCurSize++;
      nCurMin = min(nCurMin, rvoSort[j].m_nInSeq);
      rvoSort[j].m_bDone = true;
      j = rvoSort[j].m_nInSeq;
    }
    if (nCurSize == 1)
      nCost = 0;
    else if (nMinNo == nCurMin)
      nCost = nTotal + (nCurSize - 2) * nCurMin;
    else
      nCost = min(nTotal + (nCurSize - 2) * nCurMin,
                  nTotal + nCurMin + (nCurSize + 1) * nMinNo);
    rnSwpCnt += nCost;
  }
}
void fnResult(int nSwpCnt) { cout << nSwpCnt << endl; }
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int nMaxSiz;
  vector<StCst> voSort;
  int nMinNo = INT_MAX;
  fnInput(nMaxSiz, voSort, nMinNo);
  int nSwpCnt = 0;
  fnMinCostSort(voSort, nMinNo, nSwpCnt);
  fnResult(nSwpCnt);
  return 0;
}
