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>
struct MCS {
  int cost;
  int sorder;
  int order;
};
void exchange(struct MCS *pa, struct MCS *pb) {
  struct MCS t;
  t = *pa;
  *pa = *pb;
  *pb = t;
  return;
}
int Partition(struct MCS A[], int p, int r) {
  struct MCS x;
  int i, j;
  x = A[r];
  i = p - 1;
  for (j = p; j < r; j++) {
    if (A[j].cost < x.cost) {
      i++;
      exchange(&A[i], &A[j]);
    }
  }
  exchange(&A[i + 1], &A[r]);
  return i + 1;
}
void QuickSort(struct MCS A[], int p, int r) {
  int q;
  if (p < r) {
    q = Partition(A, p, r);
    QuickSort(A, p, q - 1);
    QuickSort(A, q + 1, r);
  }
  return;
}
int tryChange(int n, struct MCS W[]) {
  int cost, miniCost;
  int i;
  int maxi, mini;
  int max;
  int min, mostmin;
  int minorder, maxorder, mostminorder;
  int limitN;
  maxi = mini = 0;
  miniCost = cost = 20000;
  limitN = n;
  maxorder = max = -1;
  mostmin = min = mostminorder = minorder = n;
  while (1) {
    for (i = 0; i < limitN; i++) {
      if (i != W[i].order) {
        if (max < W[i].sorder) {
          max = W[i].sorder;
          maxorder = i;
        }
        if (W[i].sorder < min) {
          min = W[i].sorder;
          minorder = i;
        }
      }
      if (W[i].sorder < mostmin) {
        mostmin = W[i].sorder;
        mostminorder = i;
      }
    }
    if (-1 == maxorder) {
      break;
    }
    if (W[maxorder].order != minorder) {
      if (2 * (W[minorder].cost + W[mostminorder].cost) <
          (W[maxorder].cost + W[minorder].cost)) {
        minorder = mostminorder;
      }
    }
    if (W[maxorder].order == minorder) {
      cost = (W[minorder].cost + W[maxorder].cost);
      miniCost = cost;
      mini = minorder;
      maxi = maxorder;
      break;
    }
    limitN--;
    max = -1;
    if (-1 == limitN) {
      if (20000 == miniCost) {
        cost = (W[minorder].cost + W[maxorder].cost);
        miniCost = cost;
        mini = minorder;
        maxi = maxorder;
      }
      break;
    }
  }
  if (20000 != miniCost) {
    exchange(&W[mini], &W[maxi]);
  } else {
    miniCost = 0;
  }
  return miniCost;
}
int main(void) {
  int n, i;
  struct MCS W[1000 + 1];
  int cost;
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &W[i].cost);
    W[i].order = i;
  }
  QuickSort(W, 0, n - 1);
  for (i = 0; i < n; i++) {
    W[i].sorder = i;
  }
  cost = i = 0;
  while ((i = tryChange(n, W))) {
    cost += i;
  }
  printf("%d\n", cost);
  return 0;
}
