Problem: Pasha decided to invite his friends to a tea party. For that occasion, he has a large teapot with the capacity of w milliliters and 2n tea cups, each cup is for one of Pasha's friends. The i-th cup can hold at most ai milliliters of water.

It turned out that among Pasha's friends there are exactly n boys and exactly n girls and all of them are going to come to the tea party. To please everyone, Pasha decided to pour the water for the tea as follows:

  * Pasha can boil the teapot exactly once by pouring there at most w milliliters of water; 
  * Pasha pours the same amount of water to each girl; 
  * Pasha pours the same amount of water to each boy; 
  * if each girl gets x milliliters of water, then each boy gets 2x milliliters of water. 



In the other words, each boy should get two times more water than each girl does.

Pasha is very kind and polite, so he wants to maximize the total amount of the water that he pours to his friends. Your task is to help him and determine the optimum distribution of cups between Pasha's friends.

Input

The first line of the input contains two integers, n and w (1 ≤ n ≤ 105, 1 ≤ w ≤ 109) — the number of Pasha's friends that are boys (equal to the number of Pasha's friends that are girls) and the capacity of Pasha's teapot in milliliters.

The second line of the input contains the sequence of integers ai (1 ≤ ai ≤ 109, 1 ≤ i ≤ 2n) — the capacities of Pasha's tea cups in milliliters.

Output

Print a single real number — the maximum total amount of water in milliliters that Pasha can pour to his friends without violating the given conditions. Your answer will be considered correct if its absolute or relative error doesn't exceed 10 - 6.

Examples

Input

2 4
1 1 1 1


Output

3

Input

3 18
4 4 4 2 2 2


Output

18

Input

1 5
2 3


Output

4.5

Note

Pasha also has candies that he is going to give to girls but that is another task...

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class essai3 {
    public static class Mergesort {
          private int[] numbers;
          private int[] helper;

          private int number;

          public  void sort(int[] values,int n) {
            this.numbers = values;
            number = n;
            this.helper = new int[number];
            mergesort(0, number - 1);
          }

          private void mergesort(int low, int high) {
            // check if low is smaller then high, if not then the array is sorted
            if (low < high) {
              // Get the index of the element which is in the middle
              int middle = low + (high - low) / 2;
              // Sort the left side of the array
              mergesort(low, middle);
              // Sort the right side of the array
              mergesort(middle + 1, high);
              // Combine them both
              merge(low, middle, high);
            }
          }

          private void merge(int low, int middle, int high) {

            // Copy both parts into the helper array
            for (int i = low; i <= high; i++) {
              helper[i] = numbers[i];
            }

            int i = low;
            int j = middle + 1;
            int k = low;
            // Copy the smallest values from either the left or the right side back
            // to the original array
            while (i <= middle && j <= high) {
              if (helper[i] <= helper[j]) {
                numbers[k] = helper[i];
                i++;
              } else {
                numbers[k] = helper[j];
                j++;
              }
              k++;
            }
            // Copy the rest of the left side of the array into the target array
            while (i <= middle) {
              numbers[k] = helper[i];
              k++;
              i++;
            }

          }
        } 
    
    
     public static void main(String[] args) {
          // Use the Scanner class
          Scanner sc = new Scanner(System.in);  
          int N = 200000;
          int n      = sc.nextInt();  
          int w      = sc.nextInt();// read input as integer
          /*long k     = sc.nextLong();       // read input as long
          double d   = sc.nextDouble();     // read input as double
          String str = sc.next();           // read input as String
          String s   = sc.nextLine();       // read whole line as String
          */
          int[] t = new int[N];
          for (int i=0; i<2*n;i++){
              t[i]    = sc.nextInt();
          }
          Mergesort azerty = new Mergesort();
          azerty.sort(t,2*n);
         
         
          
          double x,y ;
          boolean b = 2*t[0]<=t[n];
          if (b) {
              x= t[0];
          }
          else {
              x=(new Double(t[n])) / (new Double(2));
          }
          y = 3*x*n;
          if (y<w) {
              System.out.print(y);
          }
          else {
              System.out.print(w);
          }
          
          
        }


}