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.*;
import java.io.*;
import java.math.BigInteger;
public class B {
public static void main(String[] args) throws IOException
{
    PrintWriter out = new PrintWriter(System.out);
    input.init(System.in);

    float totalW = 0;
    int n = input.nextInt();
    int w = input.nextInt();
    List<Integer> a = new ArrayList<>();
    //int[] a = new int[2*n];
    
    for (int i = 0; i < 2*n ; i ++) {
       a.add(input.nextInt());  
    }
    
    Collections.sort(a);
    
    float maxBoys = a.get(n);
    float maxGirls = a.get(0);
    
    for (int i = 0; i < n; i++) {
      if (a.get(i)*2 < maxBoys) {
        maxBoys = a.get(i)*2;
      }
      if (a.get(n+i) < maxBoys) {
        maxBoys = a.get(n+i);
      }
    }
    
    maxBoys = Math.min((float)w/3/(float)n*2, maxBoys);
    totalW = n * maxBoys;
    
    maxGirls = maxBoys/2;
    
    totalW = n * maxGirls + totalW;
    
    out.println(totalW);
    
    
    
    //int n = input.nextInt();

    //out.println(n);
    out.close();
}
public static class input {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
    
    static String nextLine() throws IOException
    {
      return reader.readLine();
    }

    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }
}

public static int mod = 1000000007;
public static BigInteger MOD = BigInteger.valueOf(1000000007);
  
public static int binom(int n, int k) {
  long a = BigInteger.valueOf(fac(k)).modInverse(MOD).longValue();
  long b = BigInteger.valueOf(fac(n - k)).modInverse(MOD).longValue();
  long ans = fac(n);
  ans = (ans * a)%mod;
  ans = (ans * b)%mod;
  
  return (int) ans;
}

public static int fac(int n) {
  long fak = 1;
  while ( n > 1 )
  {
    fak = (fak * n) % mod;
    n   = n - 1;
  }
  
  return (int) fak;
}
}