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.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashSet;
import java.util.Random;

public class Main {
	static HashSet<String> set = new HashSet<String>();
	public static void main(String[] args) throws NumberFormatException,
	IOException {
		Solve solve = new Solve();
		solve.solve();
	}
}
class Solve{
	ContestScanner in;
	Solve() throws FileNotFoundException{
		in = new ContestScanner();
	}
	void solve() throws IOException{
		int n = in.nextInt();
		long w = in.nextInt();
		long[] a = new long[n*2];
		for(int i=0; i<2*n; i++) a[i] = in.nextInt();
		Arrays.sort(a);
		double b = Math.min(Math.min(a[0]*n+a[0]*2*n, a[n]*0.5*n+a[n]*n), w);
		System.out.println(b);
	}
}

class Timer{
	long time;
	public void set(){
		time = System.currentTimeMillis();
	}
	
	public long stop(){
		return System.currentTimeMillis()-time;
	}
}

class Node{
	int id;
	ArrayList<Node> edge = new ArrayList<Node>();
	public Node(int id) {
		this.id = id;
	}
	public void createEdge(Node node) {
		edge.add(node);
	}
}

class MyComp implements Comparator<int[]> {
	final int idx;
	public MyComp(int idx){
		this.idx = idx;
	}
	public int compare(int[] a, int[] b) {
		return a[idx] - b[idx];
	}
}

class Reverse implements Comparator<Integer> {
	public int compare(Integer arg0, Integer arg1) {
		return arg1 - arg0;
	}
}


class ContestWriter {
	private PrintWriter out;

	public ContestWriter(String filename) throws IOException {
		out = new PrintWriter(new BufferedWriter(new FileWriter(filename)));
	}

	public ContestWriter() throws IOException {
		out = new PrintWriter(System.out);
	}

	public void println(String str) {
		out.println(str);
	}
	
	public void println(Object obj) {
		out.println(obj);
	}

	public void print(String str) {
		out.print(str);
	}
	
	public void print(Object obj) {
		out.print(obj);
	}

	public void close() {
		out.close();
	}
}

class ContestScanner {
	private BufferedReader reader;
	private String[] line;
	private int idx;

	public ContestScanner() throws FileNotFoundException {
		reader = new BufferedReader(new InputStreamReader(System.in));
	}

	public ContestScanner(String filename) throws FileNotFoundException {
		reader = new BufferedReader(new InputStreamReader(new FileInputStream(
				filename)));
	}

	public String nextToken() throws IOException {
		if (line == null || line.length <= idx) {
			line = reader.readLine().trim().split(" ");
			idx = 0;
		}
		return line[idx++];
	}
	
	public String readLine() throws IOException{
		return reader.readLine();
	}

	public long nextLong() throws IOException, NumberFormatException {
		return Long.parseLong(nextToken());
	}

	public int nextInt() throws NumberFormatException, IOException {
		return (int) nextLong();
	}

	public double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(nextToken());
	}
}