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.InputStreamReader;
import java.io.OutputStreamWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
	static BufferedReader in = new BufferedReader(new InputStreamReader(
			System.in));
	static BufferedWriter out = new BufferedWriter(new OutputStreamWriter(
			System.out));
	final static int MOD = 1000000007;

	public static void main(String[] args) throws Exception {

		
		 long test = 1;
//		long test = strToLong(in.readLine().trim()); // if number of
		// test cases
		for (int i = 0; i < test; i++) {
			req();
		}
		out.flush();

		out.close();

	}

	public static void req() throws Exception {
		
		
		
		long one[] = splits(in.readLine(), 2);
		long n = one[0];
		long w = one[1];
		
		long []arr = splits(in.readLine(),2*(int)n);
		
		Arrays.sort(arr);
		long min = arr[0];
		
//		System.out.println(Arrays.toString(arr));
		
		
		long boy = arr[(int)n];
		double ans =0;
//		System.out.println(min+" "+boy);
		if(boy>2*min)
		ans = min;
		else
		{
			ans = boy/2.0;
		}
		
//		out.write(ans+"\n");
		ans = n*3*ans;
//		out.write(ans+"\n");
		if(ans>w)
		{
			ans =w;
		}
		
		out.write(ans+"\n");
		
		
		
	}
	

	// takes a string with spaces as input and produces an array of long of
	// length n
	// input should be valid
	// should know length of array beforehand
	static long[] splits(String s, int n) {

		long[] out = new long[n];
		int idx = 0;

		StringTokenizer ss = new StringTokenizer(s);
		while (ss.hasMoreTokens()) {
			out[idx] = strToLong(ss.nextToken());

			idx++;
		}

		return out;

	}

	static long[] splits2(String s) {

		long[] out;
		int idx = 0;

		StringTokenizer ss = new StringTokenizer(s);
		int n = strToInt(ss.nextToken());
		out = new long[n];
		while (ss.hasMoreTokens()) {
			out[idx] = strToLong(ss.nextToken());

			idx++;
		}

		return out;

	}

	// returns gcd of two long parameters
	// i think its algo by euclid :P
	static long gcd(long a, long b) {

		return b == 0 ? a : gcd(b, a % b);
	}

	// returns maximum among two long
	public static long max(long a, long b) {
		return a > b ? a : b;
	}

	// modulus of product of two long parameter
	public static long modPro(long a, long b) {
		// check value of MOD , may vary for different questions
		// or change the function to take mod as an input parameter :P
		return ((a % MOD) * (b % MOD)) % MOD;
	}

	public static long modInv(long a) {
		return new BigInteger(a + "").modPow(new BigInteger((MOD - 2) + ""),
				new BigInteger(MOD + "")).longValue();
	}

	// returns minimum among two long
	public static long min(long a, long b) {
		return a < b ? a : b;
	}

	// take a string as input and convert it to an integer
	// takes care of negatives
	// no commas or space expected in string
	// copied from codechef
	public static int strToInt(String str) {
		int i = 0;
		int num = 0;
		boolean isNeg = false;
		// Check for negative sign; if it's there, set the isNeg flag
		if (str.charAt(0) == '-') {
			isNeg = true;
			i = 1;
		}
		// Process each character of the string;
		while (i < str.length()) {
			num *= 10;
			num += str.charAt(i++) - '0'; // Minus the ASCII code of
											// '0' to get
			// the value of the charAt(i++).
		}
		if (isNeg)
			num = -num;
		return num;
	}

	// take a string as input and convert it to a long
	// takes care of negatives
	// no commas or space expected in string
	// copied from codechef
	public static long strToLong(String str) {
		int i = 0;
		long num = 0;
		boolean isNeg = false;
		// Check for negative sign; if it's there, set the isNeg flag
		if (str.charAt(0) == '-') {
			isNeg = true;
			i = 1;
		}
		// Process each character of the string;
		while (i < str.length()) {
			num *= 10;
			num += str.charAt(i++) - '0'; // Minus the ASCII code of
											// '0' to get
			// the value of the charAt(i++).
		}
		if (isNeg)
			num = -num;
		return num;
	}

}