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.math.*;
import java.io.*;
public class Luck{
	public static InputReader sc;
    public static PrintWriter out;
    public static final long MOD = (long)1e9 + 7L;
    public static void main(String[] args){
    	sc=new InputReader(System.in);	
    	out=new PrintWriter(System.out);
    	int n=sc.nextInt();
    	double w=sc.nextLong();
    	double[] A=new double[2*n];
    	for(int i=0;i<2*n;i++){
    		A[i]=(double)sc.nextLong();
    	}
    	Arrays.sort(A);
    	double res=0D;
    	if(2D*A[0]<=A[n]){
    		res=A[0];
    	}
    	else{
    		res=A[n]/2D;
    	}
    	//out.println("res: "+res);
    	if(res*3D*(double)n>w){
    		res=w;
    	}
    	else{
    		res*=3D*(double)n;
    	}
    	out.println(res);
    	out.close();
    }
   
//    static class Pair{
//    	String x;
//    	int y;
//    	Pair(){
//    		this.x="";
//    		this.y=-1;
//    	}
//    	Pair(String profit,int val,int count){
//    		this.x=profit;
//    		this.y=val;
//    	}
//    	public static Comparator<Pair> Val=new Comparator<Pair>(){
//    		public int compare(Pair p1,Pair p2){
//    			if(p1.x==p2.y){
//    				return p1.y-p2.y;
//    			}
//    			return (int)p1.x-(int)p2.x;
//    		}
//    	};
//    	public int hashCode() {
//    		final int prime = 31;
//    		int result = 1;
//    		result = prime * result + x;
//    		result = prime * result + x;
//    		return result;
//    	}
//    	public boolean equals(Object obj){
//    		if (this == obj)
//    	        return true;
//    	    if (!(obj instanceof Pair)) {
//    	        return false;
//    	    }
//    	 
//    	    Pair p = (Pair) obj;
//    	    if(p.x!=this.x){
//    	    	return false;
//    	    }
//    	    else if(p.y!=p.y){
//    	    	return false;
//    	    }
//    	    return true;
//    	}
//    }
    static class DisjointSet{
    	int n;
    	int[] par;
    	int[] rank;
    	DisjointSet(int n){
    		this.n=n;
    		this.par=new int[n];
    		this.rank=new int[n];
    		makeSet();
    	}
    	void makeSet(){
    		for(int i=0;i<n;i++){
    			par[i]=i;
    			rank[i]=1;
    		}
    	}
    	void union(int x,int y){
    		int parX=parent(x);
    		int parY=parent(y);
    		if(parX!=parY){
    			if(rank[parX]>=rank[parY]){
    				rank[parX]+=rank[parY];
    				rank[parY]=0;
    				par[parY]=parX;
    			}
    			else{
    				rank[parY]+=rank[parX];
    				rank[parX]=0;
    				par[parX]=parY;
    			}
    		}
    	}
    	int parent(int c){
    		int i=c;
    		while(i!=par[i]){
    			i=par[i];
    		}
    		return i;
    	}
    }
    static int gcd(int a,int b){
    	if(b==0){
    		return a;
    	}
    	return gcd(b,a%b);
    	
    }
    static int lcm(int a,int b){
    	int g;
    	if(a<b){
    		g=gcd(b,a);
    	}
    	else{
    		g=gcd(a,b);
    	}
    	return (a*b)/g;
    }
    static long bigmod ( long a, long p, long m ) {
        long res = 1 % m, x = a % m;
        while ( p>0 ) {
            if ( (p & 1)==1 ) res = ( res * x ) % m;
            x = ( x * x ) % m; p >>= 1;
        }
        return res;
    }
    static boolean isPrime(int n){
    	 if (n == 2)
    	        return true;
    	    for (long i = 2; i * i <= n; i++) {
    	        if (n % i == 0)
    	            return false;
    	    }
    	    return true;
    }
    
    static void shuffle(int[] A){
    	for(int i=A.length-1;i>0;i--){
    		int j=(int)(Math.random()*(i+1));
    		int temp=A[j];
    		A[j]=A[i];
    		A[i]=temp;
    	}
    }
    
//	public static class Node implements Comparable<Node>{
//	    int u;
//	    int v;
//	    public Node(){
//	    	;
//	    }
//	    public Node (int u, int v) {
//	    	this.u = u;
//	        this.v = v;
//	    }
//	    
//	    public void print() {
//	        out.println(v + " " + u + " ");
//	    }
//	   
//	    public int compareTo(Node n1){
//	    	return this.u-n1.u;
//	    }
//	}
	public static long pow(long base,long exp,long mod){
		if(exp==0){
			return 1;
		}
		if(exp==1){
			return base;
		}
		long temp=exp/2;
		long val=pow(base,temp,mod);
		long result=val*val;
		result=(result%mod);
		long AND=exp&1;
		if(AND==1){
			result*=base;
			result=(result%mod);
		}
		return result;
	}
	public static BigInteger pow(BigInteger base, BigInteger exp) {
	    if(exp.equals(new BigInteger(String.valueOf(0)))){
	        return new BigInteger(String.valueOf(1));
	    }    
	    if(exp.equals(new BigInteger(String.valueOf(1))))
	        return base;
	    BigInteger temp=exp.divide(new BigInteger(String.valueOf(2)));
	    BigInteger val = pow(base, temp);
	    BigInteger result = val.multiply(val);
	    result=result.remainder(new BigInteger(String.valueOf(MOD)));
	    BigInteger AND=exp.and(new BigInteger(String.valueOf(1)));
	    if(AND.equals(new BigInteger(String.valueOf(1)))){
	        result = result.multiply(base);
	        result=result.remainder(new BigInteger(String.valueOf(MOD)));
	    }    
	    return result;
	}
	    
	static class InputReader {

	    private InputStream stream;
	    private byte[] buf = new byte[8192];
	    private int curChar, snumChars;
	    private SpaceCharFilter filter;

	    public InputReader(InputStream stream) {
	        this.stream = stream;
	    }

	    public int snext() {
	        if (snumChars == -1)
	            throw new InputMismatchException();
	        if (curChar >= snumChars) {
	            curChar = 0;
	            try {
	                snumChars = stream.read(buf);
	            } catch (IOException e) {
	                throw new InputMismatchException();
	            }
	            if (snumChars <= 0)
	                return -1;
	        }
	        return buf[curChar++];
	    }

	    public int nextInt() {
	        int c = snext();
	        while (isSpaceChar(c))
	            c = snext();
	        int sgn = 1;
	        if (c == '-') {
	            sgn = -1;
	            c = snext();
	        }
	        int res = 0;
	        do {
	            if (c < '0' || c > '9')
	                throw new InputMismatchException();
	            res *= 10;
	            res += c - '0';
	            c = snext();
	        } while (!isSpaceChar(c));
	        return res * sgn;
	    }

	    public long nextLong() {
	        int c = snext();
	        while (isSpaceChar(c))
	            c = snext();
	        int sgn = 1;
	        if (c == '-') {
	            sgn = -1;
	            c = snext();
	        }
	        long res = 0;
	        do {
	            if (c < '0' || c > '9')
	                throw new InputMismatchException();
	            res *= 10;
	            res += c - '0';
	            c = snext();
	        } while (!isSpaceChar(c));
	        return res * sgn;
	    }

	    public int[] nextIntArray(int n) {
	        int a[] = new int[n];
	        for (int i = 0; i < n; i++)
	            a[i] = nextInt();
	        return a;
	    }

	    public String readString() {
	        int c = snext();
	        while (isSpaceChar(c))
	            c = snext();
	        StringBuilder res = new StringBuilder();
	        do {
	            res.appendCodePoint(c);
	            c = snext();
	        } while (!isSpaceChar(c));
	        return res.toString();
	    }

	    public boolean isSpaceChar(int c) {
	        if (filter != null)
	            return filter.isSpaceChar(c);
	        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	    }

	    public interface SpaceCharFilter {
	        public boolean isSpaceChar(int ch);
	    }
	}

}