Problem: Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns. 

Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?

Input

The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively. 

The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.

Output

Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.

Examples

Input

7 15
15 5 3 7 9 14 0


Output

2.5000000000


Input

2 5
2 5


Output

2.0000000000

Note

Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.

Solution (in JAVA):

Solution:
//import sun.reflect.generics.tree.Tree;

import sun.awt.datatransfer.DataTransferer;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.util.*;
import java.util.logging.LoggingMXBean;


public class citylights {
    public static int []arr;
    public static ArrayList<Integer>p;
    public static int []val;
    public static long []facto;
    public static int mod= 1000000007;
    public static long []fillme;
    // public static int []tt;



    public static void main(String[] args) {
        arr = new int[1000001];
        p = new ArrayList<>();
        val = new int[1000001];
        facto = new long[1000007];
        //tt=new int[100];

        fillme = new long[1000007];
        //sieve();

        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);


        int n=in.nextInt();
        double l=in.nextLong();
        double []a=new double[n];
        for (int i=0;i<n;i++)
            a[i]=in.nextLong();
        Arrays.sort(a);
        double max=2*Math.max(a[0],l-a[n-1]);
        for (int i=1;i<n;i++)
        {
            max=Math.max(max,a[i]-a[i-1]);
        }
        System.out.printf("%.10f",max/2);





       out.close();
    }
    public static long bsearch(long []a,long t)
    {
        long ans=-1;
        long low=0;
        long high=a.length-1;
        while (low<=high)
        {
            long mid=(low+high)/2;
            if(a[(int) mid]<=t)
            {
                ans=mid;
                low=mid+1;
            }else
            {
                high=mid-1;
            }


        }
        return ans;


    }
    public static boolean check(String str)
    {
         Stack<Character>st=new Stack<>();
         for (int i=0;i<str.length();i++)
         {
             Character c=str.charAt(i);
               if(c=='A')
               {
                   if(st.isEmpty())
                   {
                       st.push(c);
                   }else
                   {
                        Character peek=st.peek();
                        if(peek!='A')
                        {
                            st.push(c);
                        }else
                            st.pop();

                   }




               }else
               {
                   if(st.isEmpty())
                   {
                       st.push(c);
                   }else
                   {
                       Character peek=st.peek();
                       if(peek=='B')
                       {
                           st.pop();
                       }else
                       {
                           st.push(c);
                       }
                   }




               }


         }
         return st.isEmpty();





    }

    public static int[]rotate(int []order,int by)
    {
        int length=order.length;
        int []a=new int[length];
        for (int i=0;i<length;i++)
        {
            a[(i+by)%length]=order[i];

        }
        return a;


    }
    public static long modinv(long x,long m)
    {
        return powmod(x,m-2,m);

    }
    public static long eulertoitent(long n)
    {
        long res = n;
        for (int i = 2; i * i <= n; i++)
            if (n % i == 0) {
                while (n % i == 0)
                    n /= i;
                res -= res / i;
            }
        if (n > 1)
            res -= res / n;
        return res;



    }

    //calculate factorial till modulas
    public static void fact()
    {
        facto[0]=1;
        for(int i=1;i<=mod;i++)
        {
            facto[i]=(i*facto[i-1])%mod;
        }


    }

    public static void sieve()
    {
        arr[0]=1;
        arr[1]=1;

        for(int i=2;i*i<1000001;i++)
        {
            if(arr[i]==0)
            {

                for(int j=i*i;j<1000001;j+=i)
                {
                    arr[j]=1;
                }
            }
        }
        for(int i=2;i<1000001;i++)
        {
            if(arr[i]==0)
                p.add(i);
        }
    }
    public static boolean isPrime(int n)
    {
        // Corner cases
        if (n <= 1)  return false;
        if (n <= 3)  return true;

        // This is checked so that we can skip
        // middle five numbers in below loop
        if (n%2 == 0 || n%3 == 0) return false;

        for (int i=5; i*i<=n; i=i+6)
            if (n%i == 0 || n%(i+2) == 0)
                return false;

        return true;
    }
    public static long euclgcd(long a,long b)
    {
        if(b==0)
            return a;
        else
            return euclgcd(b,a%b);

    }

    public static long powmod(long x,long n,long m) {
        long result = 1L;
        while (n > 0) {
            if (n % 2 == 1)
                result = (result * x) % m;
            x = (x * x) % m;
            n = n / 2;
        }

        return result;
    }



    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private InputReader.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);
        }
    }


}