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 java.io.*;
import java.util.InputMismatchException;


public class Experimentation9 {
    static int partition(int arr[],int low,int high){
        int pivot=arr[high];
        int i=(low-1);
        for(int j=low;j<high;j++){
            if(arr[j]<=pivot){
                i++;
                int temp=arr[i];
                arr[i]=arr[j];
                arr[j]=temp;
            }
        }
        int temp=arr[i+1];
        arr[i+1]=arr[high];
        arr[high]=temp;
        
        return i+1;
    }
    static void sort(int arr[],int low,int high){
        if(low<high){
            int pi=partition(arr,low,high);
            sort(arr,low,pi-1);
            sort(arr,pi+1,high);
        }
    }
    static int maxDiff(int[] arr,int arr_length){
        if(arr_length>1){
        int max_diff=arr[1]-arr[0];
        int next=arr[0];
        for(int i=1;i<arr_length;i++){
            if(arr[i]-next>max_diff){
                max_diff=arr[i]-next;
            }
            next=arr[i];
        }
            return max_diff;
        }
        else{
            return 0;
        }
    }
    public static void main(String args[]) throws IOException{
        InputReader in=new InputReader(System.in);
        OutputWriter out=new OutputWriter(System.out);
        double answer;
        int n=in.readInt();
        int l=in.readInt();
        int[] array=IOUtils.readIntArray(in, n);
        sort(array,0,n-1);
        if(array[0]==0 && array[n-1]==l){
            answer=(double)maxDiff(array,n)/2;
        }
        else if(array[0]==0){
            answer=Math.max((double)maxDiff(array,n)/2,(l-array[n-1]));
        }
        else if(array[n-1]==l){
            answer=Math.max((double)maxDiff(array,n)/2,array[0]);
        }
        else{
            int temp=Math.max(array[0],(l-array[n-1]));
            answer=Math.max((double)maxDiff(array,n)/2,temp);
        }
        out.print(answer);
        out.flush();
        out.close();
    } 
}

class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
		
		public int read() {
			if (numChars == -1) {
				throw new InputMismatchException();
			}
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0) {
					return -1;
				}
			}
			return buf[curChar++];
		}
		
		public int readInt() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9') {
					throw new InputMismatchException();
				}
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		
		public String readString() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} 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 String next() {
			return readString();
		}
		
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
	
	class OutputWriter {
		private final PrintWriter writer;
		
		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}
		
		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}
		
		public void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0) {
					writer.print(' ');
				}
				writer.print(objects[i]);
			}
			writer.flush();
		}

		public void close() {
			writer.close();
		}
		
		public void flush() {
			writer.flush();
		}
	}
        class IOUtils {
 
		public static int[] readIntArray(InputReader in, int size) {
			int[] array = new int[size];
			for (int i = 0; i < size; i++)
				array[i] = in.readInt();
			return array;
		}
 
	}