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 PYTHON):

Solution:
#-*- encoding:utf-8 -*-

'''
길에 랜턴을 배치함.
n l : n은 랜턴의 개수, l은 길의 총 거리
다음행은 랜턴이 배치되는 위치임

정렬한 값을 기준으로, 

첫번째 랜턴과 시작점의 거리, 각 래턴의 최대 거리/ / 2 , 마지막 랜턴과 마지막 점의 거리를 고려해줘야함

'''


n, l = map(int, raw_input().split())
lanterns = sorted(map(int, raw_input().split()))

distance =  0

for i in range(1,n,1) :
	tmp = lanterns[i] - lanterns[i-1]
	distance = max(tmp, distance)

print max(lanterns[0]/1.0,distance/2.0,l-lanterns[n-1]/1.0)


'''

7 15
15 5 3 7 9 14 0

'''