Problem:
Score : 500 points

Problem Statement

In CODE FESTIVAL XXXX, there are N+1 participants from all over the world, including Takahashi.

Takahashi checked and found that the time gap (defined below) between the local times in his city and the i-th person's city was D_i hours.
The time gap between two cities is defined as follows. For two cities A and B, if the local time in city B is d o'clock at the moment when the local time in city A is 0 o'clock, then the time gap between these two cities is defined to be min(d,24-d) hours.
Here, we are using 24-hour notation.
That is, the local time in the i-th person's city is either d o'clock or 24-d o'clock at the moment when the local time in Takahashi's city is 0 o'clock, for example.

Then, for each pair of two people chosen from the N+1 people, he wrote out the time gap between their cities. Let the smallest time gap among them be s hours.

Find the maximum possible value of s.

Constraints

1 \leq N \leq 50

0 \leq D_i \leq 12

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
D_1 D_2 ... D_N

Output

Print the maximum possible value of s.

Sample Input 1

3
7 12 8

Sample Output 1

4

For example, consider the situation where it is 7, 12 and 16 o'clock in each person's city at the moment when it is 0 o'clock in Takahashi's city. In this case, the time gap between the second and third persons' cities is 4 hours.

Sample Input 2

2
11 11

Sample Output 2

2

Sample Input 3

1
0

Sample Output 3

0

Note that Takahashi himself is also a participant.

Solution in Python (3.4.3) (judge verdict: Accepted)

import collections
n=int(input())
s=list(map(int,input().split()))
if 0 in s:
  print(0)
  quit()
s=collections.Counter(s)
l1=[0]
l2=[]
for x in s:
  if s[x]>2:
    print(0)
    quit()
  elif s[x]>1:
    l2.append(x)
    l2.append(24-x)
  else:
    l1.append(x)
x=len(l1)
an=0
for i in range(2**x):
  memo=[0]*x
  for j in range(x):
    if ((i >> j) & 1):
      memo[j]=l1[j]
    else:
      memo[j]=24-l1[j] 
  ans=12
  memo=memo+l2
  for k in range(len(memo)):
    for m in range(k+1,len(memo)):
      ans=min(ans,min(abs(memo[k]-memo[m]),24-abs(memo[k]-memo[m])))
  an=max(ans,an)
print(an)