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)

s=[0]*24
s[12]=1
n=int(input())
a=list(map(int,input().split()))
d=[a.count(i)for i in range(13)]
d[0]+=1
if max(d[0],d[12])<2 and max(d[1:-1])<3:
    if d[12]==1:
        s[0]=1
    t=[]
    for i in range(1,12):
        if d[i]==2:
            s[12-i]=1
            s[12+i]=1
        elif d[i]==1:
            t.append(i)
    k=0
    for i in range(2**len(t)):
        p=bin(i)[2:]
        p="0"*(len(t)-len(p))+p
        r=s[:]
        for j in range(len(t)):
            if p[j]=="0":
                r[12-t[j]]=1
            else:
                r[12+t[j]]=1
        h=0
        q=0
        ans=30
        for j in 2*r:
            if j==1:
                if h==0:
                    q=1
                    h=1
                else:
                    ans=min(q,ans)
                    q=1
            else:
                q+=1
        k=max(ans,k)
    print(k)
else:
    print(0)