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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

from fractions import gcd
from datetime import date, timedelta
from heapq import*
import math
from collections import defaultdict, Counter, deque
import sys
from bisect import *
import itertools
import copy
sys.setrecursionlimit(10 ** 7)
MOD = 10 ** 9 + 7


def main():
    n = int(input())
    d = list(map(int, input().split()))
    if n == 1:
        print(d[0])
        exit()
    d2 = []
    dc = defaultdict(int)
    for i in range(n):
        v = d[i]
        if dc[v] >= 2 or (dc[v] == 1 and v == 12) or v == 0:
            print(0)
            exit()
        dc[v] += 1
        d2.append(v)
    
    dd = []
    ddt = []
    for i in range(0, 13):
        if dc[i] == 1:
            dd.append(i)
        elif dc[i] == 2:
            ddt.append(i)
            ddt.append(24 - i)


    
    ans = 0
    for i in range(1 << len(dd)):
        d3 = []
        for j in range(len(ddt)):
            d3.append(ddt[j])

        for j in range(len(dd)):
            if (i & (1 << j)):
                d3.append(dd[j])
            else:
                d3.append(24 - dd[j])
        
        d3 = sorted(d3)
        t = float("inf")
        for i in range(len(d3) - 1):
            t = min(t, d3[i + 1] - d3[i])
        ans = max(t, ans)
    print(ans)
 


if __name__ == '__main__':
    main()