Score : 500 points
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.
Input is given from Standard Input in the following format:
N D_1 D_2 ... D_N
Print the maximum possible value of s.
3 7 12 8
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.
2 11 11
2
1 0
0
Note that Takahashi himself is also a participant.