CODE FESTIVAL 2017 Final (Parallel)

C - Time Gap

Time limit時間制限 : 2sec / Memory limitメモリ制限 : 256MB

問題文

XXXX年のCODE FESTIVALには、世界中から高橋君を含めて N+1 人の参加者が集まりました。

s として考えられる最大値を求めて下さい。

制約

• 1 \leq N \leq 50
• 0 \leq D_i \leq 12
• 入力は全て整数である。

入力

N
D_1 D_2 ... D_N


出力

s として考えられる最大値を出力せよ。

入力例 1

3
7 12 8


出力例 1

4


入力例 2

2
11 11


出力例 2

2


入力例 3

1
0


出力例 3

0


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.