Time Gap

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.

Examples

Input

3 7 12 8

Output

4

Input

2 11 11

Output

2

Input

1 0

Output

0

inputFormat

input values are integers.

Input

Input is given from Standard Input in the following format:

N D_1 D_2 ... D_N

outputFormat

Output

Print the maximum possible value of s.

Examples

Input

3 7 12 8

Output

4

Input

2 11 11

Output

2

Input

1 0

Output

0

样例

2
11 11

2