{"problem":{"name":"Time Gap","description":{"content":"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 an","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"cf17_final_c"},"statements":[{"statement_type":"Markdown","content":"In CODE FESTIVAL XXXX, there are $N+1$ participants from all over the world, including Takahashi.\nTakahashi 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.\nThen, 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.\nFind the maximum possible value of $s$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 50$\n*   $0 \\leq D_i \\leq 12$\n*   All input values are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$D_1$ $D_2$ $...$ $D_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"cf17_final_c","tags":[],"sample_group":[["3\n7 12 8","4\n\nFor 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\n11 11","2"],["1\n0","0\n\nNote that Takahashi himself is also a participant."]],"created_at":"2026-03-03 11:01:14"}}