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
import collections


def main(N, D):
    Dcounter = collections.Counter(D)
    a = [0, 24]
    b = []
    for i, v in Dcounter.items():
        if v > 2 or (i == 0 and v > 0) or (i == 12 and v > 1):
            print(0)
            return

        if v == 2:
            a.append(i)
            a.append(24-i)
        if v == 1:
            b.append(i)
    ans = 0
    for i in range(1 << len(b)):
        use = a.copy()
        for j in range(len(b)):
            if ((i >> j) & 1) == 1:
                use.append(b[j])
            else:
                use.append(24-b[j])
        use = sorted(use)
        distance = [use[i+1] - use[i] for i in range(len(use)-1)]
        ans = max(ans, min(distance))
    print(ans)

if __name__ == "__main__":
    N = int(input())
    D = list(map(int, input().split(" ")))
    main(N, D)
