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
def solve(N, D):
    fill = [0] * 24
    fill[0] = 1

    left = False
    for i in range(N):
        if D[i] == 0:
            print(0)
            return 0
        elif D[i] == 12:
            if fill[12] == 1:
                print(0)
                return 0
            else:
                fill[12] = 1
        else:
            if not left:
                if fill[D[i]] == 0:
                    fill[D[i]] = 1
                    left = True
                elif fill[24-D[i]] == 0:
                    fill[24-D[i]] = 1
                    left = False
                else:
                    print(0)
                    return 0
            else:
                if fill[24-D[i]] == 0:
                    fill[24-D[i]] = 1
                    left = False
                elif fill[D[i]] == 0:
                    fill[D[i]] = 1
                    left = True
                else:
                    print(0)
                    return 0

    s = 24
    cnt = 0
    for i in range(1, 24):
        if i == 23:
            if fill[i] == 0:
                cnt += 1
                s = min(s, cnt + 1)
            else:
                s = min(s, cnt + 1)
        else:
            if fill[i] == 0:
                cnt += 1
            else:
                s = min(s, cnt + 1)
                cnt = 0
    print(s)

if __name__ == '__main__':
    N = int(input())
    D = list(map(int, input().split()))
    solve(N, sorted(D))
