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
# coding: utf-8

import itertools
import collections


def main():
    n = int(input())
    c = collections.Counter(map(int, input().split()))
    if c[0] > 0:
        return 0
    if c.most_common(1)[0][1] >= 3:
        return 0
    l1 = []
    l2 = []
    for i, cnt in c.most_common():
        if cnt == 2:
            l2.append(i)
        elif cnt == 1:
            l1.append(i)
    s = 0
    for i in range(len(l1) + 1):
        for invs in itertools.combinations(l1, i):
            l = [0]
            for k in l1:
                l.append(-k if k in invs else k)
            for k in l2:
                l.append(k)
                l.append(-k)
            l.sort()
            ss = 24
            for j in range(len(l)-1):
                ss = min(l[j + 1] - l[j], ss)
            d = l[-1] - l[0]
            ss = min(min(d, 24-d), ss)
            s = max(s, ss)

    return s

print(main())
