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
from collections import Counter
import itertools

N = int(input())
Ds = list(map(int, input().split())) + [0]

cnt = Counter(Ds)

if max(cnt.values()) >= 3:
    print(0)
    exit()

citys = []
rest = []
for k, v in cnt.items():
    if v == 2:
        if k == 0 or k == 12:
            print(0)
            exit()
        citys.append(k)
        citys.append(24 -k)
    else:
        rest.append(k)


def check(citys):
    if len(citys) <= 1:
        return 24

    citys.sort()

    ans = 24
    prev = citys[-1] - 24
    for c in citys:
        ans = min(ans, c - prev)
        prev = c

    return ans


if check(citys) == 1:
    print(1)
    exit()

ans = 0
for ops in itertools.product('+-', repeat=len(rest)):
    citys2 = citys.copy()
    for i in range(len(rest)):
        if ops[i] == '+':
            citys2.append(rest[i])
        else:
            citys2.append(24 - rest[i])

    ans = max(ans, check(citys2))

print(ans)
