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 sys

N = int(input())
ds = list(map(int,input().split()))
ctr = Counter(ds)
if 0 in ctr:
    print(0)
    sys.exit()

hs = (1 << 24) + 1
undef = []
for d,c in ctr.items():
    if c > 2:
        print(0)
        sys.exit()
    elif c == 2:
        hs |= (1 << d)
        hs |= (1 << (24-d))
    else: #c == 1
        undef.append(d)

ans = 0
for i in range(2**len(undef)):
    _hs = hs
    for j,u in enumerate(undef):
        if (i >> j) & 1:
            _hs |= (1 << u)
        else:
            _hs |= (1 << (24-u))
    min_interval = 24
    prev = 0
    for k in range(1,25):
        if (_hs >> k) & 1 == 0: continue
        min_interval = min(min_interval, k - prev)
        prev = k
    ans = max(ans, min_interval)
print(ans)
