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
N=int(input())
from collections import defaultdict
data=defaultdict(int)
data[0]+=1
for d in map(int,input().split()):
    data[d]+=1
check=[[]]
ans=1
for d in data.keys():
    if data[d]>2:
        ans=0
        break
    checkc=check.copy()
    if data[d]==2:
        if d==0 or d==12:
            ans=0
            break
        for c in check:
            c+=[d,-1*d]
    elif data[d]==1:
        if d==0:
            for c in check:
                c.append(d)
            continue
        check=[]
        for c in checkc:
            check.append(c+[d])
            check.append(c+[-1*d])
if ans!=0:
    ans=0
    for c in check:
        c.sort()
        now=24
        for i in range(len(c)):
            now=min(now,(c[i]-c[i-1])%24)
        ans=max(now,ans)
print(ans)