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
import sys
N=int(input())
D=[int(i) for i in input().split()]
L=[0]*13
L[0]=1
for d in D:
    L[d]+=1
for s in L:
    if s>=3:
        print(0)
        sys.exit()
if L[0]>=2 or L[12]>=2:
    print(0)
    sys.exit()
#print(L)
def check(K):
    sta=0
    #end=0
    num=10**9
    ans=10**9
    while sta<24:
        if K[sta]==1:
            ans=min(ans,num)
            num=0
        sta+=1
        num+=1
        #print(num,sta,ans)
    ans=min(num,ans)
    return ans


ans=-1
for s in range(1<<11):
    K=[0]*24
    K[0]=1
    if L[12]==1:
        K[12]=1
    for j in range(11):
        if L[j+1]==0:
            continue
        if L[j+1]==2:
            K[j+1]=1
            K[24-(j+1)]=1
            continue
        if (s&(1<<j)):
            K[j+1]=1
        else:
            K[24-(j+1)]=1
    ans=max(ans,check(K))
print(ans)