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(d) for d in input().split()]
# N = 5
# D = [3, 5, 7, 9, 12]
counts = [0] * 13

if 0 in D or D.count(12) > 1:
    print(0)
    sys.exit()

for i in range(N):
    if D[i] > 12:
        D[i] = 24 - D[i]
D.append(0)

for d in D:
    counts[d] += 1

E = []
F = []
for idx, count in enumerate(counts):
    if count > 2:
        print(0)
        sys.exit()
    elif count == 2:
        E.append(idx)
        E.append(24 - idx)
    elif idx == 0 or (idx == 12 and count > 0):
        E.append(idx)
    elif count == 1:
        F.append(idx)

max_val = 0


def update(arr):
    global max_val
    min_val = 24
    arr.sort()
    for i in range(1, len(arr)):
        if arr[i] - arr[i - 1] < min_val:
            min_val = arr[i] - arr[i - 1]
    if 24 - arr[-1] < min_val:
        min_val = 24 - arr[-1]
    if min_val > max_val:
        max_val = min_val

for i in range(2 ** len(F)):
    G = [0] * len(F)
    for j in range(len(F)):
        if i & (2 ** j):
            G[j] = 24 - F[j]
        else:
            G[j] = F[j]
    update(E + G)

print(max_val)
