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 copy import copy
import sys
from collections import Counter
n = int(input())
d = sorted(list(map(int, input().split())))
if d[0] == 0:
	print(0)
	sys.exit()
c = Counter(d)
if max(c.values()) >= 3:
	print(0)
	sys.exit()
if c[12] >= 2:
	print(0)
	sys.exit()

reserved = []
alternatives = []
for k, v in c.items():
	if v == 2:
		reserved.append(k)
		reserved.append(24-k)
	elif k == 12:
		reserved.append(12)
	else:
		alternatives.append(k)

m = len(alternatives)
#print(m)
ans = 0
for i in range(2**m):
	zones = copy(reserved)
	for j, a in enumerate(alternatives):
		if (i>>j)&1:
			zones.append(24-a)
		else:
			zones.append(a)
	zones.sort()
	zones = [0] + zones + [24]
	#print(zones)
	res = 24
	for j in range(len(zones)-1):
		res = min(res, zones[j+1]-zones[j])
	ans = max(ans, res)

print(ans)