Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

3
7 12 8

Sample Output 1

4

For example, consider the situation where it is 7, 12 and 16 o'clock in each person's city at the moment when it is 0 o'clock in Takahashi's city. In this case, the time gap between the second and third persons' cities is 4 hours.

Sample Input 2

2
11 11

Sample Output 2

2

Sample Input 3

1
0

Sample Output 3

0

Note that Takahashi himself is also a participant.

Solution in Julia (0.5.0) (judge verdict: Accepted)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function moveup(x::Array{Int,1},n)
	k = length(x)
	for i in 1:k-1
		if x[k-i+1] > n-1
			x[k-i] += div(x[k-i+1],n)
			x[k-i+1] = x[k-i+1]%n
		end
	end
	if x[1] > n-1
		0
	else
		x
	end
end

function main()
	n = readline() |> parseInt
	d = readline() |> split |> parseMap
	z = zeros(Int,13)
	for i in 1:n
		z[d[i]+1]+=1
	end
	f = z[1]
	for i in 2:13
		if z[i]>2
			f = 1
		end
	end
	if f>0
		println(0)
	else
		a = Int[]
		base = zeros(Int,24)
		base[1] = 1
		for i in 1:12
			if z[i+1]==1
				push!(a,i)
			elseif z[i+1]>1
				base[i+1]+=1
				base[25-i]+=1
			end
		end
		l = length(a)
		z = zeros(Int,l)
		q = 0
		while z!=0
			c = copy(base)
			for i in 1:l
				if z[i]==0
					c[a[i]+1]+=1
				else
					c[25-a[i]]+=1
				end
			end
			dis = 24
			nd = 1
			for i in 2:24
				if c[i]>1
					dis = 0
				elseif c[i]==1
					dis = min(dis,nd)
					nd = 1
				else
					nd += 1
				end
			end
			if c[1]>1
				dis = 0
			elseif c[1]==1
				dis = min(dis,nd)
				nd = 1
			end
			q = max(q,dis)
			if isempty(z)
				z=0
			else
				z[l]+=1
				z=moveup(z,2)
			end
		end
		println(q)
	end
end

main()