Problem:
Score : 700 points

Problem Statement

Given is a sequence of N digits a_1a_2\ldots a_N, where each element is 1, 2, or 3.
Let x_{i,j} defined as follows:

x_{1,j} := a_j \quad (1 \leq j \leq N)

x_{i,j} := | x_{i-1,j} - x_{i-1,j+1} | \quad (2 \leq i \leq N and 1 \leq j \leq N+1-i)

Find x_{N,1}.

Constraints

2 \leq N \leq 10^6

a_i = 1,2,3 (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N
a_1a_2\ldotsa_N

Output

Print x_{N,1}.

Sample Input 1

4
1231

Sample Output 1

1

x_{1,1},x_{1,2},x_{1,3},x_{1,4} are respectively 1,2,3,1.

x_{2,1},x_{2,2},x_{2,3} are respectively |1-2| = 1,|2-3| = 1,|3-1| = 2.

x_{3,1},x_{3,2} are respectively |1-1| = 0,|1-2| = 1.

Finally, x_{4,1} = |0-1| = 1, so the answer is 1.

Sample Input 2

10
2311312312

Sample Output 2

0

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

def bits(n)
	a = []
	until n == 0
		a << (1<<(n.bit_length-1))
		n -= a[-1]
	end
	return a
end

H = {
	'00'=>'0',
	'01'=>'1',
	'02'=>'2',
	'03'=>'3',
	'10'=>'1',
	'11'=>'0',
	'12'=>'1',
	'13'=>'2',
	'20'=>'2',
	'21'=>'1',
	'22'=>'0',
	'23'=>'1',
	'30'=>'3',
	'31'=>'2',
	'32'=>'1',
	'33'=>'0'
}
H.default_proc = lambda{|h,k|
	until 1 == len = k.size
		str = ''
		bits(len).each{|l|
			next if l == 1
			s = k[len-l, l]
			str += h[s[0,l/2] + h[s[l/2,l/2]]]
			len -= l-1
		}
		str += h[k[0,len]] if 1 < len
		k = str
	end
	k
}

gets
puts H[gets.chomp]