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)

n = gets.to_i
a = gets.chomp.tr!("1-3", "0-2")

$h = {
  %w(0 0) => 0, %w(0 1) => 1, %w(0 2) => 2, 
  %w(1 0) => 1, %w(1 1) => 0, %w(1 2) => 1, 
  %w(2 0) => 2, %w(2 1) => 1, %w(2 2) => 0, 
}

def g(str)
  while str.length > 1
    str.gsub!(/^0+2/, "2")
    str.gsub!(/20+$/, "2")
#    str.gsub!(/^([12])0*/, "\\1")
#    str.gsub!(/0*([12])$/, "\\1")
    str = str.each_char.each_cons(2).map(&$h).join
  end

  return "0" if str.length == 0
  return str if str.length == 1
end

puts g(a)

load __FILE__ unless $stdin.eof?