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)

# frozen_string_literal: true

N = gets.to_i
a = gets.chomp

x = a.squeeze.split('').map(&:to_i)

def tri(x, y)
  if x == 1
    case y
    when 2 then 1
    when 3 then 2
    end
  elsif x == 2
    case y
    when 1 then 1
    when 3 then 1
    end
  else
    case y
    when 1 then 2
    when 2 then 1
    end
  end
end

if x.size == 1
  puts 0
  exit
end

loop do
  y = []

  0.upto(x.size - 2) do |i|
    next if x[i] == x[i + 1]
    y << tri(x[i], x[i + 1])
  end

  x = y

  if x.size < 2
    puts(x.size == 1 ? x[0] : 0)
    exit
  end
end