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: Time Limit Exceeded)

N = gets.to_i
ary = gets.split("").map(&:to_i)
mtx = Array.new(N){Array.new()}

mtx[0] = ary

if N == 2
    if ary[0] <= ary[1]
        puts ary[1] - ary[0]
    else
        puts ary[0] - ary[1]
    end
else
    (N - 1).times do |j|
        (N - j - 1).times  do |i|
            if mtx[j][i] <= mtx[j][i + 1]
                mtx[j + 1] <<  mtx[j][i + 1] -  mtx[j][i]
            else
                mtx[j + 1] << mtx[j][i] -  mtx[j][i + 1]
            end
        end
    end
    puts mtx[N - 1]
end