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: Accepted)

N = gets.to_i
a = gets.scan(/./).map{|i|i.to_i - 1}
while a.size > 1
    l = 2 ** Math.log2(a.size).floor
    s = a[0, l]
    c1 = s.count(1)
    c2 = s.count(2) % 2
    r = []
    (a.size - l + 1).times{|i|
        if c2 == 1 and c1 == 0
            r << 2
        else
            r << (c1 % 2)
        end
        case a[i]
        when 1
            c1 -= 1
        when 2
            c2 = (c2 + 1) % 2
        end
        case a[i + l]
        when 1
            c1 += 1
        when 2
            c2 = (c2 + 1) % 2
        end
    }
    a = r
end
puts a[0]