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.chomp.to_i
x = Array.new(N,0)
str = gets.chomp
for i in 0...N do
    x[i] = str[i].to_i
end

y = Array.new(0)
m = N-1
l = 1
while m > 0
    if m%2 == 1
        y.push(l)
    end
    l *= 2
    m /= 2
end

z = Array.new(1,0)
while !y.empty?
    a = y.pop
    b = z.size
    for i in 0...b do
        z.push(z[i]+a)
    end
end

w = Array.new(0)
for i in 0...z.size do
    a = z[i]
    w.push(x[a])
end

while w.size > 1
    a = w.size
    b = a/2
    for i in 0...b do
        j = i*2
        w[i] = (w[j+1] - w[j]).abs
    end
    for i in 0...b do
        w.pop
    end
end
puts w[0]