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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
def main():
    input = sys.stdin.readline
    N = int(input())
    iS = input().rstrip()

    S = []
    for i in range(N-1):
        S.append(abs(int(iS[i])-int(iS[i+1])))
    N -= 1

    f = FactorialUtils(N)
    n1 = n2 = 0
    for i in range(N):
        t = f.choose(N-1,i)
        #print(t,S[i])
        if S[i] == 1: n1 += t
        elif S[i] == 2: n2 += t
    if n1&1 and n2&1: print(1)
    elif n1&1: print(1)
    elif n2&1 and n1==0: print(2)
    else: print(0)
    #print(n1,n2)

class FactorialUtils:
    def __init__(self, n):
        self.fac = [1] * (n+1)
        for i in range(2, n+1): self.fac[i] = self.fac[i-1] + (i&(-i)).bit_length()

    def choose(self, n, r):
        if r < 0 or r > n: return 0
        return 2 if (self.fac[n] - self.fac[n-r] - self.fac[r]) > 0 else 1

if __name__ == '__main__':
    main()