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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

import sys
input = sys.stdin.readline
from functools import reduce
from itertools import starmap
from operator import xor, mul
N = int(input())
A = list(map(int ,input().strip()))

def solve(A):
    A = [abs(x-y) for x,y in zip(A,A[1:])]
    n = len(A)
    coef = 1
    for i in range(n-1):
        coef = coef ^ (coef << 1)
    coef = map(int, bin(coef)[2:])
    if 1 in A:
        B = [x % 2 for x in A]
        ans = reduce(xor, starmap(mul, zip(B,coef)))
    else:
        B = [x // 2 for x in A]
        ans = reduce(xor, starmap(mul, zip(B,coef)))*2
    return ans 

print(solve(A))