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)

N=int(input())
a=[int(i)-1 for i in list(input())]
def solve(seq):
    if {0}==set(seq):
        return 0
    res=0
    for k in range(N):
        tmp=0
        if ((N-1)&k)==k:
            tmp=1
        #print(tmp)
        res+=tmp*seq[k]
        res%=2
    #print("#"*30)
    if res%2==1:
        return 1
    if 1 in set(seq):
        return 0
    seq2=[seq[i]//2 for i in range(N)]
    return solve(seq2)*2
print(solve(a))