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)

#!/usr/bin/env python3
import sys
import random
input = sys.stdin.readline

n = int(input())
s = input().rstrip()
a = [int(ch) for ch in s]
# a = [random.randrange(0,3) for _ in range(12)]

def naive(a):
    c = a[:]
    while len(c) > 1:
        b = []
        for c1, c2 in zip(c, c[1:]):
            b.append(abs(c1 - c2))
        c = b[:]
    return c[0]

def solve(a):
    c = a[:]
    while len(c) > 1:
        b = []
        if len(c) % 2 == 0:
            for c1, c2 in zip(c[::2], c[1::2]):
                b.append(abs(c1 - c2))
        else:
            for c1, c2 in zip(c, c[1:]):
                b.append(abs(c1 - c2))
        c = b[:]
    return c[0]

b = []
for a1, a2 in zip(a, a[1:]):
    b.append(abs(a1 - a2))
if 1 not in b:
    tmp = []
    for item in b:
        if item == 2:
            tmp.append(1)
        else:
            tmp.append(0)
    ret = solve(tmp)
    if ret == 1:
        print(2)
    else:
        print(0)
else:
    tmp = []
    for item in b:
        if item == 2:
            tmp.append(0)
        else:
            tmp.append(item)
    ret = solve(tmp)
    print(ret)