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: Wrong Answer)

import sys
sys.setrecursionlimit(4100000)
N= int(input())
an=  [int(x) for x in list(input())]

#print(an)
#print(len(an))

#if len(an)==1:
#    print(an[0])
#    exit()

ans_array=[]
def calc(prm):
    global ans_array
    bn=[]
    hasZero=False
    hasOne=False
    hasTwo=False
    threeKind = False
    for i in range(len(prm)-1):
        b = abs(prm[i]-prm[i+1])
        if b==0:
            hasZero=True
        elif b==1:
            hasOne=True
        else:
            hasTwo=True
        bn.append(b)
    if len(bn)==1:
        #print("要素数が1だよ")
        #print(bn)
        ans_array=bn
        return
    elif hasZero and hasOne and hasTwo:
        threeKind=True
        #print("3種類あるよ")
        #print(bn)
        calc(bn)
    else:
        #print("2種類以下だよ")
        #print(bn)
        ans_array=bn
        return
calc(an)

if len(ans_array)==1:
    print(ans_array[0])
else:
    appears=[]
    num_zero = ans_array.count(0)
    num_one = ans_array.count(1)
    num_two = ans_array.count(2)
    appears.append(num_one)
    appears.append(num_zero)
    appears.append(num_two)
    appears.sort()
    minor = appears[1]
    if (len(ans_array)%2==0) and (minor%2==0):
        print(0)
    elif (len(ans_array)%2==1) and (minor%2==1):
        print(0)
    else:
        if num_zero==0:
            print(1)
        elif num_one==0:
            print(2)
        else:
            print(1)