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 (3.4.3) (judge verdict: Wrong Answer)

def calc(P):
    #Pはリスト
    Q=[]
    for str in A:
        if str=="1":
            pass
        elif str=="2":
            Q.append("1")
        else:
            Q.append("2")
    return Q

def solve(P):
    #Pはリスト
    N=len(P)
    if N>1:
        Q=[]
        for i in range(N-1):
            if   abs( int(P[i])-int(P[i+1]) )==0:
                pass
            elif abs( int(P[i])-int(P[i+1]) )==1:
                Q.append("1")
            else:
                Q.append("2")
        return solve(Q)
    elif N==0:
    	return(0)
    else:
        return P[0]

N=int(input())
A=input()
B=list(A)

#print(A)
#print(B) 
short=calc(B)
#print(short)

ans=solve(short)
print(ans)