Problem: 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}.

Examples

Input

4
1231


Output

1


Input

10
2311312312


Output

0

Solution (in PYTHON3):

Solution:
import sys
input = sys.stdin.readline

N=int(input())
A=list(map(int,list(input().strip())))

def next(A):
    B=[]
    for i in range(1,len(A)):
        B.append(abs(A[i]-A[i-1]))
    return B

A=next(A)

if len(A)<=3:
    while len(A)>1:
        A=next(A)
    print(A[0])
    sys.exit()

def in2(x):
    if x==0:
        return 0
    ANS=0
    while x%2==0:
        ANS+=1
        x//=2
    return ANS


if not (1 in A):
    LEN=len(A)
    SUM=0
    COMBI=0

    for i in range(LEN):
        if COMBI==0:
            SUM+=A[i]//2

        COMBI=COMBI+in2(LEN-1-i)-in2(i+1)

    if SUM%2==1:
        print(2)
    else:
        print(0)
else:
    LEN=len(A)
    SUM=0
    COMBI=0

    for i in range(LEN):
        if COMBI==0:
            SUM+=A[i]

        COMBI=COMBI+in2(LEN-1-i)-in2(i+1)

    if SUM%2==1:
        print(1)
    else:
        print(0)