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:
def ord(N,n):#N,nは正の整数、Nで割り切れる回数、許容はN^1000
    if n%N!=0:
        return 0
    else:
        return 1+ord(N,n//N)

N=int(input())
A=input()
A=[int(A[i]) for i in range(0,N)]
X=[abs(A[i]-A[i+1]) for i in range(0,N-1)]


cmb=[0 for i in range(0,N-1)]
cmb[0]=0
for i in range(1,N-1):
    cmb[i]=cmb[i-1]+ord(2,N-2-(i-1))-ord(2,i)
data=[0 for i in range(0,N-1)]
for i in range(0,N-1):
    if cmb[i]>0:
        data[i]=0
    else:
        data[i]=1

s=0
for i in range(0,N-1):
    s=(s+X[i]*data[i])%2
if s==1:
    print(1)
else:
    if 1 in X:
        print(0)
    else:
        X=[X[i]//2 for i in range(0,N-1)]
        s=0
        for i in range(0,N-1):
            s=(s+X[i]*data[i])%2
        if s==1:
            print(2)
        else:
            print(0)