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:
n=int(input())
def f(n,r):
    return n==r|(n-r)
s=list(map(int,list(input())))
b=[]
for i in range(n-1):b.append(abs(s[i]-s[i+1]))
if (0 in b and len(set(b))==2) or len(set(b))==1:
    ans=0
    anss=0
    for i in range(n-1):
        if b[i]:
            anss=b[i]
            ans+=f(n-2,i)
    if ans%2==0:
        print(0)
    else:
        print(anss)
    quit()
ans=0
for i in range(n-1):
    if b[i]%2==1:
        anss=b[i]
        ans+=f(n-2,i)
if ans%2==0:
    print(0)
else:
    print(1)