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())
a=[int(i)-1 for i in list(input())]
def solve(seq):
    if {0}==set(seq):
        return 0
    res=0
    for k in range(N):
        tmp=0
        if ((N-1)&k)==k:
            tmp=1
        #print(tmp)
        res+=tmp*seq[k]
        res%=2
    #print("#"*30)
    if res%2==1:
        return 1
    if 1 in set(seq):
        return 0
    seq2=[seq[i]//2 for i in range(N)]
    return solve(seq2)*2
print(solve(a))