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
from functools import reduce
from itertools import starmap
from operator import xor, mul
N = int(input())
A = list(map(int ,input().strip()))

A = [abs(x-y) for x,y in zip(A,A[1:])]
n = len(A)
# Lucas
coef = [((n-1)&k)==k for k in range(n)]
if 1 in A:
    B = [x % 2 for x in A]
    ans = reduce(xor, starmap(mul, zip(B,coef)))
else:
    B = [x // 2 for x in A]
    ans = reduce(xor, starmap(mul, zip(B,coef)))*2

print(ans)