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 comb(n, r):
  return n == ( r | (n - r) ) 
  
N=int(input())
S=input()
x=0;
b=1;
for i in range(N):
  s=int(S[i])%2;
  x=(x+s*(comb(N-1,i)))%2;
  b*=s%2;
if(x%2 or b==0):
  print(x%2);exit();
x=0;
for i in range(N):
  s=(int(S[i])//2)%2;
  x=(x+s*(comb(N-1,i)))%2;

print((x%2)*2);