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
sys.setrecursionlimit(10**9)

N = int(input())
A = list(map(int,input()))
X = 2 in A

while len(A) > 1:
    if len(A) % 2 == 1:
        for i in range(len(A)-1):
            A[i] = abs(A[i]-A[i+1])
        A.pop()
    B = []
    for i in range(len(A)//2):
        B.append(abs(A[i*2]-A[i*2+1]))
    A = B[:]

if X:
    A[0] %= 2
print(A[0])