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 = list(map(int, list(input())))

def mod2_pascal(n):
    res = []
    for r in range(n+1):
        res.append(1 if n == (r | (n-r)) else 0)
    return res

b = []

if N >= 3:
    for i in range(N-1):
        b.append(abs(a[i]-a[i+1]))
    mod2_line = mod2_pascal(N-2)
    ans = 0
    for i in range(N-1):
        if mod2_line[i] == 1:
            ans += b[i]
    if b.count(0) == N-1 - b.count(2):
        b_divided_by_2 = list(map(lambda x:x//2, b))
        for i in range(N - 1):
            if mod2_line[i] == 1:
                ans += b_divided_by_2[i]
        if ans%2 == 1:
            print(2)
        else:
            print(0)
    else:
        print(ans % 2)

else:
    print(abs(a[1]-a[0]))