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(lambda x:int(x)-1,input()))
ans = 0
for i in range(n):
    if (n-1) & i == i:
        ans += a[i]
if ans % 2 == 1:
    print(1)
else:
    if a.count(1) != 0:
        print(0)
    else:
        ans = 0
        b = list(map(lambda x:x//2,a))
        for i in range(n):
            if (n-1) & i == i:
                ans += b[i]
        if ans % 2 == 1:
            print(2)
        else:
            print(0)