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, input()))
l = [0] * (n - 1)
for i in range(n - 1):
    l[i] = abs(a[i + 1] - a[i])
n -= 1
if 1 in l:
    for i in range(n):
        if l[i] == 2:
            l[i] = 0
ans = 0
for i, x in enumerate(l):
    if not (i ^ (n - 1)) & i:
        ans ^= x
print(ans)