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()))
if n <= 1:
    print(a[0])
    exit()
for i in range(n - 1):
    a[i] = abs(a[i + 1] - a[i])
a.pop()
n -= 1
def bc(u, v):
    return (u & v) == v
def solve(t):
    ans = 0
    for i in range(n):
        if a[i] == 1:
            ans ^= bc(n - 1, i)
    print(ans * t)
if 1 in a:
    solve(1)
else:
    for i in range(n):
        a[i] >>= 1
    solve(2)