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:
def popcount_parity(x, a):
    x ^= x >> 2
    x ^= x >> 4
    x ^= x >> 8
    x ^= x >> 16
    x ^= x >> 32
    x ^= x >> 64
    x ^= x >> 128
    x ^= x >> 256
    x ^= x >> 512
    x ^= x >> 1024
    x ^= x >> 2048
    x ^= x >> 4096
    x ^= x >> 8192
    x ^= x >> 16384
    x ^= x >> 32768
    x ^= x >> 65536
    x ^= x >> 131072
    x ^= x >> 262144
    x ^= x >> 524288
    x ^= x >> 1048576
    return x & a

N = int(input()) - 1 << 1
s = 1
while N:
    l = N & -N
    s |= s << l
    N ^= l

A = input()
if "2" in A:
    a = ~int(A, 4)
    print(popcount_parity(a & s, 1))
else:
    a = int(A, 4)
    print(popcount_parity(a & (s << 1), 2))