Problem:
Score : 700 points

Problem Statement

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}.

Sample Input 1

4
1231

Sample Output 1

1

x_{1,1},x_{1,2},x_{1,3},x_{1,4} are respectively 1,2,3,1.

x_{2,1},x_{2,2},x_{2,3} are respectively |1-2| = 1,|2-3| = 1,|3-1| = 2.

x_{3,1},x_{3,2} are respectively |1-1| = 0,|1-2| = 1.

Finally, x_{4,1} = |0-1| = 1, so the answer is 1.

Sample Input 2

10
2311312312

Sample Output 2

0

Solution in Python (3.4.3) (judge verdict: Accepted)

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

def include_2(a):
    x = (~a) & (a >> 1)
    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 & 1

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

a = int(input(), 4)
if include_2(a):
    print(popcount_parity((~a) & s, 1))
else:
    print(popcount_parity(a & (s << 1), 2))