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 Rust (1.15.1) (judge verdict: Accepted)

fn count2(x: usize) -> i32 {
    let mut i = x;
    let mut ret = 0;
    while i % 2 == 0 && i > 0 {
        i /= 2;
        ret += 1;
    }
    ret
}

fn main() {
    let mut fac = vec![0; 1000002];
    for i in 0..(fac.len() - 1) {
        fac[i + 1] = fac[i] + count2(i + 1);
    }
    fn comb_mod2(fac: &Vec<i32>, i: usize, j: usize) -> u8 {
        if fac[i] - fac[j] - fac[i - j] > 0 {
            0
        } else {
            1
        }
    }
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    let mut b = line.trim().as_bytes();
    let mut a = vec![0; b.len()];
    for i in 0..a.len() {
        a[i] = b[i] - 0x31;
    }
    let mut coeff = 1;
    if a.iter().all(|&x| x != 1) {
        for num in &mut a {
            *num /= 2;
        }
        coeff = 2;
    } else {
        for num in &mut a {
            *num %= 2;
        }
    }
    let mut ret = 0;
    for i in 0..a.len() {
        ret = (ret + comb_mod2(&fac, a.len() - 1, i) * a[i]) % 2;
    }
    println!("{}", ret * coeff);
}