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)

use std::io::Read;

fn run() {
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut it = s.trim().split_whitespace();
    let n: usize = it.next().unwrap().parse().unwrap();
    let mut s: Vec<usize> = it.next().unwrap().chars().map(|c| c.to_digit(10).unwrap() as usize - 1).collect();
    let mut fact = vec![0usize; n + 1];
    for i in 1..(n + 1) {
        fact[i] = fact[i - 1];
        let mut k = i;
        while k % 2 == 0 {
            fact[i] += 1;
            k /= 2;
        }
    }
    let comb = |n: usize, k: usize| -> usize {
        if fact[n] - fact[n - k] - fact[k] > 0 {
            0
        } else {
            1
        }
    };
    if s.contains(&1) {
        for c in s.iter_mut() {
            if *c == 2 {
                *c = 0;
            }
        }
    }
    let mut v = 0;
    for (i, c) in s.iter().enumerate() {
        if *c != 0 {
            v ^= (comb(n - 1, i) & 1) * *c;
        }
    }
    println!("{}", v);
}

fn main() {
    run();
}