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: Wrong Answer)

use std::io;
use std::str::FromStr;

fn input<T:FromStr>() -> T {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    line.trim().parse().ok().unwrap()
}

fn xor(n: i32, m: i32) -> i32 {
    if n == m {
        return 0;
    } else {
        return 1;
    }
}

fn main() {
    let n: String = input();
    let n: usize = n.parse().unwrap();
    let a_vec: String = input();
    let a_vec: Vec<char> = a_vec.chars().collect();
    let mut a_vec_num: Vec<i32> = Vec::new();
    for a in a_vec {
        a_vec_num.push(a as i32 - 48);
    }
    let mut b_vec: Vec<i32> = Vec::new();
    for i in 0..(n-1) {
        b_vec.push((a_vec_num[i] - a_vec_num[i+1]).abs());
    }
    if n == 2 {
        println!("{}", b_vec[0]);
        return;
    }

    let mut c_vec: Vec<i32> = Vec::new();
    for i in 0..(n-2) {
        c_vec.push((b_vec[i] - b_vec[i+1]).abs());
    }

    if n - 2 == 2 {
        println!("{}", xor(c_vec[0], c_vec[1]));
        return;
    }

    if n % 2 == 0 {
        let buf = c_vec[0];
        c_vec.remove(0);
        let num = xor(c_vec[0], c_vec[c_vec.len() - 1]);
        println!("{}", xor(buf, num));
    } else {
        println!("{}", xor(c_vec[0], c_vec[c_vec.len() - 1]));
    }
}