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)

#[macro_use]
mod input_mcr {
    // ref: tanakh <https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8>
    // diff: using Parser
    #[macro_export(local_inner_macros)]
    macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut parser = Parser::from_str($s);
        input_inner!{parser, $($r)*}
    };
    (parser = $parser:ident, $($r:tt)*) => {
        input_inner!{$parser, $($r)*}
    };
    (new_stdin_parser = $parser:ident, $($r:tt)*) => {
        let stdin = std::io::stdin();
        let reader = std::io::BufReader::new(stdin.lock());
        let mut $parser = Parser::new(reader);
        input_inner!{$parser, $($r)*}
    };
    ($($r:tt)*) => {
        input!{new_stdin_parser = parser, $($r)*}
    };
}

    #[macro_export(local_inner_macros)]
    macro_rules! input_inner {
    ($parser:ident) => {};
    ($parser:ident, ) => {};
    ($parser:ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($parser, $t);
        input_inner!{$parser $($r)*}
    };
}

    #[macro_export(local_inner_macros)]
    macro_rules! read_value {
    ($parser:ident, ( $($t:tt),* )) => {
        ( $(read_value!($parser, $t)),* )
    };
    ($parser:ident, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($parser, $t)).collect::<Vec<_>>()
    };
    ($parser:ident, chars) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()
    };
    ($parser:ident, char_) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()[0]
    };
    ($parser:ident, usize1) => {
        read_value!($parser, usize) - 1
    };
    ($parser:ident, line) => {
        $parser.next_line()
    };
    ($parser:ident, line_) => {
        $parser.next_line().chars().collect::<Vec<char>>()
    };
    ($parser:ident, i64_) => {
        $parser.fast_i64()
    };
    ($parser:ident, usize_) => {
        $parser.fast_i64() as usize
    };
    ($parser:ident, usize1_) => {
        ($parser.fast_i64() - 1) as usize
    };
    ($parser:ident, $t:ty) => {
        $parser.next::<$t>().expect("Parse error")
    };
}

    use std::io;
    use std::io::BufRead;
    use std::str;

    // ref: tatsuya6502 <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e>
    // ref: wariuni <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e#comment-7040a5ae96305e884eb9>
    // diff: using std::io::BufRead::fill_buf()
    pub struct Parser<R> {
        pub reader: R,
        buf: Vec<u8>,
        pos: usize,
    }

    impl Parser<io::Empty> {
        pub fn from_str(s: &str) -> Parser<io::Empty> {
            Parser {
                reader: io::empty(),
                buf: s.as_bytes().to_vec(),
                pos: 0,
            }
        }
    }

    impl<R: BufRead> Parser<R> {
        pub fn new(reader: R) -> Parser<R> {
            Parser {
                reader: reader,
                buf: vec![],
                pos: 0,
            }
        }
        pub fn update_buf(&mut self) {
            self.buf.clear();
            self.pos = 0;
            loop {
                let (len, complete) = {
                    let buf2 = self.reader.fill_buf().unwrap();
                    self.buf.extend_from_slice(buf2);
                    let len = buf2.len();
                    (len, buf2[len - 1] <= 0x20)
                };
                self.reader.consume(len);
                if complete {
                    break;
                }
            }
        }
        pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
            loop {
                let mut begin = self.pos;
                while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                    begin += 1;
                }
                let mut end = begin;
                while end < self.buf.len() && (self.buf[end] > 0x20) {
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.parse::<T>();
                } else {
                    self.update_buf();
                }
            }
        }
        pub fn next_line(&mut self) -> String {
            loop {
                let mut begin = self.pos;
                if begin < self.buf.len() && (self.buf[begin] < 0x20) {
                    begin += 1;
                }
                let mut end = begin;
                while end < self.buf.len() && (self.buf[end] >= 0x20) {
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.to_string();
                } else {
                    self.update_buf();
                }
            }
        }
        pub fn fast_i64(&mut self) -> i64 {
            loop {
                let mut begin = self.pos;
                while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                    begin += 1;
                }
                if begin == self.buf.len() {
                    self.update_buf();
                    continue;
                }
                let mut res = 0;
                let (is_positive, mut end) = match self.buf[begin] {
                    b'+' => (true, begin + 1),
                    b'-' => (false, begin + 1),
                    _ => (true, begin),
                };
                while end < self.buf.len() && (self.buf[end] > 0x20) {
                    res = res * 10 + (self.buf[end] as i64 - '0' as i64);
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return if is_positive { res } else { -res };
                } else {
                    self.update_buf();
                }
            }
        }
    }
}

use input_mcr::*;
use std::cmp::*;

fn f(xs: &Vec<i64>) -> i64 {
    let mut xs = xs.clone();
    while xs.len() != 1 {
        let mut ys = vec![];
        for i in 1..xs.len() {
            ys.push((xs[i] - xs[i - 1]).abs());
        }
        xs = ys;
    }
    xs[0]
}

fn g(xs: &Vec<i64>, facts: &Vec<(i64, i64)>) -> i64 {
    //let mut xs = xs.clone();
    //xs.sort();
    let n = xs.len();
    let nCr = |n: usize, r: usize| {
        let pow2 = facts[n].1 - facts[n - r].1 - facts[r].1;
        let x = facts[n].0 * facts[n - r].0 * facts[r].0;
        // // eprintln!("pow2 = {}, x = {}", pow2, x);
        2i64.pow(min(2, pow2) as u32) * x % 4
    };
    let mut res = 0;
    for i in 0..n {
        let v = xs[i];
        let a = nCr(n - 1, i);
        //// eprintln!("i = {}, v = {}, a = {}", i, v, a);
        if (n - i) % 2 == 0 {
            res = (res - v * a + 400000) % 4;
        } else {
            res = (res + v * a + 400000) % 4;
        }
    }
    res
}

fn g2(xs: &Vec<i64>) -> i64 {
    let original_len = xs.len();
    let mut xs = xs.clone();
    while xs.len() == original_len || xs.len() % 2 == 0 {
        let mut ys = vec![];
        for i in 1..xs.len() {
            ys.push((xs[i] - xs[i - 1]).abs());
        }
        xs = ys;
    }
    let x = xs[0];
    let y = xs[xs.len() - 1];
    if xs.iter().all(|&x| x == 0 || x == 2) && (x + y == 2) {
        return 2;
    }
    if x == y || x + y == 2 {
        0
    } else {
        1
    }
}

fn main() {
    input! {
        n: usize,
        s: chars,
    }
    let mut xs = vec![];
    for &c in &s {
        let v = c as i64 - '0' as i64;
        xs.push(v);
    }
    let res = g2(&xs);
    println!("{}", res);

    return;

    /*
    // (x.0 mod 4) * 2^(x.1)
    let mut facts: Vec<(i64,i64)> = vec![(1,0)];
    for i in 1..3_000_000 {
        let mut res = facts[i-1];
        let mut x = i as i64;
        while x % 2 == 0 {
            res.1 += 1;
            x /= 2;
        }
        res.0 = (res.0 * x) % 4;
        facts.push(res);
    }
    // eprintln!("facts = {:?}", &facts[0..10]);

    use gentest_vec::*;
    let tests = gen_all_vec(5, 1, 4);
    let mut count = vec![0; 4];
    for test in &tests {
        let rg = g2(test, &facts);
        let rf = f(test);
        let mut test2 = test.clone();
        //test2.sort();

        //let rf2 = f(&test2);

        // // eprintln!("test = {:?}, expected = {}", test, rf);
        count[rf as usize] += 1;
        //if rf != rf2 {
        //    // eprintln!("test = {:?}, rf = {}, rf2 = {}", test, rf, rf2);
        //}
        if rf != rg {
            // eprintln!("error: test = {:?}, res = {}, expected = {}", test, rg, rf);
        }
    }
    // eprintln!("count = {:?}", count);

    return;
    input! {
        n: usize,
        s: chars,
    }


    // (x.0 mod 4) * 2^(x.1)
    let mut facts: Vec<(i64,i64)> = vec![(1,0)];
    for i in 1..3_000_000 {
        let mut res = facts[i-1];
        let mut x = i as i64;
        while x % 2 == 0 {
            res.1 += 1;
            x /= 2;
        }
        res.0 = (res.0 * x) % 4;
        facts.push(res);
    }
    // eprintln!("facts = {:?}", &facts[0..10]);
    let nCr = |n: usize, r: usize| {
        let pow2 = facts[n].1 - facts[n-r].1 - facts[r].1;
        let x = facts[n].0 * facts[n-r].0 * facts[r].0;
        // // eprintln!("pow2 = {}, x = {}", pow2, x);
        2i64.pow(min(2, pow2) as u32) * x % 4
    };
    // eprintln!("3C1 = {}", nCr(3,1));
    // return;
    for i in 0..10 {
        for j in 0..i+1 {
            // eprint!("{} ", nCr(i,j));
        }
        // eprintln!();
    }
    let mut res = 0;
    for i in 0..n {
        let v = s[i] as i64 - '0' as i64;
        let a = nCr(n-1, i);
        if (n - i) % 2 == 0 {
            res = (res + v * a + 400000) % 4;
        }
        else {
            res = (res - v * a + 400000) % 4;
        }
    }
    println!("{}", res);
    */
}