Problem:
Score : 500 points

Problem Statement

Alice and Brown loves games. Today, they will play the following game.

In this game, there are two piles initially consisting of X and Y stones, respectively.
Alice and Bob alternately perform the following operation, starting from Alice:

Take 2i stones from one of the piles. Then, throw away i of them, and put the remaining i in the other pile. Here, the integer i (1≤i) can be freely chosen as long as there is a sufficient number of stones in the pile.

The player who becomes unable to perform the operation, loses the game.

Given X and Y, determine the winner of the game, assuming that both players play optimally.

Constraints

0 ≤ X, Y ≤ 10^{18}

Input

Input is given from Standard Input in the following format:

X Y

Output

Print the winner: either Alice or Brown.

Sample Input 1

2 1

Sample Output 1

Brown

Alice can do nothing but taking two stones from the pile containing two stones. As a result, the piles consist of zero and two stones, respectively. Then, Brown will take the two stones, and the piles will consist of one and zero stones, respectively. Alice will be unable to perform the operation anymore, which means Brown's victory.

Sample Input 2

5 0

Sample Output 2

Alice

Sample Input 3

0 0

Sample Output 3

Brown

Sample Input 4

4 8

Sample Output 4

Alice

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::collections::{BTreeMap, BTreeSet};
fn main() {
    let mut sc = Scanner::new();
    let x: u64 = sc.read();
    let y: u64 = sc.read();
    let (x, y) = if x > y { (y, x) } else { (x, y) };
    println!("{}", if y - x <= 1 { "Brown" } else { "Alice" });
    // exp();
}

fn exp() {
    let mut map = BTreeMap::new();
    map.insert((0, 0), 0);
    map.insert((0, 1), 0);
    map.insert((1, 1), 0);

    for i in 0..1000 {
        for j in i..1000 {
            grundy(i, j, &mut map);
        }
    }
}

fn grundy(x: usize, y: usize, map: &mut BTreeMap<(usize, usize), usize>) -> usize {
    let (x, y) = if x > y { (y, x) } else { (x, y) };

    if map.contains_key(&(x, y)) {
        return map[&(x, y)];
    }

    let mut grundy_nums = BTreeSet::new();
    for x_to_y in 1..(x / 2 + 1) {
        let next_x = x - x_to_y * 2;
        let next_y = y + x_to_y;
        grundy_nums.insert(grundy(next_x, next_y, map));
    }
    for y_to_x in 1..(y / 2 + 1) {
        let next_x = x + y_to_x;
        let next_y = y - y_to_x * 2;
        grundy_nums.insert(grundy(next_x, next_y, map));
    }

    let mut g = 0;
    loop {
        if !grundy_nums.contains(&g) {
            map.insert((x, y), g);
            if g == 0 {
                println!("{} {}", x, y);
            }
            return g;
        }
        g += 1;
    }
}

struct Scanner {
    ptr: usize,
    length: usize,
    buf: Vec<u8>,
    small_cache: Vec<u8>,
}

impl Scanner {
    fn new() -> Scanner {
        Scanner {
            ptr: 0,
            length: 0,
            buf: vec![0; 1024],
            small_cache: vec![0; 1024],
        }
    }

    fn load(&mut self) {
        use std::io::Read;
        let mut s = std::io::stdin();
        self.length = s.read(&mut self.buf).unwrap();
    }

    fn byte(&mut self) -> u8 {
        if self.ptr >= self.length {
            self.ptr = 0;
            self.load();
            if self.length == 0 {
                self.buf[0] = b'\n';
                self.length = 1;
            }
        }

        self.ptr += 1;
        return self.buf[self.ptr - 1];
    }

    fn is_space(b: u8) -> bool {
        b == b'\n' || b == b'\r' || b == b'\t' || b == b' '
    }

    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        let mut b = self.byte();
        while Scanner::is_space(b) {
            b = self.byte();
        }

        for pos in 0..self.small_cache.len() {
            self.small_cache[pos] = b;
            b = self.byte();
            if Scanner::is_space(b) {
                return String::from_utf8_lossy(&self.small_cache[0..(pos + 1)])
                    .parse()
                    .unwrap();
            }
        }

        let mut v = self.small_cache.clone();
        while !Scanner::is_space(b) {
            v.push(b);
            b = self.byte();
        }
        return String::from_utf8_lossy(&v).parse().unwrap();
    }
}