fn main() { let _n = { let mut line = String::new(); std::io::stdin().read_line(&mut line).unwrap(); line.trim().parse::().unwrap() }; let mm: Vec<_> = { let mut line = String::new(); std::io::stdin().read_line(&mut line).unwrap(); line.split_whitespace() .map(|x| x.parse::().unwrap()) .collect() }; let mut xor = 0; for m in mm { for (_, exp) in prime_factorization(m) { xor ^= exp % 3; } } println!("{}", if xor != 0 { "Alice" } else { "Bob" }); } /// Performs prime factorization of `n`. /// /// The result of the prime factorization is returned as a /// list of prime factor and exponent pairs. /// /// # Examples /// /// ``` /// assert_eq!(prime_factorization(1), vec![]); /// assert_eq!(prime_factorization(12), vec![(2, 2), (3, 1)]); /// assert_eq!(prime_factorization(19), vec![(19, 1)]); /// assert_eq!(prime_factorization(27), vec![(3, 3)]); /// ``` pub fn prime_factorization(n: usize) -> Vec<(usize, usize)> { assert_ne!(n, 0, "`n` must be at least 1."); let mut factors = vec![]; let mut t = n; for p in 2.. { if p * p > t { break; } let mut e = 0; while t % p == 0 { t /= p; e += 1; } if e != 0 { factors.push((p, e)); } } if t != 1 { factors.push((t, 1)); } factors }