use std::collections::HashMap; fn main() { let n = read_input(); let factorization = factorize(n); let mut p_candidates = HashMap::new(); for (p, e) in factorization.iter() { for i in 0..=*e { let c = comb(*p as i64, i as i64); *p_candidates.entry(c).or_insert(0) += 1; } } for (p, e) in factorization.iter() { if p_candidates.contains_key(p) && *p_candidates.get(p).unwrap() == *e as usize { println!("{} {}", p, e); return; } } println!("-1 -1"); } fn read_input() -> i64 { let mut input = String::new(); std::io::stdin().read_line(&mut input).unwrap(); let n = input.trim().parse::().unwrap(); n } fn factorize(n: i64) -> HashMap { let mut factorization = HashMap::new(); let mut n = n; for i in 2.. { if n == 1 { break; } if n % i == 0 { *factorization.entry(i as i64).or_insert(0) += 1; n /= i; } } factorization } fn comb(n: i64, r: i64) -> i64 { if r > n { return 0; } let mut res = 1; for i in 0..r { res = res * (n - i) / (i + 1); } res }