fn gcd(mut a: u64, mut b: u64) -> u64 { while b > 0 { let r = a % b; a = b; b = r; } a } fn pow_mod(r: u64, mut n: u64, m: u32) -> u64 { assert!(m > 0); if m == 1 { return 0; } let m = m as u64; let mut t = 1; let mut s = r % m; while n > 0 { if n & 1 == 1 { t = t * s % m; } s = s * s % m; n >>= 1; } t } fn factorize(mut n: u64) -> Vec<(u64, u32)> { let mut res = vec![]; for &p in [2, 3].iter() { let mut c = 0; while n % p == 0 { c += 1; n /= p; } if c > 0 { res.push((p, c)); } } let mut k = 5; let mut add = 2; while k * k <= n { let mut c = 0; while n % k == 0 { n /= k; c += 1; } if c > 0 { res.push((k, c)); } k += add; add ^= 6; } if n > 1 { res.push((n, 1)); } res } fn divisor(mut n: u64) -> Vec { let f = factorize(n); let mut res = Vec::with_capacity(f.iter().fold(1, |s, p| s * (p.1 + 1)) as usize); res.push(1); for (p, c) in f { let len = res.len(); let mut mul = 1; for i in 1..=c { mul *= p; for j in 0..len { let v = res[j] * mul; res.push(v); } } res.sort(); } res } fn is_prime(n: u64) -> bool { n > 1 && (2u64..).take_while(|p| p * p <= n).all(|p| n % p != 0) } // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- use std::io::Write; fn run() { input! { q: usize, ask: [usize; q], } let n = *ask.iter().max().unwrap(); let mut ans = vec![vec![]; n + 1]; let mut val = (0..=n).map(|p| p * p + 1).collect::>(); for i in 1..=n { let p = val[i]; if p > 1 { for s in [i, p - i].iter() { let mut j = *s; while j <= n { while val[j] % p == 0 { ans[j].push(p); val[j] /= p; } j += p; } } } } let out = std::io::stdout(); let mut out = std::io::BufWriter::new(out.lock()); for x in ask { let mut s = String::new(); ans[x].sort(); for p in ans[x].iter() { s.push_str(&format!("{} ", *p)); } s.pop(); writeln!(out, "{}", s).ok(); } } fn main() { run(); }