#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr,) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => (read_value!($next, usize) - 1); ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); read_value!($next, [$t; len]) }}; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } /// Generates an Iterator over subsets of univ, in the descending order. /// Verified by: http://judge.u-aizu.ac.jp/onlinejudge/review.jsp?rid=3050308 struct SubsetIter { bits: Option, univ: usize } impl Iterator for SubsetIter { type Item = usize; fn next(&mut self) -> Option { match self.bits { None => None, Some(bits) => { let ans = bits; self.bits = if bits == 0 { None } else { Some((bits - 1) & self.univ) }; Some(ans) } } } } fn subsets(univ: usize) -> SubsetIter { SubsetIter { bits: Some(univ), univ: univ } } const MOD: i64 = 998_244_353; // m <= 7 なので 3^m <= 2187 fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); } fn solve() { input! { n: usize, a: [usize; n], } const W: usize = 1_000_001; let mut fac = vec![vec![]; W]; for i in 2..W { if !fac[i].is_empty() { continue; } for j in 1..(W - 1) / i + 1 { fac[i * j].push(i); } } let mut dp = vec![0; W]; for a in a { let f = &fac[a]; let m = f.len(); let mut tot = 0; for bits in 1usize..1 << m { let mut prod = 1; for i in 0..m { if (bits & 1 << i) != 0 { prod *= f[i]; } } if bits.count_ones() % 2 == 0 { tot = tot + MOD - dp[prod]; } else { tot += dp[prod]; } if tot >= MOD { tot -= MOD; } } for bits in 0..1 << m { let mut prod = 1; for i in 0..m { if (bits & 1 << i) != 0 { prod *= f[i]; } } dp[prod] = (dp[prod] + tot + 1) % MOD; } } let mut tot = 0; for i in (1..W).rev() { for j in 2..(W - 1) / i + 1 { dp[i] += MOD - dp[i * j]; if dp[i] >= MOD { dp[i] -= MOD; } } tot += dp[i]; if tot >= MOD { tot -= MOD; } } println!("{}", tot); }