use std::io::Write; use std::collections::*; type Map = BTreeMap; type Set = BTreeSet; type Deque = VecDeque; fn main() { input! { n: usize, a: [usize; n], } let m = 5000; let src = 0; let dst = m + 1; let sieve = Sieve::new(m); let mut g = maxflow::Graph::new(dst + 1); for i in 1..=m { let mut j = i; while let Some(p) = sieve.factor(j) { g.add_edge(i, i / p, n as i32); while j % p == 0 { j /= p; } } } for a in a { g.add_edge(src, a, 1); } let mut ans = 0; loop { g.add_edge(ans + 1, dst, 1); if g.flow(src, dst) == 0 { break; } ans += 1; } println!("{}", ans); } // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 #[macro_export] 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_export] 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_export] 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 ---------- // --------- end sieve ---------- pub struct Sieve { size: usize, factor: Vec, } impl Sieve { pub fn new(size: usize) -> Sieve { let mut factor = (0..(size + 1)).collect::>(); for i in (2..).take_while(|p| p * p <= size) { if i == factor[i] { for j in i..(size / i + 1) { factor[j * i] = i; } } } Sieve { size: size, factor: factor, } } pub fn factor(&self, n: usize) -> Option { assert!(n <= self.size); if n == 1 { None } else { Some(self.factor[n]) } } pub fn factorize(&self, mut n: usize, res: &mut Vec) { assert!(n <= self.size); res.clear(); res.push(1); while let Some(p) = self.factor(n) { let len = res.len(); while n % p == 0 { n /= p; for _ in 0..len { let v = res[res.len() - len] * p; res.push(v); } } } } } // --------- end sieve ---------- // ---------- begin max flow (Dinic) ---------- mod maxflow { pub trait MaxFlowCapacity: Copy + Ord + std::ops::Add + std::ops::Sub { fn zero() -> Self; fn inf() -> Self; } macro_rules! impl_primitive_integer_capacity { ($x:ty, $y:expr) => { impl MaxFlowCapacity for $x { fn zero() -> Self { 0 } fn inf() -> Self { $y } } }; } impl_primitive_integer_capacity!(u32, std::u32::MAX); impl_primitive_integer_capacity!(u64, std::u64::MAX); impl_primitive_integer_capacity!(i32, std::i32::MAX); impl_primitive_integer_capacity!(i64, std::i64::MAX); #[derive(Clone)] struct Edge { to_: u32, inv_: u32, cap_: Cap, } impl Edge { fn new(to: usize, inv: usize, cap: Cap) -> Self { Edge { to_: to as u32, inv_: inv as u32, cap_: cap, } } fn to(&self) -> usize { self.to_ as usize } fn inv(&self) -> usize { self.inv_ as usize } } impl Edge { fn add(&mut self, cap: Cap) { self.cap_ = self.cap_ + cap; } fn sub(&mut self, cap: Cap) { self.cap_ = self.cap_ - cap; } fn cap(&self) -> Cap { self.cap_ } } pub struct Graph { graph: Vec>>, } #[allow(dead_code)] pub struct EdgeIndex { src: usize, dst: usize, x: usize, y: usize, } impl Graph { pub fn new(size: usize) -> Self { Self { graph: vec![vec![]; size], } } pub fn add_edge(&mut self, src: usize, dst: usize, cap: Cap) -> EdgeIndex { assert!(src.max(dst) < self.graph.len()); assert!(cap >= Cap::zero()); assert!(src != dst); let x = self.graph[src].len(); let y = self.graph[dst].len(); self.graph[src].push(Edge::new(dst, y, cap)); self.graph[dst].push(Edge::new(src, x, Cap::zero())); EdgeIndex { src, dst, x, y } } // src, dst, used, intial_capacity #[allow(dead_code)] pub fn get_edge(&self, e: &EdgeIndex) -> (usize, usize, Cap, Cap) { let max = self.graph[e.src][e.x].cap() + self.graph[e.dst][e.y].cap(); let used = self.graph[e.dst][e.y].cap(); (e.src, e.dst, used, max) } pub fn flow(&mut self, src: usize, dst: usize) -> Cap { let size = self.graph.len(); assert!(src.max(dst) < size); assert!(src != dst); let mut queue = std::collections::VecDeque::new(); let mut level = vec![0; size]; let mut it = vec![0; size]; let mut ans = Cap::zero(); loop { (|| { level.clear(); level.resize(size, 0); level[src] = 1; queue.clear(); queue.push_back(src); while let Some(v) = queue.pop_front() { let d = level[v] + 1; for e in self.graph[v].iter() { let u = e.to(); if e.cap() > Cap::zero() && level[u] == 0 { level[u] = d; if u == dst { return; } queue.push_back(u); } } } })(); if level[dst] == 0 { break; } it.clear(); it.resize(size, 0); loop { let f = self.dfs(dst, src, Cap::inf(), &mut it, &level); if f == Cap::zero() { break; } ans = ans + f; } } ans } fn dfs(&mut self, v: usize, src: usize, cap: Cap, it: &mut [usize], level: &[u32]) -> Cap { if v == src { return cap; } while let Some((u, inv)) = self.graph[v].get(it[v]).map(|p| (p.to(), p.inv())) { if level[u] + 1 == level[v] && self.graph[u][inv].cap() > Cap::zero() { let cap = cap.min(self.graph[u][inv].cap()); let c = self.dfs(u, src, cap, it, level); if c > Cap::zero() { self.graph[v][it[v]].add(c); self.graph[u][inv].sub(c); return c; } } it[v] += 1; } Cap::zero() } } } // ---------- end max flow (Dinic) ----------