fn getline() -> String { let mut ret = String::new(); std::io::stdin().read_line(&mut ret).unwrap(); ret } // Dinic's algorithm for maximum flow problem. // This implementation uses O(n) stack space. // Verified by: // - yukicoder No.177 (http://yukicoder.me/submissions/148371) // - ABC239-G (https://atcoder.jp/contests/abc239/submissions/29497217) #[derive(Clone)] struct Edge { to: usize, cap: T, rev: usize, // rev is the position of the reverse edge in graph[to] } struct Cut { is_t: Vec, } #[allow(unused)] impl Cut { pub fn is_cut(&self, s: usize, t: usize) -> bool { !self.is_t[s] && self.is_t[t] } pub fn t(&self) -> Vec { (0..self.is_t.len()).filter(|&v| self.is_t[v]).collect() } pub fn s(&self) -> Vec { (0..self.is_t.len()).filter(|&v| !self.is_t[v]).collect() } } struct Dinic { graph: Vec>>, iter: Vec, zero: T, } impl Dinic where T: Clone, T: Copy, T: Ord, T: std::ops::Add, T: std::ops::Sub, T: std::ops::AddAssign, T: std::ops::SubAssign, { fn bfs(&self, s: usize, t: usize, level: &mut [Option]) { let n = level.len(); for i in 0..n { level[i] = None; } let mut que = std::collections::VecDeque::new(); level[s] = Some(0); que.push_back(s); while let Some(v) = que.pop_front() { for e in self.graph[v].iter() { if e.cap > self.zero && level[e.to] == None { level[e.to] = Some(level[v].unwrap() + 1); if e.to == t { return; } que.push_back(e.to); } } } } // search an augment path with dfs. // if f == None, f is treated as infinity. fn dfs(&mut self, v: usize, s: usize, f: Option, level: &mut [Option]) -> T { if v == s { return f.unwrap(); } let mut res = self.zero; while self.iter[v] < self.graph[v].len() { let i = self.iter[v]; let e = self.graph[v][i].clone(); let cap = self.graph[e.to][e.rev].cap; if cap > self.zero && level[e.to].is_some() && level[v] > level[e.to] { let newf = std::cmp::min(f.unwrap_or(cap + res) - res, cap); let d = self.dfs(e.to, s, Some(newf), level); if d > self.zero { self.graph[v][i].cap += d; self.graph[e.to][e.rev].cap -= d; res += d; if Some(res) == f { return res; } } } self.iter[v] += 1; } res } pub fn new(n: usize, zero: T) -> Self { Dinic { graph: vec![Vec::new(); n], iter: vec![0; n], zero: zero, } } pub fn add_edge(&mut self, from: usize, to: usize, cap: T) { if from == to { return; } let added_from = Edge { to: to, cap: cap, rev: self.graph[to].len() }; let added_to = Edge { to: from, cap: self.zero, rev: self.graph[from].len() }; self.graph[from].push(added_from); self.graph[to].push(added_to); } pub fn max_flow(&mut self, s: usize, t: usize) -> (T, Cut) { let mut flow = self.zero; let n = self.graph.len(); let mut level = vec![None; n]; loop { self.bfs(s, t, &mut level); if level[t] == None { let is_t: Vec = (0..n).map(|v| level[v].is_none()) .collect(); return (flow, Cut { is_t: is_t }); } self.iter.clear(); self.iter.resize(n, 0); let f = self.dfs(t, s, None, &mut level); flow += f; } } } fn main() { getline(); let a = getline().trim().split_whitespace() .map(|x| x.parse::().unwrap()) .collect::>(); const W: usize = 5000; let mut f = vec![0; W]; for a in a { f[a - 1] += 1; } let mut din = Dinic::new(2 + W * 2, 0i32); for i in 0..W { if f[i] != 0 { din.add_edge(2 + W + i, 1, f[i]); } } let mut ok = 0; for i in 1..W + 1 { din.add_edge(0, 2 + i - 1, 1); for j in 1..=W / i { if f[i * j - 1] != 0 { din.add_edge(2 + i - 1, 2 + W + i * j - 1, 1); } } if din.max_flow(0, 1).0 == 0 { break; } ok = i; } println!("{ok}"); }