#![allow(unused_imports,non_snake_case,dead_code)] use std::{cmp::Reverse as Rev,ops::Range,collections::*,iter::*,mem::swap}; use proconio::{marker::*,*}; #[fastout] fn main(){ input!{ n:usize, a:[usize;n], } let mut g=vec![vec![];n]; for i in 0..n{ for j in 0..n{ if a[j]%(i+1)==0{ g[i].push(j); } } } let ans=binary_search(0,n+1,|x|{ let mut flow=MfGraph::new(n*2+2); let s=n*2; let t=s+1; for i in 0..n{ flow.add_edge(s,i,1); flow.add_edge(i+n,t,1); } for u in 0..x{ for &v in &g[u]{ flow.add_edge(u,v+n,1); } } flow.flow(s,t)>=x }); println!("{ans}"); } use std::cmp::min; use std::iter; impl MfGraph where Cap: Integral, { pub fn new(n: usize) -> MfGraph { MfGraph { _n: n, pos: Vec::new(), g: iter::repeat_with(Vec::new).take(n).collect(), } } pub fn add_edge(&mut self, from: usize, to: usize, cap: Cap) -> usize { assert!(from < self._n); assert!(to < self._n); assert!(Cap::zero() <= cap); let m = self.pos.len(); self.pos.push((from, self.g[from].len())); let rev = self.g[to].len() + usize::from(from == to); self.g[from].push(_Edge { to, rev, cap }); let rev = self.g[from].len() - 1; self.g[to].push(_Edge { to: from, rev, cap: Cap::zero(), }); m } } #[derive(Debug, PartialEq, Eq)] pub struct Edge { pub from: usize, pub to: usize, pub cap: Cap, pub flow: Cap, } impl MfGraph where Cap: Integral, { pub fn get_edge(&self, i: usize) -> Edge { let m = self.pos.len(); assert!(i < m); let _e = &self.g[self.pos[i].0][self.pos[i].1]; let _re = &self.g[_e.to][_e.rev]; Edge { from: self.pos[i].0, to: _e.to, cap: _e.cap + _re.cap, flow: _re.cap, } } pub fn edges(&self) -> Vec> { let m = self.pos.len(); (0..m).map(|i| self.get_edge(i)).collect() } pub fn change_edge(&mut self, i: usize, new_cap: Cap, new_flow: Cap) { let m = self.pos.len(); assert!(i < m); assert!(Cap::zero() <= new_flow && new_flow <= new_cap); let (to, rev) = { let _e = &mut self.g[self.pos[i].0][self.pos[i].1]; _e.cap = new_cap - new_flow; (_e.to, _e.rev) }; let _re = &mut self.g[to][rev]; _re.cap = new_flow; } /// `s != t` must hold, otherwise it panics. pub fn flow(&mut self, s: usize, t: usize) -> Cap { self.flow_with_capacity(s, t, Cap::max_value()) } /// # Parameters /// * `s != t` must hold, otherwise it panics. /// * `flow_limit >= 0` pub fn flow_with_capacity(&mut self, s: usize, t: usize, flow_limit: Cap) -> Cap { let n_ = self._n; assert!(s < n_); assert!(t < n_); // By the definition of max flow in appendix.html, this function should return 0 // when the same vertices are provided. On the other hand, it is reasonable to // return infinity-like value too, which is what the original implementation // (and this implementation without the following assertion) does. // Since either return value is confusing, we'd rather deny the parameters // of the two same vertices. // For more details, see https://github.com/rust-lang-ja/ac-library-rs/pull/24#discussion_r485343451 // and https://github.com/atcoder/ac-library/issues/5 . assert_ne!(s, t); // Additional constraint assert!(Cap::zero() <= flow_limit); let mut calc = FlowCalculator { graph: self, s, t, flow_limit, level: vec![0; n_], iter: vec![0; n_], que: SimpleQueue::default(), }; let mut flow = Cap::zero(); while flow < flow_limit { calc.bfs(); if calc.level[t] == -1 { break; } calc.iter.iter_mut().for_each(|e| *e = 0); while flow < flow_limit { let f = calc.dfs(t, flow_limit - flow); if f == Cap::zero() { break; } flow += f; } } flow } pub fn min_cut(&self, s: usize) -> Vec { let mut visited = vec![false; self._n]; let mut que = SimpleQueue::default(); que.push(s); while let Some(&p) = que.pop() { visited[p] = true; for e in &self.g[p] { if e.cap != Cap::zero() && !visited[e.to] { visited[e.to] = true; que.push(e.to); } } } visited } } struct FlowCalculator<'a, Cap> { graph: &'a mut MfGraph, s: usize, t: usize, flow_limit: Cap, level: Vec, iter: Vec, que: SimpleQueue, } impl FlowCalculator<'_, Cap> where Cap: Integral, { fn bfs(&mut self) { self.level.iter_mut().for_each(|e| *e = -1); self.level[self.s] = 0; self.que.clear(); self.que.push(self.s); while !self.que.empty() { let v = *self.que.front().unwrap(); self.que.pop(); for e in &self.graph.g[v] { if e.cap == Cap::zero() || self.level[e.to] >= 0 { continue; } self.level[e.to] = self.level[v] + 1; if e.to == self.t { return; } self.que.push(e.to); } } } fn dfs(&mut self, v: usize, up: Cap) -> Cap { if v == self.s { return up; } let mut res = Cap::zero(); let level_v = self.level[v]; for i in self.iter[v]..self.graph.g[v].len() { self.iter[v] = i; let &_Edge { to: e_to, rev: e_rev, .. } = &self.graph.g[v][i]; if level_v <= self.level[e_to] || self.graph.g[e_to][e_rev].cap == Cap::zero() { continue; } let d = self.dfs(e_to, min(up - res, self.graph.g[e_to][e_rev].cap)); if d <= Cap::zero() { continue; } self.graph.g[v][i].cap += d; self.graph.g[e_to][e_rev].cap -= d; res += d; if res == up { return res; } } self.iter[v] = self.graph.g[v].len(); res } } #[derive(Default)] pub struct MfGraph { _n: usize, pos: Vec<(usize, usize)>, g: Vec>>, } struct _Edge { to: usize, rev: usize, cap: Cap, } #[derive(Default)] pub(crate) struct SimpleQueue { payload: Vec, pos: usize, } impl SimpleQueue { pub(crate) fn reserve(&mut self, n: usize) { if n > self.payload.len() { self.payload.reserve(n - self.payload.len()); } } pub(crate) fn size(&self) -> usize { self.payload.len() - self.pos } pub(crate) fn empty(&self) -> bool { self.pos == self.payload.len() } pub(crate) fn push(&mut self, t: T) { self.payload.push(t); } // Do we need mutable version? pub(crate) fn front(&self) -> Option<&T> { if self.pos < self.payload.len() { Some(&self.payload[self.pos]) } else { None } } pub(crate) fn clear(&mut self) { self.payload.clear(); self.pos = 0; } pub(crate) fn pop(&mut self) -> Option<&T> { if self.pos < self.payload.len() { self.pos += 1; Some(&self.payload[self.pos - 1]) } else { None } } } use std::{ fmt, iter::{Product, Sum}, ops::{ Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Div, DivAssign, Mul, MulAssign, Not, Rem, RemAssign, Shl, ShlAssign, Shr, ShrAssign, Sub, SubAssign, }, }; // Skipped: // // - `is_signed_int_t` (probably won't be used directly in `modint.rs`) // - `is_unsigned_int_t` (probably won't be used directly in `modint.rs`) // - `to_unsigned_t` (not used in `fenwicktree.rs`) /// Corresponds to `std::is_integral` in C++. // We will remove unnecessary bounds later. // // Maybe we should rename this to `PrimitiveInteger` or something, as it probably won't be used in the // same way as the original ACL. pub trait Integral: 'static + Send + Sync + Copy + Ord + Not + Add + Sub + Mul + Div + Rem + AddAssign + SubAssign + MulAssign + DivAssign + RemAssign + Sum + Product + BitOr + BitAnd + BitXor + BitOrAssign + BitAndAssign + BitXorAssign + Shl + Shr + ShlAssign + ShrAssign + fmt::Display + fmt::Debug + fmt::Binary + fmt::Octal + Zero + One + BoundedBelow + BoundedAbove { } /// Class that has additive identity element pub trait Zero { /// The additive identity element fn zero() -> Self; } /// Class that has multiplicative identity element pub trait One { /// The multiplicative identity element fn one() -> Self; } pub trait BoundedBelow { fn min_value() -> Self; } pub trait BoundedAbove { fn max_value() -> Self; } macro_rules! impl_integral { ($($ty:ty),*) => { $( impl Zero for $ty { #[inline] fn zero() -> Self { 0 } } impl One for $ty { #[inline] fn one() -> Self { 1 } } impl BoundedBelow for $ty { #[inline] fn min_value() -> Self { Self::min_value() } } impl BoundedAbove for $ty { #[inline] fn max_value() -> Self { Self::max_value() } } impl Integral for $ty {} )* }; } impl_integral!(i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, usize); // true,true,..,true,false,false で一番右のtrue // ok>ngでも大丈夫 fn binary_search(mut ok:usize,mut ng:usize,mut f:impl FnMut(usize)->bool)->usize{ assert!(ok!=ng); while 1