#[allow(unused_imports)] #[cfg(feature = "dbg")] use dbg::lg; use hopkarp::hopkarp; use std::collections::HashMap; const MAX: usize = 500_001; fn main() { let mut buf = ngtio::with_stdin(); let h = buf.usize(); let w = buf.usize(); let mut a = vec![Vec::new(); MAX]; for i in 0..h { for j in 0..w { a[buf.usize()].push([i, j]); } } let mut ans = 0; for v in a[1..].iter().rev().filter(|v| !v.is_empty()) { let mut is = HashMap::new(); let mut js = HashMap::new(); for &[i, j] in v { if is.get(&i).is_none() { let x = is.len(); is.insert(i, x); }; if js.get(&j).is_none() { let x = js.len(); js.insert(j, x); }; } let mut g = vec![Vec::new(); is.len()]; v.iter() .map(|&[i, j]| [is[&i], js[&j]]) .for_each(|[i, j]| g[i].push(j)); let aug = hopkarp(js.len(), &g).count; ans += aug; } println!("{}", ans); } // hopkarp {{{ #[allow(dead_code)] mod hopkarp { use std::collections::VecDeque; #[derive(Clone, Debug, Default, Hash, PartialEq)] pub struct HopkarpResult { pub count: usize, pub forward: Box<[Option]>, pub backward: Box<[Option]>, pub left: Box<[bool]>, pub right: Box<[bool]>, } pub fn hopkarp(w: usize, graph: &[Vec]) -> HopkarpResult { let h = graph.len(); let mut forward = vec![None; h].into_boxed_slice(); let mut backward = vec![None; w].into_boxed_slice(); let (left, right) = loop { let dist = bfs(graph, &forward, &backward); if !dfs(&graph, &dist, &mut forward, &mut backward) { break construct_minimum_cut(graph, &dist, &backward); } }; let count = forward.iter().filter(|b| b.is_some()).count(); HopkarpResult { count, forward, backward, left, right, } } fn construct_minimum_cut( graph: &[Vec], dist: &[u32], backward: &[Option], ) -> (Box<[bool]>, Box<[bool]>) { use std::u32::MAX; let left = dist .iter() .map(|&x| x != MAX) .collect::>() .into_boxed_slice(); let mut right = vec![false; backward.len()].into_boxed_slice(); for x in left.iter().enumerate().filter(|&(_, &b)| b).map(|(x, _)| x) { graph[x] .iter() .copied() .filter(|&y| backward[y] != Some(x)) .for_each(|y| right[y] = true); } (left, right) } fn dfs( graph: &[Vec], dist: &[u32], forward: &mut [Option], backward: &mut [Option], ) -> bool { fn rec( x: usize, graph: &[Vec], dist: &[u32], used: &mut [bool], forward: &mut [Option], backward: &mut [Option], ) -> bool { used[x] = true; for &y in &graph[x] { let found = if let Some(z) = backward[y] { !used[z] && dist[x] + 1 == dist[z] && rec(z, graph, dist, used, forward, backward) } else { true }; if found { backward[y] = Some(x); forward[x] = Some(y); return true; } } false } let mut has_aug = false; let mut used = vec![false; forward.len()]; for x in 0..used.len() { if forward[x].is_none() { has_aug |= rec(x, graph, dist, &mut used, forward, backward); } } has_aug } fn bfs( graph: &[Vec], forward: &[Option], backward: &[Option], ) -> Vec { use std::u32::MAX; let mut dist = vec![MAX; forward.len()]; let mut queue = forward .iter() .enumerate() .filter(|&(_, b)| b.is_none()) .map(|(i, _)| i) .inspect(|&i| dist[i] = 0) .collect::>(); while let Some(x) = queue.pop_front() { for &y in &graph[x] { if let Some(z) = backward[y] { if dist[z] == MAX { dist[z] = dist[x] + 1; queue.push_back(z); } } } } dist } } // }}} // template {{{ #[cfg(not(feature = "dbg"))] #[allow(unused_macros)] #[macro_export] macro_rules! lg { ($($expr:expr),*) => {}; } #[allow(dead_code)] mod ngtio { mod i { use std::{ io::{self, BufRead}, iter, }; pub use self::{ multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen}, token::{Token, Usize1}, }; pub fn with_stdin() -> Tokenizer> { io::BufReader::new(io::stdin()).tokenizer() } pub fn with_str(src: &str) -> Tokenizer<&[u8]> { src.as_bytes().tokenizer() } pub struct Tokenizer { queue: Vec, // FIXME: String のみにすると速そうです。 scanner: S, } macro_rules! prim_method { ($name:ident: $T:ty) => { pub fn $name(&mut self) -> $T { <$T>::leaf().parse(self) } }; ($name:ident) => { prim_method!($name: $name); }; } macro_rules! prim_methods { ($name:ident: $T:ty; $($rest:tt)*) => { prim_method!($name:$T); prim_methods!($($rest)*); }; ($name:ident; $($rest:tt)*) => { prim_method!($name); prim_methods!($($rest)*); }; () => () } impl Tokenizer { pub fn token(&mut self) -> String { self.load(); self.queue.pop().expect("入力が終了したのですが。") } pub fn new(scanner: S) -> Self { Self { queue: Vec::new(), scanner, } } fn load(&mut self) { while self.queue.is_empty() { let mut s = String::new(); let length = self.scanner.read_line(&mut s).unwrap(); // 入力が UTF-8 でないときにエラーだそうです。 if length == 0 { break; } self.queue = s.split_whitespace().rev().map(str::to_owned).collect(); } } pub fn skip_line(&mut self) { assert!( self.queue.is_empty(), "行の途中で呼ばないでいただきたいです。現在のトークンキュー: {:?}", &self.queue ); self.load(); } pub fn end(&mut self) { self.load(); assert!(self.queue.is_empty(), "入力はまだあります!"); } pub fn parse(&mut self) -> T::Output { T::parse(&self.token()) } pub fn parse_collect(&mut self, n: usize) -> B where B: iter::FromIterator, { iter::repeat_with(|| self.parse::()).take(n).collect() } pub fn tuple(&mut self) -> ::Output { T::leaf_tuple().parse(self) } pub fn vec(&mut self, len: usize) -> Vec { T::leaf().vec(len).parse(self) } pub fn vec_tuple( &mut self, len: usize, ) -> Vec<::Output> { T::leaf_tuple().vec(len).parse(self) } pub fn vec2(&mut self, height: usize, width: usize) -> Vec> { T::leaf().vec(width).vec(height).parse(self) } pub fn vec2_tuple( &mut self, height: usize, width: usize, ) -> Vec::Output>> where T: RawTuple, { T::leaf_tuple().vec(width).vec(height).parse(self) } prim_methods! { u8; u16; u32; u64; u128; usize; i8; i16; i32; i64; i128; isize; f32; f64; char; string: String; } } mod token { use super::multi_token::Leaf; use std::{any, fmt, marker, str}; pub trait Token: Sized { type Output; fn parse(s: &str) -> Self::Output; fn leaf() -> Leaf { Leaf(marker::PhantomData) } } impl Token for T where T: str::FromStr, ::Err: fmt::Debug, { type Output = T; fn parse(s: &str) -> Self::Output { s.parse().unwrap_or_else(|_| { panic!("Parse error!: ({}: {})", s, any::type_name::(),) }) } } pub struct Usize1 {} impl Token for Usize1 { type Output = usize; fn parse(s: &str) -> Self::Output { usize::parse(s) .checked_sub(1) .expect("Parse error! (Zero substruction error of Usize1)") } } } mod multi_token { use super::{Token, Tokenizer}; use std::{io::BufRead, iter, marker}; pub trait Parser: Sized { type Output; fn parse(&self, server: &mut Tokenizer) -> Self::Output; fn vec(self, len: usize) -> VecLen { VecLen { len, elem: self } } } pub struct Leaf(pub(super) marker::PhantomData); impl Parser for Leaf { type Output = T::Output; fn parse(&self, server: &mut Tokenizer) -> T::Output { server.parse::() } } pub struct VecLen { pub len: usize, pub elem: T, } impl Parser for VecLen { type Output = Vec; fn parse(&self, server: &mut Tokenizer) -> Self::Output { iter::repeat_with(|| self.elem.parse(server)) .take(self.len) .collect() } } pub trait RawTuple { type LeafTuple: Parser; fn leaf_tuple() -> Self::LeafTuple; } pub trait ParserTuple { type Tuple: Parser; fn tuple(self) -> Self::Tuple; } pub struct Tuple(pub T); macro_rules! impl_tuple { ($($t:ident: $T:ident),*) => { impl<$($T),*> Parser for Tuple<($($T,)*)> where $($T: Parser,)* { type Output = ($($T::Output,)*); #[allow(unused_variables)] fn parse(&self, server: &mut Tokenizer) -> Self::Output { match self { Tuple(($($t,)*)) => { ($($t.parse(server),)*) } } } } impl<$($T: Token),*> RawTuple for ($($T,)*) { type LeafTuple = Tuple<($(Leaf<$T>,)*)>; fn leaf_tuple() -> Self::LeafTuple { Tuple(($($T::leaf(),)*)) } } impl<$($T: Parser),*> ParserTuple for ($($T,)*) { type Tuple = Tuple<($($T,)*)>; fn tuple(self) -> Self::Tuple { Tuple(self) } } }; } impl_tuple!(); impl_tuple!(t1: T1); impl_tuple!(t1: T1, t2: T2); impl_tuple!(t1: T1, t2: T2, t3: T3); impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4); impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5); impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6); impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6, t7: T7); impl_tuple!( t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6, t7: T7, t8: T8 ); } trait Scanner: BufRead + Sized { fn tokenizer(self) -> Tokenizer { Tokenizer::new(self) } } impl Scanner for R {} } pub use self::i::{with_stdin, with_str}; pub mod prelude { pub use super::i::{Parser, ParserTuple, RawTuple, Token, Usize1}; } } // }}}