pub fn main() { crate::prepare!(); sc!(n, m, l, e: [(Usize1, Usize1); l]); let dm = dulmage_mendelsohn(n, m, &e); let mut fixed = HashSet::new(); for (d0, d1) in dm.iter() { if d0.len() == 1 && d1.len() == 1 { fixed.insert((d0[0], d1[0])); } } for e in &e { pp!(if !fixed.contains(e) { "Yes" } else { "No" }); } } pub fn dulmage_mendelsohn( l: usize, r: usize, edges: &[(usize, usize)], ) -> Vec<(Vec, Vec)> { let m = edges.len(); let mut builder = Dinic::builder(l + r + 2, l + r + m); for &(u, v) in edges { builder.add_edge(u, v + l, 1); } for i in 0..l { builder.add_edge(l + r, i, 1); } for j in 0..r { builder.add_edge(j + l, l + r + 1, 1); } let dinic_g = builder.gen_graph(); let mut dinic = builder.build(&dinic_g); dinic.maximum_flow(l + r, l + r + 1); let mut matching = vec![!0usize; l + r]; let mut medges: Vec<_> = edges.iter().map(|&(u, v)| (u, v + l)).collect(); for (k, &(u, v)) in edges.iter().enumerate() { if dinic.get_flow(k) == 1 { medges.push((v + l, u)); matching[u] = v + l; matching[v + l] = u; } } let rmedges = medges.iter().map(|&(u, v)| (v, u)).collect(); let g = DirectedSparseGraph::from_edges(l + r, medges); let rg = DirectedSparseGraph::from_edges(l + r, rmedges); let scc = StronglyConnectedComponent::new(&g); let csize = scc.size(); let mut cmap = vec![!0usize - 1; csize]; let mut visited = vec![false; l + r]; let mut stack = vec![]; for u in 0..l { if matching[u] == !0 && !visited[u] { visited[u] = true; stack.push(u); while let Some(u) = stack.pop() { cmap[scc[u]] = !0; for a in g.adjacencies(u) { if !visited[a.to] { visited[a.to] = true; stack.push(a.to); } } } } } for u in l..l + r { if matching[u] == !0 && !visited[u] { visited[u] = true; stack.push(u); while let Some(u) = stack.pop() { cmap[scc[u]] = 0; for a in rg.adjacencies(u) { if !visited[a.to] { visited[a.to] = true; stack.push(a.to); } } } } } let mut nset = 1usize; for i in 0..csize { if cmap[i] == !0 - 1 { cmap[i] = nset; nset += 1; } } for v in &mut cmap { if *v == !0 { *v = nset; } } nset += 1; let mut groups = vec![(vec![], vec![]); nset]; for u in 0..l { if matching[u] != !0 { let c = cmap[scc[u]]; groups[c].0.push(u); groups[c].1.push(matching[u] - l); } } for u in 0..l { if matching[u] == !0 { let c = cmap[scc[u]]; groups[c].0.push(u); } } for u in 0..r { if matching[u + l] == !0 { let c = cmap[scc[u + l]]; groups[c].1.push(u); } } groups } #[allow(unused_imports)]use std::{cmp::{Ordering,Reverse},collections::{BTreeMap,BTreeSet,BinaryHeap,HashMap,HashSet,VecDeque}}; mod main_macros{#[doc=" Prepare useful macros."]#[doc=" - `prepare!();`: default (all input scanner (`sc!`, `sv!`) + buf print (`pp!`))"]#[doc=" - `prepare!(?);`: interactive (line scanner (`scln!`) + buf print (`pp!`))"]#[macro_export]macro_rules!prepare{(@normal($dol:tt))=>{#[allow(unused_imports)]use std::io::Write as _;let __out=std::io::stdout();#[allow(unused_mut,unused_variables)]let mut __out=std::io::BufWriter::new(__out.lock());#[allow(unused_macros)]macro_rules!pp{($dol($dol t:tt)*)=>{$dol crate::iter_print!(__out,$dol($dol t)*)}}let __in_buf=read_stdin_all_unchecked();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);#[allow(unused_macros)]macro_rules!sc{($dol($dol t:tt)*)=>{$dol crate::scan!(__scanner,$dol($dol t)*)}}#[allow(unused_macros)]macro_rules!sv{($dol($dol t:tt)*)=>{$dol crate::scan_value!(__scanner,$dol($dol t)*)}}};(@interactive($dol:tt))=>{#[allow(unused_imports)]use std::io::Write as _;let __out=std::io::stdout();#[allow(unused_mut,unused_variables)]let mut __out=std::io::BufWriter::new(__out.lock());#[allow(unused_macros)]#[doc=" - to flush: `pp!(@flush);`"]macro_rules!pp{($dol($dol t:tt)*)=>{$dol crate::iter_print!(__out,$dol($dol t)*)}}#[allow(unused_macros)]#[doc=" Scan a line, and previous line will be truncated in the next call."]macro_rules!scln{($dol($dol t:tt)*)=>{let __in_buf=read_stdin_line();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);$dol crate::scan!(__scanner,$dol($dol t)*)}}};()=>{$crate::prepare!(@normal($))};(?)=>{$crate::prepare!(@interactive($))};}} mod iter_print{use std::{fmt::Display,io::{Error,Write}};pub trait IterPrint{fn iter_print(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display;}macro_rules!iter_print_tuple_impl{(@impl$($A:ident$a:ident)?,$($B:ident$b:ident)*)=>{impl<$($A,)?$($B),*>IterPrint for($($A,)?$($B),*)where$($A:Display,)?$($B:Display),*{#[allow(unused_variables)]fn iter_print(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display{let($($a,)?$($b,)*)=self;$(if is_head{::std::write!(writer,"{}",$a)?;}else{::std::write!(writer,"{}{}",sep,$a)?;})?$(::std::write!(writer,"{}{}",sep,$b)?;)*Ok(())}}};(@inc,,$C:ident$c:ident$($D:ident$d:ident)*)=>{iter_print_tuple_impl!(@impl,);iter_print_tuple_impl!(@inc$C$c,,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,$C:ident$c:ident$($D:ident$d:ident)*)=>{iter_print_tuple_impl!(@impl$A$a,$($B$b)*);iter_print_tuple_impl!(@inc$A$a,$($B$b)*$C$c,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,)=>{iter_print_tuple_impl!(@impl$A$a,$($B$b)*);};($($t:tt)*)=>{iter_print_tuple_impl!(@inc,,$($t)*);};}iter_print_tuple_impl!(A a B b C c D d E e F f G g H h I i J j K k);#[doc=" Print expressions with a separator."]#[doc=" - `iter_print!(writer, args...)`"]#[doc=" - `@sep $expr`: set separator (default: `' '`)"]#[doc=" - `@fmt $lit => {$($expr),*}`: print `format!($lit, $($expr),*)`"]#[doc=" - `@flush`: flush writer (auto insert `!`)"]#[doc=" - `@iter $expr`: print iterator"]#[doc=" - `@iterns $expr`: print iterator with no separators"]#[doc=" - `@iterln $expr`: print iterator with separator `'\\n'`"]#[doc=" - `@iter2d $expr`: print 2d-iterator"]#[doc=" - `@tuple $expr`: print tuple (need to import [`IterPrint`], each elements impls `Display`)"]#[doc=" - `$expr`: print expr"]#[doc=" - `;`: print `'\\n'`"]#[doc=" - `!`: not print `'\\n'` at the end"]#[macro_export]macro_rules!iter_print{(@@fmt$writer:expr,$sep:expr,$is_head:expr,$lit:literal,$($e:expr),*)=>{if!$is_head{::std::write!($writer,"{}",$sep).expect("io error");}::std::write!($writer,$lit,$($e),*).expect("io error");};(@@item$writer:expr,$sep:expr,$is_head:expr,$e:expr)=>{$crate::iter_print!(@@fmt$writer,$sep,$is_head,"{}",$e);};(@@line_feed$writer:expr$(,)?)=>{::std::writeln!($writer).expect("io error");};(@@iter$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,item);}}};(@@iterns$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@item$writer,$sep,true,item);}}};(@@iterln$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,'\n',$is_head,item);}for item in iter{$crate::iter_print!(@@item$writer,'\n',false,item);}}};(@@iter2d$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@iter$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@iter$writer,$sep,true,item);}};(@@tuple$writer:expr,$sep:expr,$is_head:expr,$tuple:expr)=>{IterPrint::iter_print($tuple,&mut$writer,$sep,$is_head).expect("io error");};(@@assert_tag item)=>{};(@@assert_tag iter)=>{};(@@assert_tag iterns)=>{};(@@assert_tag iterln)=>{};(@@assert_tag iter2d)=>{};(@@assert_tag tuple)=>{};(@@assert_tag$tag:ident)=>{::std::compile_error!(::std::concat!("invalid tag in `iter_print!`: `",std::stringify!($tag),"`"));};(@@inner$writer:expr,$sep:expr,$is_head:expr,@sep$e:expr,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$e,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@flush$($t:tt)*)=>{$writer.flush().expect("io error");$crate::iter_print!(@@inner$writer,$sep,$is_head,!$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@fmt$lit:literal=>{$($e:expr),*$(,)?}$($t:tt)*)=>{$crate::iter_print!(@@fmt$writer,$sep,$is_head,$lit,$($e),*);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr,$($t:tt)*)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@inner$writer,$sep,false,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr;$($t:tt)*)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@inner$writer,$sep,true,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@inner$writer,$sep,false,);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$($t:tt)*)=>{::std::compile_error!(::std::concat!("invalid expr in `iter_print!`: `",std::stringify!($($t)*),"`"));};(@@inner$writer:expr,$sep:expr,$is_head:expr,,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,;$($t:tt)*)=>{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,!$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,!)=>{};(@@inner$writer:expr,$sep:expr,$is_head:expr,)=>{$crate::iter_print!(@@line_feed$writer);};(@@inner$writer:expr,$sep:expr,$is_head:expr,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,@item$($t)*);};($writer:expr,$($t:tt)*)=>{{$crate::iter_print!(@@inner$writer,' ',true,$($t)*);}};}} pub use self::scanner::*; mod scanner{use std::{iter::{repeat_with,FromIterator},marker::PhantomData};pub fn read_stdin_all()->String{use std::io::Read as _;let mut s=String::new();std::io::stdin().read_to_string(&mut s).expect("io error");s}pub fn read_stdin_all_unchecked()->String{use std::io::Read as _;let mut buf=Vec::new();std::io::stdin().read_to_end(&mut buf).expect("io error");unsafe{String::from_utf8_unchecked(buf)}}pub fn read_all(mut reader:impl std::io::Read)->String{let mut s=String::new();reader.read_to_string(&mut s).expect("io error");s}pub fn read_all_unchecked(mut reader:impl std::io::Read)->String{let mut buf=Vec::new();reader.read_to_end(&mut buf).expect("io error");unsafe{String::from_utf8_unchecked(buf)}}pub fn read_stdin_line()->String{let mut s=String::new();std::io::stdin().read_line(&mut s).expect("io error");s}pub trait IterScan:Sized{type Output;fn scan<'a,I:Iterator>(iter:&mut I)->Option;}pub trait MarkedIterScan:Sized{type Output;fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option;}#[derive(Clone,Debug)]pub struct Scanner<'a>{iter:std::str::SplitAsciiWhitespace<'a>}impl<'a>Scanner<'a>{#[inline]pub fn new(s:&'a str)->Self{let iter=s.split_ascii_whitespace();Self{iter}}#[inline]pub fn scan(&mut self)->::Output where T:IterScan{::scan(&mut self.iter).expect("scan error")}#[inline]pub fn mscan(&mut self,marker:T)->::Output where T:MarkedIterScan{marker.mscan(&mut self.iter).expect("scan error")}#[inline]pub fn scan_vec(&mut self,size:usize)->Vec<::Output>where T:IterScan{(0..size).map(|_|::scan(&mut self.iter).expect("scan error")).collect()}#[inline]pub fn iter<'b,T>(&'b mut self)->ScannerIter<'a,'b,T>where T:IterScan{ScannerIter{inner:self,_marker:std::marker::PhantomData}}}macro_rules!iter_scan_impls{($($t:ty)*)=>{$(impl IterScan for$t{type Output=Self;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{iter.next()?.parse::<$t>().ok()}})*};}iter_scan_impls!(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String);macro_rules!iter_scan_tuple_impl{(@impl$($T:ident)*)=>{impl<$($T:IterScan),*>IterScan for($($T,)*){type Output=($(<$T as IterScan>::Output,)*);#[inline]fn scan<'a,It:Iterator>(_iter:&mut It)->Option{Some(($(<$T as IterScan>::scan(_iter)?,)*))}}};(@inner$($T:ident)*,)=>{iter_scan_tuple_impl!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{iter_scan_tuple_impl!(@impl$($T)*);iter_scan_tuple_impl!(@inner$($T)*$U,$($Rest)*);};($($T:ident)*)=>{iter_scan_tuple_impl!(@inner,$($T)*);};}iter_scan_tuple_impl!(A B C D E F G H I J K);pub struct ScannerIter<'a,'b,T>{inner:&'b mut Scanner<'a>,_marker:std::marker::PhantomDataT>}impl<'a,'b,T>Iterator for ScannerIter<'a,'b,T>where T:IterScan{type Item=::Output;#[inline]fn next(&mut self)->Option{::scan(&mut self.inner.iter)}}#[doc=" - `scan_value!(scanner, ELEMENT)`"]#[doc=""]#[doc=" ELEMENT :="]#[doc=" - `$ty`: IterScan"]#[doc=" - `@$expr`: MarkedIterScan"]#[doc=" - `[ELEMENT; $expr]`: vector"]#[doc=" - `[ELEMENT]`: iterator"]#[doc=" - `($(ELEMENT)*,)`: tuple"]#[macro_export]macro_rules!scan_value{(@repeat$scanner:expr,[$($t:tt)*]$($len:expr)?)=>{::std::iter::repeat_with(||$crate::scan_value!(@inner$scanner,[]$($t)*))$(.take($len).collect::>())?};(@tuple$scanner:expr,[$([$($args:tt)*])*])=>{($($($args)*,)*)};(@$tag:ident$scanner:expr,[[$($args:tt)*]])=>{$($args)*};(@$tag:ident$scanner:expr,[$($args:tt)*]@$e:expr)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.mscan($e)]])};(@$tag:ident$scanner:expr,[$($args:tt)*]@$e:expr,$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.mscan($e)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*]($($tuple:tt)*)$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@tuple$scanner,[]$($tuple)*)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][@$e:expr;$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[@$e]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][[$($tt:tt)*];$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[[$($tt)*]]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][($($tt:tt)*);$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[($($tt)*)]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][$ty:ty;$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[$ty]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[$($tt)*])]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*]$ty:ty)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.scan::<$ty>()]])};(@$tag:ident$scanner:expr,[$($args:tt)*]$ty:ty,$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.scan::<$ty>()]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*],$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*])=>{::std::compile_error!(::std::stringify!($($args)*))};($scanner:expr,$($t:tt)*)=>{$crate::scan_value!(@inner$scanner,[]$($t)*)}}#[doc=" - `scan!(scanner, $($pat $(: ELEMENT)?),*)`"]#[macro_export]macro_rules!scan{(@assert$p:pat)=>{};(@assert$($p:tt)*)=>{::std::compile_error!(::std::concat!("expected pattern, found `",::std::stringify!($($p)*),"`"));};(@pat$scanner:expr,[][])=>{};(@pat$scanner:expr,[][],$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]$x:ident$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*$x][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]::$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*::][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]&$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*&][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]($($x:tt)*)$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*($($x)*)][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][][$($x:tt)*]$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*[$($x)*]][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]{$($x:tt)*}$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*{$($x)*}][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]:$($t:tt)*)=>{$crate::scan!(@ty$scanner,[$($p)*][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][usize]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]@$e:expr)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*@$e])};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]@$e:expr,$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*@$e],$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]($($x:tt)*)$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*($($x)*)]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*][$($x:tt)*]$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*[$($x)*]]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]$ty:ty)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*$ty])};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]$ty:ty,$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*$ty],$($t)*)};(@let$scanner:expr,[$($p:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::scan!{@assert$($p)*}let$($p)* =$crate::scan_value!($scanner,$($tt)*);$crate::scan!(@pat$scanner,[][]$($t)*)};($scanner:expr,$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)}}#[derive(Debug,Copy,Clone)]pub struct Usize1;impl IterScan for Usize1{type Output=usize;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{::scan(iter)?.checked_sub(1)}}#[derive(Debug,Copy,Clone)]pub struct CharWithBase(pub char);impl MarkedIterScan for CharWithBase{type Output=usize;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{Some((::scan(iter)?as u8-self.0 as u8)as usize)}}#[derive(Debug,Copy,Clone)]pub struct Chars;impl IterScan for Chars{type Output=Vec;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{Some(iter.next()?.chars().collect())}}#[derive(Debug,Copy,Clone)]pub struct CharsWithBase(pub char);impl MarkedIterScan for CharsWithBase{type Output=Vec;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{Some(iter.next()?.chars().map(|c|(c as u8-self.0 as u8)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub struct ByteWithBase(pub u8);impl MarkedIterScan for ByteWithBase{type Output=usize;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{Some((::scan(iter)?as u8-self.0)as usize)}}#[derive(Debug,Copy,Clone)]pub struct Bytes;impl IterScan for Bytes{type Output=Vec;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{Some(iter.next()?.bytes().collect())}}#[derive(Debug,Copy,Clone)]pub struct BytesWithBase(pub u8);impl MarkedIterScan for BytesWithBase{type Output=Vec;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{Some(iter.next()?.bytes().map(|c|(c-self.0)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub struct Collect::Output>>where T:IterScan,B:FromIterator<::Output>{size:usize,_marker:PhantomData(T,B)>}implCollectwhere T:IterScan,B:FromIterator<::Output>{pub fn new(size:usize)->Self{Self{size,_marker:PhantomData}}}implMarkedIterScan for Collectwhere T:IterScan,B:FromIterator<::Output>{type Output=B;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{repeat_with(||::scan(iter)).take(self.size).collect()}}#[derive(Debug,Copy,Clone)]pub struct SizedCollect::Output>>where T:IterScan,B:FromIterator<::Output>{_marker:PhantomData(T,B)>}implIterScan for SizedCollectwhere T:IterScan,B:FromIterator<::Output>{type Output=B;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{let size=usize::scan(iter)?;repeat_with(||::scan(iter)).take(size).collect()}}implMarkedIterScan for F where F:Fn(&str)->Option{type Output=T;fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{self(iter.next()?)}}} pub use self::maximum_flow::{Dinic,DinicBuilder}; mod maximum_flow{use super::BidirectionalSparseGraph;use std::collections::VecDeque;#[derive(Debug,Clone)]pub struct DinicBuilder{vsize:usize,edges:Vec<(usize,usize)>,capacities:Vec}impl DinicBuilder{pub fn new(vsize:usize,esize_expect:usize)->Self{Self{vsize,edges:Vec::with_capacity(esize_expect),capacities:Vec::with_capacity(esize_expect*2)}}pub fn add_edge(&mut self,from:usize,to:usize,cap:u64){self.edges.push((from,to));self.capacities.push(cap);self.capacities.push(0);}pub fn gen_graph(&mut self)->BidirectionalSparseGraph{let edges=std::mem::take(&mut self.edges);BidirectionalSparseGraph::from_edges(self.vsize,edges)}pub fn build(self,graph:&BidirectionalSparseGraph)->Dinic<'_>{let DinicBuilder{vsize,capacities,..}=self;Dinic{graph,capacities,iter:Vec::with_capacity(vsize),level:Vec::with_capacity(vsize),deq:VecDeque::with_capacity(vsize)}}}impl Extend<(usize,usize,u64)>for DinicBuilder{fn extend>(&mut self,iter:T){for(from,to,cap)in iter{self.add_edge(from,to,cap)}}}#[derive(Debug,Clone)]pub struct Dinic<'a>{graph:&'a BidirectionalSparseGraph,capacities:Vec,iter:Vec,level:Vec,deq:VecDeque}impl<'a>Dinic<'a>{pub fn builder(vsize:usize,esize_expect:usize)->DinicBuilder{DinicBuilder::new(vsize,esize_expect)}fn bfs(&mut self,s:usize,t:usize)->bool{use std::usize::MAX;self.level.clear();self.level.resize(self.graph.vertices_size(),MAX);self.level[s]=0;self.deq.clear();self.deq.push_back(s);while let Some(u)=self.deq.pop_front(){for a in self.graph.adjacencies(u){if self.capacities[a.id]>0&&self.level[a.to]==MAX{self.level[a.to]=self.level[u]+1;if a.to==t{return false;}self.deq.push_back(a.to);}}}self.level[t]==MAX}fn dfs(&mut self,s:usize,u:usize,upper:u64)->u64{if u==s{return upper;}let mut res=0;for a in self.graph.adjacencies(u).skip(self.iter[u]){if self.level[u]>self.level[a.to]&&self.capacities[a.id^1]>0{let d=self.dfs(s,a.to,(upper-res).min(self.capacities[a.id^1]));if d>0{self.capacities[a.id^1]-=d;self.capacities[a.id]+=d;res+=d;if upper==res{break;}}}self.iter[u]+=1;}res}pub fn maximum_flow_limited(&mut self,s:usize,t:usize,limit:u64)->u64{let mut flow=0;while flowu64{self.maximum_flow_limited(s,t,std::u64::MAX)}pub fn get_flow(&self,eid:usize)->u64{self.capacities[eid*2+1]}pub fn change_edge(&mut self,eid:usize,cap:u64,flow:u64){assert!(flow<=cap);self.capacities[eid*2]=cap-flow;self.capacities[eid*2+1]=flow;}}} pub use self::sparse_graph::*; mod sparse_graph{use super::{IterScan,MarkedIterScan};use std::{marker::PhantomData,ops,slice};type Marker=PhantomDataT>;#[derive(Clone,Copy,Debug,Default,Eq,PartialEq,Ord,PartialOrd,Hash)]pub struct DirectedEdge;#[derive(Clone,Copy,Debug,Default,Eq,PartialEq,Ord,PartialOrd,Hash)]pub struct UndirectedEdge;#[derive(Clone,Copy,Debug,Default,Eq,PartialEq,Ord,PartialOrd,Hash)]pub struct BidirectionalEdge;#[derive(Clone,Copy,Debug,Default,Eq,PartialEq,Ord,PartialOrd,Hash)]pub struct Adjacency{pub id:usize,pub to:usize}impl Adjacency{pub fn new(id:usize,to:usize)->Adjacency{Adjacency{id,to}}}#[doc=" Static Sparse Graph represented as Compressed Sparse Row."]#[derive(Debug,Clone)]pub struct SparseGraph{vsize:usize,pub start:Vec,pub elist:Vec,pub edges:Vec<(usize,usize)>,_marker:Marker}implSparseGraph{#[doc=" Return the number of vertices."]pub fn vertices_size(&self)->usize{self.vsize}#[doc=" Return the number of edges."]pub fn edges_size(&self)->usize{self.edges.len()}#[doc=" Return an iterator over graph vertices."]pub fn vertices(&self)->ops::Range{0..self.vertices_size()}#[doc=" Return a slice of adjacency vertices."]pub fn adjacencies(&self,v:usize)->slice::Iter<'_,Adjacency>{self.elist[self.start[v]..self.start[v+1]].iter()}}pub trait SparseGraphConstruction:Sized{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph;}implSparseGraph{#[doc=" Construct graph from edges."]pub fn from_edges(vsize:usize,edges:Vec<(usize,usize)>)->Self{D::construct_graph(vsize,edges)}}impl SparseGraphConstruction for DirectedEdge{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph{let mut start:Vec<_>=vec![0usize;vsize+1];for(from,_)in edges.iter().cloned(){start[from]+=1;}for i in 1..=vsize{start[i]+=start[i-1];}let mut elist=Vec::::with_capacity(edges.len());let ptr=elist.as_mut_ptr();for(id,(from,to))in edges.iter().cloned().enumerate(){start[from]-=1;unsafe{ptr.add(start[from]).write(Adjacency::new(id,to))};}unsafe{elist.set_len(edges.len())};SparseGraph{vsize,start,elist,edges,_marker:PhantomData}}}impl SparseGraphConstruction for UndirectedEdge{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph{let mut start:Vec<_>=vec![0usize;vsize+1];for(from,to)in edges.iter().cloned(){start[to]+=1;start[from]+=1;}for i in 1..=vsize{start[i]+=start[i-1];}let mut elist=Vec::::with_capacity(edges.len()*2);let ptr=elist.as_mut_ptr();for(id,(from,to))in edges.iter().cloned().enumerate(){start[from]-=1;unsafe{ptr.add(start[from]).write(Adjacency::new(id,to))};start[to]-=1;unsafe{ptr.add(start[to]).write(Adjacency::new(id,from))};}unsafe{elist.set_len(edges.len()*2)};SparseGraph{vsize,start,elist,edges,_marker:PhantomData}}}impl SparseGraphConstruction for BidirectionalEdge{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph{let mut start:Vec<_>=vec![0usize;vsize+1];for(from,to)in edges.iter().cloned(){start[to]+=1;start[from]+=1;}for i in 1..=vsize{start[i]+=start[i-1];}let mut elist=Vec::::with_capacity(edges.len()*2);let ptr=elist.as_mut_ptr();for(id,(from,to))in edges.iter().cloned().enumerate(){start[from]-=1;unsafe{ptr.add(start[from]).write(Adjacency::new(id*2,to))};start[to]-=1;unsafe{ptr.add(start[to]).write(Adjacency::new(id*2+1,from))};}unsafe{elist.set_len(edges.len()*2)};SparseGraph{vsize,start,elist,edges,_marker:PhantomData}}}pub type DirectedSparseGraph=SparseGraph;pub type UndirectedSparseGraph=SparseGraph;pub type BidirectionalSparseGraph=SparseGraph;pub struct SparseGraphScanner,T:IterScan,D>{vsize:usize,esize:usize,_marker:Marker<(U,T,D)>}impl,T:IterScan,D>SparseGraphScanner{pub fn new(vsize:usize,esize:usize)->Self{Self{vsize,esize,_marker:PhantomData}}}impl,T:IterScan,D:SparseGraphConstruction>MarkedIterScan for SparseGraphScanner{type Output=(SparseGraph,Vec<::Output>);fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{let mut edges=Vec::with_capacity(self.esize);let mut rest=Vec::with_capacity(self.esize);for _ in 0..self.esize{edges.push((U::scan(iter)?,U::scan(iter)?));rest.push(T::scan(iter)?);}let graph=SparseGraph::from_edges(self.vsize,edges);Some((graph,rest))}}pub type DirectedGraphScanner=SparseGraphScanner;pub type UndirectedGraphScanner=SparseGraphScanner;pub type BidirectionalGraphScanner=SparseGraphScanner;pub struct TreeGraphScanner,T:IterScan=()>{vsize:usize,_marker:Marker<(U,T)>}impl,T:IterScan>TreeGraphScanner{pub fn new(vsize:usize)->Self{Self{vsize,_marker:PhantomData}}}impl,T:IterScan>MarkedIterScan for TreeGraphScanner{type Output=(UndirectedSparseGraph,Vec<::Output>);fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{UndirectedGraphScanner::::new(self.vsize,self.vsize-1).mscan(iter)}}} pub use self::strongly_connected_component::StronglyConnectedComponent; mod strongly_connected_component{use super::DirectedSparseGraph;#[derive(Debug,Clone)]pub struct StronglyConnectedComponent<'a>{graph:&'a DirectedSparseGraph,visited:Vec,csize:usize,low:Vec,ord:Vec,comp:Vec}impl std::ops::Indexfor StronglyConnectedComponent<'_>{type Output=usize;fn index(&self,index:usize)->&Self::Output{&self.comp[index]}}impl<'a>StronglyConnectedComponent<'a>{pub fn new(graph:&'a DirectedSparseGraph)->Self{let mut now_ord=0;let mut self_=Self{graph,csize:0,visited:Vec::with_capacity(graph.vertices_size()),low:vec![0;graph.vertices_size()],ord:vec![std::usize::MAX;graph.vertices_size()],comp:vec![0;graph.vertices_size()]};for u in graph.vertices(){if self_.ord[u]==std::usize::MAX{self_.dfs(u,&mut now_ord);}}for x in self_.comp.iter_mut(){*x=self_.csize-1-*x;}self_}}impl StronglyConnectedComponent<'_>{fn dfs(&mut self,u:usize,now_ord:&mut usize){self.low[u]=*now_ord;self.ord[u]=*now_ord;*now_ord+=1;self.visited.push(u);for a in self.graph.adjacencies(u){if self.ord[a.to]==std::usize::MAX{self.dfs(a.to,now_ord);self.low[u]=self.low[u].min(self.low[a.to]);}else{self.low[u]=self.low[u].min(self.ord[a.to]);}}if self.low[u]==self.ord[u]{while let Some(v)=self.visited.pop(){self.ord[v]=self.graph.vertices_size();self.comp[v]=self.csize;if v==u{break;}}self.csize+=1;}}pub fn gen_cgraph(&self)->DirectedSparseGraph{let mut used=std::collections::HashSet::new();let mut edges=vec![];for u in self.graph.vertices(){for a in self.graph.adjacencies(u){if self.comp[u]!=self.comp[a.to]{let(x,y)=(self.comp[u],self.comp[a.to]);if!used.contains(&(x,y)){used.insert((x,y));edges.push((x,y));}}}}DirectedSparseGraph::from_edges(self.size(),edges)}pub fn components(&self)->Vec>{let mut counts=vec![0;self.size()];for&x in self.comp.iter(){counts[x]+=1;}let mut groups=vec![vec![];self.size()];for(g,c)in groups.iter_mut().zip(counts.into_iter()){g.reserve(c);}for u in self.graph.vertices(){groups[self[u]].push(u);}groups}pub fn has_loop(&self)->bool{self.graph.vertices_size()!=self.csize}pub fn size(&self)->usize{self.csize}}}