pub fn main() {
    crate::prepare!();
    sc!(n, m, l, e: [(Usize1, Usize1); l]);
    let dm = dulmage_mendelsohn_decomposition(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" });
    }
}
#[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!`, `dg!`))"]#[doc=" - `prepare!(?);`: interactive (line scanner (`scln!`) + buf print (`pp!`, `dg!`))"]#[macro_export]macro_rules!prepare{(@output($dol:tt))=>{#[allow(unused_imports)]use std::io::Write as _;let __out=std::io::stdout();#[allow(unused_mut,unused_variables)]let mut __out=std::io::BufWriter::new(__out.lock());#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stdout."]macro_rules!pp{($dol($dol t:tt)*)=>{$dol crate::iter_print!(__out,$dol($dol t)*)}}#[cfg(debug_assertions)]#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stderr. Do nothing in release mode."]macro_rules!dg{($dol($dol t:tt)*)=>{{#[allow(unused_imports)]use std::io::Write as _;let __err=std::io::stderr();#[allow(unused_mut,unused_variables)]let mut __err=std::io::BufWriter::new(__err.lock());$dol crate::iter_print!(__err,$dol($dol t)*);let _=__err.flush();}}}#[cfg(not(debug_assertions))]#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stderr. Do nothing in release mode."]macro_rules!dg{($dol($dol t:tt)*)=>{}}};(@normal($dol:tt))=>{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($dol:tt))=>{#[allow(unused_macros)]#[doc=" Scan a line, and previous line will be truncated in the next call."]macro_rules!scln{($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)*)}}};()=>{$crate::prepare!(@output($));$crate::prepare!(@normal($))};(?)=>{$crate::prepare!(@output($));$crate::prepare!(@interactive($))};}}
pub use self::iter_print::IterPrint;
mod iter_print{use std::{fmt::Display,io::{Error,Write}};pub trait IterPrint{fn iter_print<W,S>(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<W,S>(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=" - `@ns`: alias for `@sep \"\"`"]#[doc=" - `@lf`: alias for `@sep '\\n'`"]#[doc=" - `@sp`: alias for `@sep ' '`"]#[doc=" - `@fmt $lit => {$($expr),*}`: print `format!($lit, $($expr),*)`"]#[doc=" - `@flush`: flush writer (auto insert `!`)"]#[doc=" - `@it $expr`: print iterator"]#[doc=" - `@it2d $expr`: print 2d-iterator"]#[doc=" - `@tup $expr`: print tuple (need to import [`IterPrint`])"]#[doc=" - `@ittup $expr`: print iterative tuple (need to import [`IterPrint`])"]#[doc=" - `$expr`: print expr"]#[doc=" - `{ args... }`: scoped"]#[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!($writer).expect("io error");};(@@it$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,$sep,false,item);}}};(@@it2d$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@it$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@it$writer,$sep,true,item);}};(@@tup$writer:expr,$sep:expr,$is_head:expr,$tuple:expr)=>{IterPrint::iter_print($tuple,&mut$writer,$sep,$is_head).expect("io error");};(@@ittup$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@tup$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@tup$writer,$sep,true,item);}};(@@assert_tag item)=>{};(@@assert_tag it)=>{};(@@assert_tag it2d)=>{};(@@assert_tag tup)=>{};(@@assert_tag ittup)=>{};(@@assert_tag$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,@ns$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,"",$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@lf$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,'\n',$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@sp$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,' ',$is_head,$($t)*);};(@@inner$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,!$(,)?)=>{};(@@inner$writer:expr,$sep:expr,$is_head:expr,!$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,)=>{$crate::iter_print!(@@line_feed$writer);};(@@inner$writer:expr,$sep:expr,$is_head:expr,{$($t:tt)*}$($rest:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*,!);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($rest)*);};(@@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::{from_fn,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<Item=&'a str>>(iter:&mut I)->Option<Self::Output>;}pub trait MarkedIterScan:Sized{type Output;fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>;}#[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<T>(&mut self)-><T as IterScan>::Output where T:IterScan{<T as IterScan>::scan(&mut self.iter).expect("scan error")}#[inline]pub fn mscan<T>(&mut self,marker:T)-><T as MarkedIterScan>::Output where T:MarkedIterScan{marker.mscan(&mut self.iter).expect("scan error")}#[inline]pub fn scan_vec<T>(&mut self,size:usize)->Vec<<T as IterScan>::Output>where T:IterScan{(0..size).map(|_|<T as IterScan>::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<Item=&'a str>>(iter:&mut I)->Option<Self>{iter.next()?.parse::<$t>().ok()}})*};}iter_scan_impls!(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String);macro_rules!iter_scan_tuple_impl{(@impl$($T:ident)*)=>{impl<$($T:IterScan),*>IterScan for($($T,)*){type Output=($(<$T as IterScan>::Output,)*);#[inline]fn scan<'a,It:Iterator<Item=&'a str>>(_iter:&mut It)->Option<Self::Output>{Some(($(<$T as IterScan>::scan(_iter)?,)*))}}};(@inner$($T:ident)*,)=>{iter_scan_tuple_impl!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{iter_scan_tuple_impl!(@impl$($T)*);iter_scan_tuple_impl!(@inner$($T)*$U,$($Rest)*);};($($T:ident)*)=>{iter_scan_tuple_impl!(@inner,$($T)*);};}iter_scan_tuple_impl!(A B C D E F G H I J K);pub struct ScannerIter<'a,'b,T>{inner:&'b mut Scanner<'a>,_marker:std::marker::PhantomData<fn()->T>}impl<'a,'b,T>Iterator for ScannerIter<'a,'b,T>where T:IterScan{type Item=<T as IterScan>::Output;#[inline]fn next(&mut self)->Option<Self::Item>{<T as IterScan>::scan(&mut self.inner.iter)}}#[doc=" - `scan_value!(scanner, ELEMENT)`"]#[doc=""]#[doc=" ELEMENT :="]#[doc=" - `$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($len).collect::<Vec<_>>())?};(@tuple$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 enum Usize1{}impl IterScan for Usize1{type Output=usize;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{<usize as IterScan>::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<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{Some((<char as IterScan>::scan(iter)?as u8-self.0 as u8)as usize)}}#[derive(Debug,Copy,Clone)]pub enum Chars{}impl IterScan for Chars{type Output=Vec<char>;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{Some(iter.next()?.chars().collect())}}#[derive(Debug,Copy,Clone)]pub struct CharsWithBase(pub char);impl MarkedIterScan for CharsWithBase{type Output=Vec<usize>;#[inline]fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{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<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{Some((<char as IterScan>::scan(iter)?as u8-self.0)as usize)}}#[derive(Debug,Copy,Clone)]pub enum Bytes{}impl IterScan for Bytes{type Output=Vec<u8>;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{Some(iter.next()?.bytes().collect())}}#[derive(Debug,Copy,Clone)]pub struct BytesWithBase(pub u8);impl MarkedIterScan for BytesWithBase{type Output=Vec<usize>;#[inline]fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{Some(iter.next()?.bytes().map(|c|(c-self.0)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub struct Collect<T,B=Vec<<T as IterScan>::Output>>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{size:usize,_marker:PhantomData<fn()->(T,B)>}impl<T,B>Collect<T,B>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{pub fn new(size:usize)->Self{Self{size,_marker:PhantomData}}}impl<T,B>MarkedIterScan for Collect<T,B>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{type Output=B;#[inline]fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{repeat_with(||<T as IterScan>::scan(iter)).take(self.size).collect()}}#[derive(Debug,Copy,Clone)]pub struct SizedCollect<T,B=Vec<<T as IterScan>::Output>>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{_marker:PhantomData<fn()->(T,B)>}impl<T,B>IterScan for SizedCollect<T,B>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{type Output=B;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{let size=usize::scan(iter)?;repeat_with(||<T as IterScan>::scan(iter)).take(size).collect()}}#[derive(Debug,Copy,Clone)]pub struct Splitted<T,P>where T:IterScan{pat:P,_marker:PhantomData<fn()->T>}impl<T,P>Splitted<T,P>where T:IterScan{pub fn new(pat:P)->Self{Self{pat,_marker:PhantomData}}}impl<T>MarkedIterScan for Splitted<T,char>where T:IterScan{type Output=Vec<<T as IterScan>::Output>;fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{let mut iter=iter.next()?.split(self.pat);Some(from_fn(||<T as IterScan>::scan(&mut iter)).collect())}}impl<T>MarkedIterScan for Splitted<T,&str>where T:IterScan{type Output=Vec<<T as IterScan>::Output>;fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{let mut iter=iter.next()?.split(self.pat);Some(from_fn(||<T as IterScan>::scan(&mut iter)).collect())}}impl<T,F>MarkedIterScan for F where F:Fn(&str)->Option<T>{type Output=T;fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{self(iter.next()?)}}}
pub use self::dulmage_mendelsohn_decomposition::dulmage_mendelsohn_decomposition;
mod dulmage_mendelsohn_decomposition{use super::{BipartiteMatching,DirectedSparseGraph,StronglyConnectedComponent};pub fn dulmage_mendelsohn_decomposition(l:usize,r:usize,edges:&[(usize,usize)])->Vec<(Vec<usize>,Vec<usize>)>{let mut matching=vec![!0usize;l+r];let mut medges:Vec<_>=edges.iter().map(|&(u,v)|(u,v+l)).collect();for(u,v)in BipartiteMatching::from_edges(l,r,edges).maximum_matching(){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 v in&mut cmap{if*v==!0-1{*v=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}}
pub use self::bipartite_matching::BipartiteMatching;
mod bipartite_matching{use std::{collections::VecDeque,mem::swap};#[derive(Debug,Clone)]pub struct BipartiteMatching{left_size:usize,right_size:usize,left_graph:Vec<Vec<usize>>,left_match:Vec<Option<usize>>,right_match:Vec<Option<usize>>,matching_size:usize}impl BipartiteMatching{pub fn new(left_size:usize,right_size:usize)->Self{Self{left_size,right_size,left_graph:vec![vec![];left_size],left_match:vec![None;left_size],right_match:vec![None;right_size],matching_size:0}}pub fn add_edge(&mut self,l:usize,r:usize){assert!(l<self.left_size);assert!(r<self.right_size);self.left_graph[l].push(r);self.matching_size=!0;}pub fn from_edges(left_size:usize,right_size:usize,lr:&[(usize,usize)])->Self{let mut deg=vec![0usize;left_size];for&(l,_)in lr{deg[l]+=1;}let mut left_graph:Vec<_>=deg.into_iter().map(Vec::with_capacity).collect();for&(l,r)in lr{assert!(l<left_size);assert!(r<right_size);left_graph[l].push(r);}Self{left_size,right_size,left_graph,left_match:vec![None;left_size],right_match:vec![None;right_size],matching_size:!0}}pub fn hopcroft_karp(&mut self){fn bfs(bm:&mut BipartiteMatching,deq:&mut VecDeque<usize>,level:&mut[usize]){deq.clear();for(i,r)in bm.left_match.iter().enumerate(){if r.is_none(){deq.push_back(i);level[i]=0;}}while let Some(l)=deq.pop_front(){for&r in&bm.left_graph[l]{if let Some(nl)=bm.right_match[r]{if level[nl]==!0{deq.push_back(nl);level[nl]=level[l]+1;}}}}}fn dfs(bm:&mut BipartiteMatching,l:usize,level:&mut[usize],used:&mut[bool])->bool{used[l]=true;for i in 0..bm.left_graph[l].len(){let r=bm.left_graph[l][i];if let Some(nl)=bm.right_match[r]{if used[nl]||level[l]+1!=level[nl]||!dfs(bm,nl,level,used){continue;}}bm.right_match[r]=Some(l);bm.left_match[l]=Some(r);return true;}false}if self.matching_size!=!0{return;}self.matching_size=self.left_match.iter().filter(|r|r.is_some()).count();let mut used=vec![false;self.left_size];let mut level=vec![!0;self.left_size];let mut deq=VecDeque::with_capacity(self.left_size);loop{bfs(self,&mut deq,&mut level);let prev_size=self.matching_size;for l in 0..self.left_size{if self.left_match[l].is_none(){self.matching_size+=dfs(self,l,&mut level,&mut used)as usize;}}if self.matching_size==prev_size{break;}for item in level.iter_mut(){*item=!0;}for item in used.iter_mut(){*item=false;}}}pub fn kuhn_multi_start_bfs(&mut self){if self.matching_size!=!0{return;}self.matching_size=self.left_match.iter().filter(|r|r.is_some()).count();let mut deq=VecDeque::with_capacity(self.left_size);let mut prev=vec![!0usize;self.left_size];let mut root=vec![!0usize;self.left_size];loop{let mut changed=false;for(l,r)in self.left_match.iter().enumerate(){if r.is_none(){root[l]=l;deq.push_back(l);}}while let Some(mut l)=deq.pop_front(){if self.left_match[root[l]].is_some(){continue;}for mut r in self.left_graph[l].iter().cloned(){if let Some(nl)=self.right_match[r]{if prev[nl]==!0{prev[nl]=l;root[nl]=root[l];deq.push_back(nl);}}else{loop{self.right_match[r]=Some(l);if let Some(nr)=&mut self.left_match[l]{swap(nr,&mut r);l=prev[l];}else{self.left_match[l]=Some(r);break;}}changed=true;self.matching_size+=1;break;}}}if!changed{break;}for item in prev.iter_mut(){*item=!0;}for item in root.iter_mut(){*item=!0;}}}pub fn maximum_matching(&mut self)->Vec<(usize,usize)>{self.kuhn_multi_start_bfs();self.left_match.iter().enumerate().filter_map(|(l,r)|r.map(|r|(l,r))).collect()}pub fn minimum_edge_cover(&mut self)->Vec<(usize,usize)>{self.kuhn_multi_start_bfs();let mut res=Vec::with_capacity(self.left_size+self.right_size-self.matching_size);let mut left_used:Vec<_>=self.left_match.iter().map(Option::is_some).collect();let mut right_used:Vec<_>=self.right_match.iter().map(Option::is_some).collect();for(l,lg)in self.left_graph.iter().enumerate(){if let Some(r)=self.left_match[l]{res.push((l,r));}for&r in lg{if!left_used[l]||!right_used[r]{left_used[l]=true;right_used[r]=true;res.push((l,r));}}}res}fn reachable(&mut self)->(Vec<bool>,Vec<bool>){#[derive(Clone,Copy)]enum Either{Left(usize),Right(usize)}self.kuhn_multi_start_bfs();let mut left_used=vec![false;self.left_size];let mut right_used=vec![false;self.right_size];let mut deq=VecDeque::new();for(l,r)in self.left_match.iter().enumerate(){if r.is_none(){left_used[l]=true;deq.push_back(Either::Left(l));}}loop{match deq.pop_front(){Some(Either::Left(l))=>{for&r in&self.left_graph[l]{if self.left_match[l]!=Some(r)&&!right_used[r]{right_used[r]=true;deq.push_back(Either::Right(r));}}}Some(Either::Right(r))=>{if let Some(l)=self.right_match[r]{if!left_used[l]{left_used[l]=true;deq.push_back(Either::Left(l));}}}None=>break,}}(left_used,right_used)}pub fn minimum_vertex_cover(&mut self)->(Vec<usize>,Vec<usize>){let(left_used,right_used)=self.reachable();(left_used.into_iter().enumerate().filter_map(|(l,b)|if!b{Some(l)}else{None}).collect(),right_used.into_iter().enumerate().filter_map(|(r,b)|if b{Some(r)}else{None}).collect())}pub fn maximum_independent_set(&mut self)->(Vec<usize>,Vec<usize>){let(left_used,right_used)=self.reachable();(left_used.into_iter().enumerate().filter_map(|(l,b)|if b{Some(l)}else{None}).collect(),right_used.into_iter().enumerate().filter_map(|(r,b)|if!b{Some(r)}else{None}).collect())}}}
pub use self::sparse_graph::*;
mod sparse_graph{use super::{IterScan,MarkedIterScan};use std::{marker::PhantomData,ops,slice};type Marker<T>=PhantomData<fn()->T>;#[derive(Clone,Copy,Debug,Eq,PartialEq,Ord,PartialOrd,Hash)]pub enum DirectedEdge{}#[derive(Clone,Copy,Debug,Eq,PartialEq,Ord,PartialOrd,Hash)]pub enum UndirectedEdge{}#[derive(Clone,Copy,Debug,Eq,PartialEq,Ord,PartialOrd,Hash)]pub enum 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<D>{vsize:usize,pub start:Vec<usize>,pub elist:Vec<Adjacency>,pub edges:Vec<(usize,usize)>,_marker:Marker<D>}impl<D>SparseGraph<D>{#[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<usize>{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<Self>;}impl<D:SparseGraphConstruction>SparseGraph<D>{#[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<Self>{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::<Adjacency>::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<Self>{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::<Adjacency>::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<Self>{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::<Adjacency>::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<DirectedEdge>;pub type UndirectedSparseGraph=SparseGraph<UndirectedEdge>;pub type BidirectionalSparseGraph=SparseGraph<BidirectionalEdge>;pub struct SparseGraphScanner<U:IterScan<Output=usize>,T:IterScan,D>{vsize:usize,esize:usize,_marker:Marker<(U,T,D)>}impl<U:IterScan<Output=usize>,T:IterScan,D>SparseGraphScanner<U,T,D>{pub fn new(vsize:usize,esize:usize)->Self{Self{vsize,esize,_marker:PhantomData}}}impl<U:IterScan<Output=usize>,T:IterScan,D:SparseGraphConstruction>MarkedIterScan for SparseGraphScanner<U,T,D>{type Output=(SparseGraph<D>,Vec<<T as IterScan>::Output>);fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{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<U,T=()>=SparseGraphScanner<U,T,DirectedEdge>;pub type UndirectedGraphScanner<U,T=()>=SparseGraphScanner<U,T,UndirectedEdge>;pub type BidirectionalGraphScanner<U,T=()>=SparseGraphScanner<U,T,BidirectionalEdge>;pub struct TreeGraphScanner<U:IterScan<Output=usize>,T:IterScan=()>{vsize:usize,_marker:Marker<(U,T)>}impl<U:IterScan<Output=usize>,T:IterScan>TreeGraphScanner<U,T>{pub fn new(vsize:usize)->Self{Self{vsize,_marker:PhantomData}}}impl<U:IterScan<Output=usize>,T:IterScan>MarkedIterScan for TreeGraphScanner<U,T>{type Output=(UndirectedSparseGraph,Vec<<T as IterScan>::Output>);fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{UndirectedGraphScanner::<U,T>::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<usize>,csize:usize,low:Vec<usize>,ord:Vec<usize>,comp:Vec<usize>}impl std::ops::Index<usize>for 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<Vec<usize>>{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}}}