pub fn solve() {
    crate::prepare!();
    sc!(n, m, es: [(Usize1, @|s: &str| Some(s == "<==>"), Usize1); m]);
    let mut ts = TwoSatisfiability::new(n);
    for (i, b, j) in es {
        if b {
            ts.add_clause(i, true, j, false);
            ts.add_clause(i, false, j, true);
        } else {
            ts.add_clause(i, true, j, true);
            ts.add_clause(i, false, j, false);
        }
    }
    if let Some(mut bs) = ts.two_satisfiability() {
        if (0..n).filter(|&i| bs[i]).count() * 2 < n {
            for b in &mut bs {
                *b ^= true;
            }
        }
        pp!("Yes");
        let ans: Vec<_> = (0..n).filter(|&i| bs[i]).collect();
        pp!(ans.len(); @it1 ans);
    } else {
        pp!("No");
    }
}
crate::main!();
#[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]#[allow(clippy::crate_in_macro_def)]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)*)}}};()=>{$crate::prepare!(@output($));$crate::prepare!(@normal($))};(?)=>{$crate::prepare!(@output($));$crate::prepare!(@interactive($))};}#[macro_export]macro_rules!main{()=>{fn main(){solve();}};(avx2)=>{fn main(){#[target_feature(enable="avx2")]unsafe fn solve_avx2(){solve();}unsafe{solve_avx2()}}};(large_stack)=>{fn main(){const STACK_SIZE:usize=512*1024*1024;::std::thread::Builder::new().stack_size(STACK_SIZE).spawn(solve).unwrap().join().unwrap();}};}}
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!impl_iter_print_tuple{(@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)*)=>{impl_iter_print_tuple!(@impl,);impl_iter_print_tuple!(@inc$C$c,,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,$C:ident$c:ident$($D:ident$d:ident)*)=>{impl_iter_print_tuple!(@impl$A$a,$($B$b)*);impl_iter_print_tuple!(@inc$A$a,$($B$b)*$C$c,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,)=>{impl_iter_print_tuple!(@impl$A$a,$($B$b)*);};($($t:tt)*)=>{impl_iter_print_tuple!(@inc,,$($t)*);};}impl_iter_print_tuple!(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=" - `@it1 $expr`: print iterator as 1-indexed"]#[doc=" - `@cw ($char $expr)`: print iterator as `(elem as u8 + $char as u8) as char`"]#[doc=" - `@bw ($byte $expr)`: print iterator as `(elem as u8 + $byte) as char`"]#[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);}}};(@@it1$writer:expr,$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,$is_head,item+1);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,item+1);}}};(@@cw$writer:expr,$sep:expr,$is_head:expr,($ch:literal$iter:expr))=>{{let mut iter=$iter.into_iter();let b=$ch as u8;if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,(item as u8+b)as char);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,(item as u8+b)as char);}}};(@@bw$writer:expr,$sep:expr,$is_head:expr,($b:literal$iter:expr))=>{{let mut iter=$iter.into_iter();let b:u8=$b;if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,(item as u8+b)as char);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,(item as u8+b)as char);}}};(@@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 it1)=>{};(@@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,$is_head:expr,@fmt$arg:tt$($t:tt)*)=>{$crate::iter_print!(@@fmt$writer,$sep,$is_head,$arg);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@cw$arg:tt$($t:tt)*)=>{$crate::iter_print!(@@cw$writer,$sep,$is_head,$arg);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@bw$arg:tt$($t:tt)*)=>{$crate::iter_print!(@@bw$writer,$sep,$is_head,$arg);$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)*);}};}}
mod array{#[macro_export]macro_rules!array{[@inner$data:ident=[$init:expr;$len:expr]]=>{{use::std::mem::{ManuallyDrop,MaybeUninit};let mut$data:[MaybeUninit<_>;$len]=unsafe{MaybeUninit::uninit().assume_init()};$init;#[repr(C)]union __Transmuter<const N:usize,T:Clone>{src:ManuallyDrop<[MaybeUninit<T>;N]>,dst:ManuallyDrop<[T;N]>,}ManuallyDrop::into_inner(unsafe{__Transmuter{src:ManuallyDrop::new($data)}.dst})}};[||$e:expr;$len:expr]=>{$crate::array![@inner data=[data.iter_mut().for_each(|item|*item=MaybeUninit::new($e));$len]]};[|$i:pat_param|$e:expr;$len:expr]=>{$crate::array![@inner data=[data.iter_mut().enumerate().for_each(|($i,item)|*item=MaybeUninit::new($e));$len]]};[$e:expr;$len:expr]=>{{let e=$e;$crate::array![||Clone::clone(&e);$len]}};}}
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!impl_iter_scan{($($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::<$t>().ok()}})*};}impl_iter_scan!(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String);macro_rules!impl_iter_scan_tuple{(@impl$($T:ident)*)=>{impl<$($T:IterScan),*>IterScan for($($T,)*){type Output=($(<$T as IterScan>::Output,)*);#[inline]fn scan<'a,It:Iterator<Item=&'a str>>(_iter:&mut It)->Option<Self::Output>{Some(($(<$T as IterScan>::scan(_iter)?,)*))}}};(@inner$($T:ident)*,)=>{impl_iter_scan_tuple!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{impl_iter_scan_tuple!(@impl$($T)*);impl_iter_scan_tuple!(@inner$($T)*$U,$($Rest)*);};($($T:ident)*)=>{impl_iter_scan_tuple!(@inner,$($T)*);};}impl_iter_scan_tuple!(A B C D E F G H I J K);pub struct ScannerIter<'a,'b,T>{inner:&'b mut Scanner<'a>,_marker:std::marker::PhantomData<fn()->T>}impl<'a,'b,T>Iterator for ScannerIter<'a,'b,T>where T:IterScan{type Item=<T as IterScan>::Output;#[inline]fn next(&mut self)->Option<Self::Item>{<T as IterScan>::scan(&mut self.inner.iter)}}#[doc=" scan a value with Scanner"]#[doc=""]#[doc=" - `scan_value!(scanner, ELEMENT)`"]#[doc=""]#[doc=" ELEMENT :="]#[doc=" - `$ty`: IterScan"]#[doc=" - `@$expr`: MarkedIterScan"]#[doc=" - `[ELEMENT; $expr]`: vector"]#[doc=" - `[ELEMENT; const $expr]`: array"]#[doc=" - `[ELEMENT]`: iterator"]#[doc=" - `($(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($len).collect::<Vec<_>>())?};(@array$scanner:expr,[$($t:tt)*]$len:expr)=>{$crate::array![||$crate::scan_value!(@inner$scanner,[]$($t)*);$len]};(@tuple$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;const$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@array$scanner,[@$e]$len)]]$($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$scanner:expr,[$($args:tt)*][[$($tt:tt)*];const$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@array$scanner,[[$($tt)*]]$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$scanner:expr,[$($args:tt)*][($($tt:tt)*);const$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@array$scanner,[($($tt)*)]$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;const$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@array$scanner,[$ty]$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 and bind values with Scanner"]#[doc=""]#[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 enum Byte1{}impl IterScan for Byte1{type Output=u8;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{let bytes=iter.next()?.as_bytes();assert_eq!(bytes.len(),1);Some(bytes[0])}}#[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::two_satisfiability::TwoSatisfiability;
mod two_satisfiability{use super::{DirectedSparseGraph,StronglyConnectedComponent};#[derive(Debug,Clone)]pub struct TwoSatisfiability{vsize:usize,edges:Vec<(usize,usize)>}impl TwoSatisfiability{pub fn new(vsize:usize)->Self{Self{vsize,edges:Vec::new()}}#[doc=" (p_x = f) | (p_y = g)"]pub fn add_clause(&mut self,x:usize,f:bool,y:usize,g:bool){self.edges.push((2*x+f as usize,2*y+!g as usize));self.edges.push((2*y+g as usize,2*x+!f as usize));}pub fn add_or(&mut self,x:usize,y:usize){self.add_clause(x,true,y,true);}pub fn add_nand(&mut self,x:usize,y:usize){self.add_clause(x,false,y,false);}pub fn set_true(&mut self,x:usize){self.edges.push((2*x+1,2*x));}pub fn set_false(&mut self,x:usize){self.edges.push((2*x,2*x+1));}pub fn two_satisfiability(self)->Option<Vec<bool>>{let graph=DirectedSparseGraph::from_edges(self.vsize*2,self.edges);let scc=StronglyConnectedComponent::new(&graph);let mut res=vec![false;self.vsize];for i in 0..self.vsize{if scc[i*2]==scc[i*2+1]{return None;}res[i]=scc[i*2]>scc[i*2+1];}Some(res)}}}
pub use self::graph_base::*;
mod graph_base{use std::marker::PhantomData;pub trait GraphBase<'g>{type VIndex:Copy+Eq;}pub trait EIndexedGraph<'g>:GraphBase<'g>{type EIndex:Copy+Eq;}pub trait VertexSize<'g>:GraphBase<'g>{fn vsize(&'g self)->usize;}pub trait EdgeSize<'g>:GraphBase<'g>{fn esize(&'g self)->usize;}pub trait Vertices<'g>:GraphBase<'g>{type VIter:'g+Iterator<Item=Self::VIndex>;fn vertices(&'g self)->Self::VIter;}pub trait Edges<'g>:EIndexedGraph<'g>{type EIter:'g+Iterator<Item=Self::EIndex>;fn edges(&'g self)->Self::EIter;}pub trait AdjacencyIndex{type VIndex:Copy+Eq;fn vindex(&self)->Self::VIndex;}pub trait Adjacencies<'g>:GraphBase<'g>{type AIndex:'g+AdjacencyIndex<VIndex=Self::VIndex>;type AIter:'g+Iterator<Item=Self::AIndex>;fn adjacencies(&'g self,vid:Self::VIndex)->Self::AIter;}pub trait AdjacenciesWithEindex<'g>:EIndexedGraph<'g>{type AIndex:'g+AdjacencyIndexWithEindex<VIndex=Self::VIndex,EIndex=Self::EIndex>;type AIter:'g+Iterator<Item=Self::AIndex>;fn adjacencies_with_eindex(&'g self,vid:Self::VIndex)->Self::AIter;}pub trait AdjacencyIndexWithEindex:AdjacencyIndex{type EIndex:Copy+Eq;fn eindex(&self)->Self::EIndex;}pub trait AdjacencyIndexWithValue:AdjacencyIndex{type AValue:Clone;fn avalue(&self)->Self::AValue;}pub trait AdjacenciesWithValue<'g,T>:GraphBase<'g>where T:Clone{type AIndex:'g+AdjacencyIndexWithValue<VIndex=Self::VIndex,AValue=T>;type AIter:'g+Iterator<Item=Self::AIndex>;fn adjacencies_with_value(&'g self,vid:Self::VIndex)->Self::AIter;}impl AdjacencyIndex for usize{type VIndex=usize;fn vindex(&self)->Self::VIndex{*self}}impl<V,E>AdjacencyIndex for(V,E)where V:Copy+Eq,E:Copy+Eq{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}impl<V,E>AdjacencyIndexWithEindex for(V,E)where V:Copy+Eq,E:Copy+Eq{type EIndex=E;fn eindex(&self)->Self::EIndex{self.1}}#[derive(Debug,Clone,Copy,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct VIndex<V>(V);#[derive(Debug,Clone,Copy,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct VIndexWithEIndex<V,E>(V,E);#[derive(Debug,Clone,Copy,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct VIndexWithValue<V,T>(V,T);#[derive(Debug,Clone,Copy,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct VIndexWithEIndexValue<V,E,T>(V,E,T);impl<V>AdjacencyIndex for VIndex<V>where V:Eq+Copy{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}impl<V,E>AdjacencyIndex for VIndexWithEIndex<V,E>where V:Eq+Copy{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}impl<V,E>AdjacencyIndexWithEindex for VIndexWithEIndex<V,E>where V:Eq+Copy,E:Eq+Copy{type EIndex=E;fn eindex(&self)->Self::EIndex{self.1}}impl<V,T>AdjacencyIndex for VIndexWithValue<V,T>where V:Eq+Copy{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}impl<V,T>AdjacencyIndexWithValue for VIndexWithValue<V,T>where V:Eq+Copy,T:Clone{type AValue=T;fn avalue(&self)->Self::AValue{self.1 .clone()}}impl<V,E,T>AdjacencyIndex for VIndexWithEIndexValue<V,E,T>where V:Eq+Copy{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}impl<V,E,T>AdjacencyIndexWithEindex for VIndexWithEIndexValue<V,E,T>where V:Eq+Copy,E:Eq+Copy{type EIndex=E;fn eindex(&self)->Self::EIndex{self.1}}impl<V,E,T>AdjacencyIndexWithValue for VIndexWithEIndexValue<V,E,T>where V:Eq+Copy,T:Clone{type AValue=T;fn avalue(&self)->Self::AValue{self.2 .clone()}}impl<V>From<V>for VIndex<V>{fn from(vid:V)->Self{VIndex(vid)}}impl<V,E>From<(V,E)>for VIndexWithEIndex<V,E>{fn from((vid,eid):(V,E))->Self{VIndexWithEIndex(vid,eid)}}impl<V,T>From<(V,T)>for VIndexWithValue<V,T>{fn from((vid,value):(V,T))->Self{VIndexWithValue(vid,value)}}impl<V,E,T>From<(V,E,T)>for VIndexWithEIndexValue<V,E,T>{fn from((vid,eid,value):(V,E,T))->Self{VIndexWithEIndexValue(vid,eid,value)}}impl<V,T>VIndexWithValue<V,T>{pub fn map<U,F>(self,mut f:F)->VIndexWithValue<V,U>where F:FnMut(T)->U{VIndexWithValue(self.0,f(self.1))}}impl<V,E,T>VIndexWithEIndexValue<V,E,T>{pub fn map<U,F>(self,mut f:F)->VIndexWithEIndexValue<V,E,U>where F:FnMut(T)->U{VIndexWithEIndexValue(self.0,self.1,f(self.2))}}pub trait VertexMap<'g,T>:GraphBase<'g>{type Vmap;fn construct_vmap<F>(&self,f:F)->Self::Vmap where F:FnMut()->T;fn vmap_get<'a>(&self,map:&'a Self::Vmap,vid:Self::VIndex)->&'a T;fn vmap_get_mut<'a>(&self,map:&'a mut Self::Vmap,vid:Self::VIndex)->&'a mut T;fn vmap_set(&self,map:&mut Self::Vmap,vid:Self::VIndex,x:T){*self.vmap_get_mut(map,vid)=x;}}pub trait VertexView<'g,M,T>:GraphBase<'g>where M:?Sized{fn vview(&self,map:&M,vid:Self::VIndex)->T;}pub trait EdgeMap<'g,T>:EIndexedGraph<'g>{type Emap;fn construct_emap<F>(&self,f:F)->Self::Emap where F:FnMut()->T;fn emap_get<'a>(&self,map:&'a Self::Emap,eid:Self::EIndex)->&'a T;fn emap_get_mut<'a>(&self,map:&'a mut Self::Emap,eid:Self::EIndex)->&'a mut T;fn emap_set(&self,map:&mut Self::Emap,eid:Self::EIndex,x:T){*self.emap_get_mut(map,eid)=x;}}pub trait EdgeView<'g,M,T>:EIndexedGraph<'g>where M:?Sized{fn eview(&self,map:&M,eid:Self::EIndex)->T;}impl<'g,G,F,T>VertexView<'g,F,T>for G where G:GraphBase<'g>,F:Fn(Self::VIndex)->T{fn vview(&self,map:&F,vid:Self::VIndex)->T{(map)(vid)}}impl<'g,G,F,T>EdgeView<'g,F,T>for G where G:EIndexedGraph<'g>,F:Fn(Self::EIndex)->T{fn eview(&self,map:&F,eid:Self::EIndex)->T{(map)(eid)}}pub trait AdjacencyView<'g,'a,M,T>:GraphBase<'g>where M:?Sized{type AViewIter:Iterator<Item=VIndexWithValue<Self::VIndex,T>>;fn aviews(&'g self,map:&'a M,vid:Self::VIndex)->Self::AViewIter;}pub struct AdjacencyViewIterFromEindex<'g,'a,G,M,T>where G:AdjacenciesWithEindex<'g>{iter:G::AIter,g:&'g G,map:&'a M,_marker:PhantomData<fn()->T>}impl<'g,'a,G,M,T>AdjacencyViewIterFromEindex<'g,'a,G,M,T>where G:AdjacenciesWithEindex<'g>{pub fn new(iter:G::AIter,g:&'g G,map:&'a M)->Self{Self{iter,g,map,_marker:PhantomData}}}impl<'g,'a,G,M,T>Iterator for AdjacencyViewIterFromEindex<'g,'a,G,M,T>where G:'g+AdjacenciesWithEindex<'g>+EdgeView<'g,M,T>,M:'a{type Item=VIndexWithValue<G::VIndex,T>;fn next(&mut self)->Option<Self::Item>{self.iter.next().map(|adj|(adj.vindex(),self.g.eview(self.map,adj.eindex())).into())}}pub struct AdjacencyViewIterFromValue<'g,'a,G,M,T,U>where G:AdjacenciesWithValue<'g,T>,T:Clone{iter:G::AIter,map:&'a M,_marker:PhantomData<fn()->U>}impl<'g,'a,G,M,T,U>AdjacencyViewIterFromValue<'g,'a,G,M,T,U>where G:AdjacenciesWithValue<'g,T>,T:Clone{pub fn new(iter:G::AIter,map:&'a M)->Self{Self{iter,map,_marker:PhantomData}}}impl<'g,'a,G,M,T,U>Iterator for AdjacencyViewIterFromValue<'g,'a,G,M,T,U>where G:'g+AdjacenciesWithValue<'g,T>,T:Clone,M:'a+Fn(T)->U{type Item=VIndexWithValue<G::VIndex,U>;fn next(&mut self)->Option<Self::Item>{self.iter.next().map(|adj|(adj.vindex(),(self.map)(adj.avalue())).into())}}}
pub use self::sparse_graph::*;
mod sparse_graph{use super::{Adjacencies,AdjacenciesWithEindex,AdjacencyIndex,AdjacencyIndexWithEindex,AdjacencyView,AdjacencyViewIterFromEindex,EIndexedGraph,EdgeMap,EdgeSize,EdgeView,GraphBase,IterScan,MarkedIterScan,VertexMap,VertexSize,VertexView,Vertices};use std::{iter::Cloned,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 fn builder<T>(vsize:usize)->SparseGraphBuilder<T,D>{SparseGraphBuilder::new(vsize)}pub fn builder_with_esize<T>(vsize:usize,esize:usize)->SparseGraphBuilder<T,D>{SparseGraphBuilder::new_with_esize(vsize,esize)}}pub trait SparseGraphConstruction:Sized{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph<Self>;}impl<D>SparseGraph<D>where D:SparseGraphConstruction{#[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 SparseGraphBuilder<T,D>{vsize:usize,edges:Vec<(usize,usize)>,rest:Vec<T>,_marker:Marker<D>}impl<T,D>SparseGraphBuilder<T,D>{pub fn new(vsize:usize)->Self{Self{vsize,edges:Default::default(),rest:Default::default(),_marker:PhantomData}}pub fn new_with_esize(vsize:usize,esize:usize)->Self{Self{vsize,edges:Vec::with_capacity(esize),rest:Vec::with_capacity(esize),_marker:PhantomData}}pub fn add_edge(&mut self,u:usize,v:usize,w:T){self.edges.push((u,v));self.rest.push(w);}}impl<T,D>SparseGraphBuilder<T,D>where D:SparseGraphConstruction{pub fn build(self)->(SparseGraph<D>,Vec<T>){let graph=SparseGraph::from_edges(self.vsize,self.edges);(graph,self.rest)}}pub struct SparseGraphScanner<U,T,D>where U:IterScan<Output=usize>,T:IterScan{vsize:usize,esize:usize,_marker:Marker<(U,T,D)>}impl<U,T,D>SparseGraphScanner<U,T,D>where U:IterScan<Output=usize>,T:IterScan{pub fn new(vsize:usize,esize:usize)->Self{Self{vsize,esize,_marker:PhantomData}}}impl<U,T,D>MarkedIterScan for SparseGraphScanner<U,T,D>where U:IterScan<Output=usize>,T:IterScan,D:SparseGraphConstruction{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 builder=SparseGraphBuilder::new_with_esize(self.vsize,self.esize);for _ in 0..self.esize{builder.add_edge(U::scan(iter)?,U::scan(iter)?,T::scan(iter)?);}Some(builder.build())}}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,T=()>where U:IterScan<Output=usize>,T:IterScan{vsize:usize,_marker:Marker<(U,T)>}impl<U,T>TreeGraphScanner<U,T>where U:IterScan<Output=usize>,T:IterScan{pub fn new(vsize:usize)->Self{Self{vsize,_marker:PhantomData}}}impl<U,T>MarkedIterScan for TreeGraphScanner<U,T>where U:IterScan<Output=usize>,T:IterScan{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)}}impl<D>GraphBase<'_>for SparseGraph<D>{type VIndex=usize;}impl<D>EIndexedGraph<'_>for SparseGraph<D>{type EIndex=usize;}impl<D>VertexSize<'_>for SparseGraph<D>{fn vsize(&self)->usize{self.vsize}}impl<D>EdgeSize<'_>for SparseGraph<D>{fn esize(&self)->usize{self.edges.len()}}impl<D>Vertices<'_>for SparseGraph<D>{type VIter=ops::Range<usize>;fn vertices(&self)->Self::VIter{0..self.vsize}}impl<'g,D>Adjacencies<'g>for SparseGraph<D>{type AIndex=Adjacency;type AIter=Cloned<slice::Iter<'g,Adjacency>>;fn adjacencies(&'g self,vid:Self::VIndex)->Self::AIter{self.elist[self.start[vid]..self.start[vid+1]].iter().cloned()}}impl<'g,D>AdjacenciesWithEindex<'g>for SparseGraph<D>{type AIndex=Adjacency;type AIter=Cloned<slice::Iter<'g,Adjacency>>;fn adjacencies_with_eindex(&'g self,vid:Self::VIndex)->Self::AIter{self.elist[self.start[vid]..self.start[vid+1]].iter().cloned()}}impl AdjacencyIndex for Adjacency{type VIndex=usize;fn vindex(&self)->Self::VIndex{self.to}}impl AdjacencyIndexWithEindex for Adjacency{type EIndex=usize;fn eindex(&self)->Self::EIndex{self.id}}impl<D,T>VertexMap<'_,T>for SparseGraph<D>{type Vmap=Vec<T>;fn construct_vmap<F>(&self,f:F)->Self::Vmap where F:FnMut()->T{let mut v=Vec::with_capacity(self.vsize);v.resize_with(self.vsize,f);v}fn vmap_get<'a>(&self,map:&'a Self::Vmap,vid:Self::VIndex)->&'a T{assert!(vid<self.vsize,"expected 0..{}, but {}",self.vsize,vid);unsafe{map.get_unchecked(vid)}}fn vmap_get_mut<'a>(&self,map:&'a mut Self::Vmap,vid:Self::VIndex)->&'a mut T{assert!(vid<self.vsize,"expected 0..{}, but {}",self.vsize,vid);unsafe{map.get_unchecked_mut(vid)}}}impl<D,T>VertexView<'_,Vec<T>,T>for SparseGraph<D>where T:Clone{fn vview(&self,map:&Vec<T>,vid:Self::VIndex)->T{self.vmap_get(map,vid).clone()}}impl<D,T>VertexView<'_,[T],T>for SparseGraph<D>where T:Clone{fn vview(&self,map:&[T],vid:Self::VIndex)->T{assert!(vid<self.vsize,"expected 0..{}, but {}",self.vsize,vid);unsafe{map.get_unchecked(vid)}.clone()}}impl<D,T>EdgeMap<'_,T>for SparseGraph<D>{type Emap=Vec<T>;fn construct_emap<F>(&self,f:F)->Self::Emap where F:FnMut()->T{let mut v=Vec::with_capacity(self.vsize);v.resize_with(self.vsize,f);v}fn emap_get<'a>(&self,map:&'a Self::Emap,eid:Self::EIndex)->&'a T{let esize=self.edges.len();assert!(eid<esize,"expected 0..{}, but {}",esize,eid);unsafe{map.get_unchecked(eid)}}fn emap_get_mut<'a>(&self,map:&'a mut Self::Emap,eid:Self::EIndex)->&'a mut T{let esize=self.edges.len();assert!(eid<esize,"expected 0..{}, but {}",esize,eid);unsafe{map.get_unchecked_mut(eid)}}}impl<D,T>EdgeView<'_,Vec<T>,T>for SparseGraph<D>where T:Clone{fn eview(&self,map:&Vec<T>,eid:Self::EIndex)->T{self.emap_get(map,eid).clone()}}impl<D,T>EdgeView<'_,[T],T>for SparseGraph<D>where T:Clone{fn eview(&self,map:&[T],eid:Self::EIndex)->T{let esize=self.edges.len();assert!(eid<esize,"expected 0..{}, but {}",esize,eid);unsafe{map.get_unchecked(eid)}.clone()}}impl<'g,'a,D:'g,M,T>AdjacencyView<'g,'a,M,T>for SparseGraph<D>where Self:AdjacenciesWithEindex<'g>+EdgeView<'g,M,T>,T:Clone,M:'a{type AViewIter=AdjacencyViewIterFromEindex<'g,'a,Self,M,T>;fn aviews(&'g self,map:&'a M,vid:Self::VIndex)->Self::AViewIter{AdjacencyViewIterFromEindex::new(self.adjacencies_with_eindex(vid),self,map)}}}
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![usize::MAX;graph.vertices_size()],comp:vec![0;graph.vertices_size()]};for u in graph.vertices(){if self_.ord[u]==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]==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}}}