pub fn main() {
    crate::prepare!();
    sc!(n, a, b, c);
    let mut bu = SparseGraphBuilder::<usize, DirectedEdge>::new(n * 2);
    for i in 0..n {
        bu.add_edge(i, i * 2 % n, c);
        bu.add_edge(i + n, i * 2 % n, c);
        bu.add_edge(i, (i + 1) % n + n, a + b);
        bu.add_edge(i + n, (i + 1) % n + n, a);
    }
    let (g, c) = bu.build();
    let d = g.dijkstra_ss::<StandardSp<AdditiveOperation<_>>, _>(n + 1, &c);
    let ans = (0..n).map(|i| d[i].min(d[i + n]).saturating_add(a + b));
    pp!(@lf @it ans);
}
#[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::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::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::shortest_path::*;
mod shortest_path{use super::*;use std::{cmp::{Ordering,Reverse},collections::{BinaryHeap,VecDeque},iter::once,marker::PhantomData};pub trait ShortestPathSemiRing{type T:Clone+Ord;fn source()->Self::T;fn inf()->Self::T;fn mul(x:&Self::T,y:&Self::T)->Self::T;fn add_assign(x:&mut Self::T,y:&Self::T)->bool;}pub struct StandardSp<M>(PhantomData<fn()->M>);impl<M>ShortestPathSemiRing for StandardSp<M>where M:Monoid,M::T:Bounded+Ord{type T=M::T;fn source()->Self::T{M::unit()}fn inf()->Self::T{M::T::maximum()}fn mul(x:&Self::T,y:&Self::T)->Self::T{M::operate(x,y)}fn add_assign(x:&mut Self::T,y:&Self::T)->bool{if&*x>y{*x=y.clone();true}else{false}}}pub struct OptionSp<M>(PhantomData<fn()->M>);impl<M>ShortestPathSemiRing for OptionSp<M>where M:Monoid,M::T:Ord{type T=Option<M::T>;fn source()->Self::T{Some(M::unit())}fn inf()->Self::T{None}fn mul(x:&Self::T,y:&Self::T)->Self::T{match(x,y){(Some(x),Some(y))=>Some(M::operate(x,y)),_=>None,}}fn add_assign(x:&mut Self::T,y:&Self::T)->bool{if let Some(y)=y{if let Some(x)=x{if&*x>y{*x=y.clone();true}else{false}}else{*x=Some(y.clone());true}}else{false}}}pub struct PathFoldingSp<M,S>(PhantomData<fn()->(M,S)>);impl<M,S>ShortestPathSemiRing for PathFoldingSp<M,S>where M:Monoid,M::T:Bounded+Ord,S:SemiRing{type T=PartialIgnoredOrd<M::T,S::T>;fn source()->Self::T{PartialIgnoredOrd(M::unit(),S::one())}fn inf()->Self::T{PartialIgnoredOrd(M::T::maximum(),S::zero())}fn mul(x:&Self::T,y:&Self::T)->Self::T{PartialIgnoredOrd(M::operate(&x.0,&y.0),S::mul(&x.1,&y.1))}fn add_assign(x:&mut Self::T,y:&Self::T)->bool{match x.0.cmp(&y.0){Ordering::Equal=>{x.1=S::add(&x.1,&y.1);false}Ordering::Greater=>{*x=y.clone();true}_=>false,}}}pub trait ShortestPathExt<'g>:GraphBase<'g>{fn bfs_distance_ss<'a,S,M>(&'g self,source:Self::VIndex,weight:&'a M)-><Self as VertexMap<'g,S::T>>::Vmap where Self:VertexMap<'g,S::T>+AdjacencyView<'g,'a,M,S::T>,S:ShortestPathSemiRing{self.bfs_distance_ms::<S,M,_>(once(source),weight)}fn bfs_distance_ms<'a,S,M,I>(&'g self,sources:I,weight:&'a M)-><Self as VertexMap<'g,S::T>>::Vmap where Self:VertexMap<'g,S::T>+AdjacencyView<'g,'a,M,S::T>,S:ShortestPathSemiRing,I:IntoIterator<Item=Self::VIndex>{let mut cost=self.construct_vmap(S::inf);let mut deq=VecDeque::new();for source in sources.into_iter(){*self.vmap_get_mut(&mut cost,source)=S::source();deq.push_back(source);}let zero=S::source();while let Some(u)=deq.pop_front(){for a in self.aviews(weight,u){let v=a.vindex();let w=a.avalue();let nd=S::mul(self.vmap_get(&cost,u),&w);if S::add_assign(self.vmap_get_mut(&mut cost,v),&nd){if w==zero{deq.push_front(v);}else{deq.push_back(v);}}}}cost}fn dijkstra_ss<'a,S,M>(&'g self,source:Self::VIndex,weight:&'a M)-><Self as VertexMap<'g,S::T>>::Vmap where Self:VertexMap<'g,S::T>+AdjacencyView<'g,'a,M,S::T>,S:ShortestPathSemiRing{self.dijkstra_ms::<S,M,_>(once(source),weight)}fn dijkstra_ms<'a,S,M,I>(&'g self,sources:I,weight:&'a M)-><Self as VertexMap<'g,S::T>>::Vmap where Self:VertexMap<'g,S::T>+AdjacencyView<'g,'a,M,S::T>,S:ShortestPathSemiRing,I:IntoIterator<Item=Self::VIndex>{let mut cost=self.construct_vmap(S::inf);let mut heap=BinaryHeap::new();for source in sources.into_iter(){*self.vmap_get_mut(&mut cost,source)=S::source();heap.push(PartialIgnoredOrd(Reverse(S::source()),source));}while let Some(PartialIgnoredOrd(Reverse(d),u))=heap.pop(){if self.vmap_get(&cost,u)!=&d{continue;}let d=self.vmap_get(&cost,u).clone();for a in self.aviews(weight,u){let v=a.vindex();let nd=S::mul(&d,&a.avalue());if S::add_assign(self.vmap_get_mut(&mut cost,v),&nd){heap.push(PartialIgnoredOrd(Reverse(nd),v));}}}cost}fn bellman_ford_ss<'a,S,M>(&'g self,source:Self::VIndex,weight:&'a M,check:bool)->Option<<Self as VertexMap<'g,S::T>>::Vmap>where Self:Vertices<'g>+VertexMap<'g,S::T>+AdjacencyView<'g,'a,M,S::T>+VertexSize<'g>,S:ShortestPathSemiRing{self.bellman_ford_ms::<S,M,_>(once(source),weight,check)}fn bellman_ford_ms<'a,S,M,I>(&'g self,sources:I,weight:&'a M,check:bool)->Option<<Self as VertexMap<'g,S::T>>::Vmap>where Self:Vertices<'g>+VertexMap<'g,S::T>+AdjacencyView<'g,'a,M,S::T>+VertexSize<'g>,S:ShortestPathSemiRing,I:IntoIterator<Item=Self::VIndex>{let mut cost=self.construct_vmap(S::inf);for source in sources.into_iter(){*self.vmap_get_mut(&mut cost,source)=S::source();}let vsize=self.vsize();for _ in 1..vsize{let mut updated=false;for u in self.vertices(){for a in self.aviews(weight,u){let v=a.vindex();let nd=S::mul(self.vmap_get(&cost,u),&a.avalue());updated|=S::add_assign(self.vmap_get_mut(&mut cost,v),&nd);}}if!updated{break;}}if check{for u in self.vertices(){for a in self.aviews(weight,u){let v=a.vindex();let nd=S::mul(self.vmap_get(&cost,u),&a.avalue());if S::add_assign(self.vmap_get_mut(&mut cost,v),&nd){return None;}}}}Some(cost)}fn warshall_floyd_ap<'a,S,M>(&'g self,weight:&'a M)-><Self as VertexMap<'g,<Self as VertexMap<'g,S::T>>::Vmap>>::Vmap where Self:Vertices<'g>+VertexMap<'g,S::T>+VertexMap<'g,<Self as VertexMap<'g,S::T>>::Vmap>+AdjacencyView<'g,'a,M,S::T>,<Self as VertexMap<'g,S::T>>::Vmap:Clone,S:ShortestPathSemiRing{let mut cost=self.construct_vmap(||self.construct_vmap(S::inf));for u in self.vertices(){*self.vmap_get_mut(self.vmap_get_mut(&mut cost,u),u)=S::source();}for u in self.vertices(){for a in self.aviews(weight,u){*self.vmap_get_mut(self.vmap_get_mut(&mut cost,u),a.vindex())=a.avalue();}}for k in self.vertices(){for i in self.vertices(){for j in self.vertices(){let d1=self.vmap_get(self.vmap_get(&cost,i),k);let d2=self.vmap_get(self.vmap_get(&cost,k),j);let nd=S::mul(d1,d2);S::add_assign(self.vmap_get_mut(self.vmap_get_mut(&mut cost,i),j),&nd);}}}cost}}impl<'g,G>ShortestPathExt<'g>for G where G:GraphBase<'g>{}}
pub use self::additive_operation_impl::AdditiveOperation;
mod additive_operation_impl{use super::*;use std::{marker::PhantomData,ops::{Add,Neg,Sub}};#[doc=" $+$"]pub struct AdditiveOperation<T:Clone+Zero+Add<Output=T>>{_marker:PhantomData<fn()->T>}impl<T:Clone+Zero+Add<Output=T>>Magma for AdditiveOperation<T>{type T=T;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{x.clone()+y.clone()}}impl<T:Clone+Zero+Add<Output=T>>Unital for AdditiveOperation<T>{#[inline]fn unit()->Self::T{Zero::zero()}}impl<T:Clone+Zero+Add<Output=T>>Associative for AdditiveOperation<T>{}impl<T:Clone+Zero+Add<Output=T>>Commutative for AdditiveOperation<T>{}impl<T:Clone+Zero+Add<Output=T>+Sub<Output=T>+Neg<Output=T>>Invertible for AdditiveOperation<T>{#[inline]fn inverse(x:&Self::T)->Self::T{-x.clone()}#[inline]fn rinv_operate(x:&Self::T,y:&Self::T)->Self::T{x.clone()-y.clone()}}}
pub use self::multiplicative_operation_impl::MultiplicativeOperation;
mod multiplicative_operation_impl{use super::*;use std::{marker::PhantomData,ops::{Div,Mul}};#[doc=" $\\times$"]pub struct MultiplicativeOperation<T:Clone+One+Mul<Output=T>>{_marker:PhantomData<fn()->T>}impl<T:Clone+One+Mul<Output=T>>Magma for MultiplicativeOperation<T>{type T=T;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{x.clone()*y.clone()}}impl<T:Clone+One+Mul<Output=T>>Unital for MultiplicativeOperation<T>{#[inline]fn unit()->Self::T{One::one()}}impl<T:Clone+One+Mul<Output=T>>Associative for MultiplicativeOperation<T>{}impl<T:Clone+One+Mul<Output=T>>Commutative for MultiplicativeOperation<T>{}impl<T:Clone+One+Mul<Output=T>+Div<Output=T>>Invertible for MultiplicativeOperation<T>{#[inline]fn inverse(x:&Self::T)->Self::T{Self::unit().div(x.clone())}#[inline]fn rinv_operate(x:&Self::T,y:&Self::T)->Self::T{(x.clone()).div(y.clone())}}}
pub use self::partial_ignored_ord::PartialIgnoredOrd;
mod partial_ignored_ord{#[derive(Debug,Default,Clone,Copy)]pub struct PartialIgnoredOrd<T,U>(pub T,pub U);impl<T:Eq,U>Eq for PartialIgnoredOrd<T,U>{}impl<T,U>PartialEq for PartialIgnoredOrd<T,U>where T:PartialEq{fn eq(&self,other:&Self)->bool{self.0.eq(&other.0)}}impl<T,U>PartialOrd for PartialIgnoredOrd<T,U>where T:PartialOrd{fn partial_cmp(&self,other:&Self)->Option<std::cmp::Ordering>{self.0.partial_cmp(&other.0)}}impl<T,U>Ord for PartialIgnoredOrd<T,U>where T:Ord{fn cmp(&self,other:&Self)->std::cmp::Ordering{self.0.cmp(&other.0)}}}
pub use self::magma::*;
mod magma{#![doc=" algebraic traits"]#[doc=" binary operaion: $T \\circ T \\to T$"]pub trait Magma{#[doc=" type of operands: $T$"]type T:Clone;#[doc=" binary operaion: $\\circ$"]fn operate(x:&Self::T,y:&Self::T)->Self::T;#[inline]fn reverse_operate(x:&Self::T,y:&Self::T)->Self::T{Self::operate(y,x)}#[inline]fn operate_assign(x:&mut Self::T,y:&Self::T){*x=Self::operate(x,y);}}#[doc=" $\\forall a,\\forall b,\\forall c \\in T, (a \\circ b) \\circ c = a \\circ (b \\circ c)$"]pub trait Associative{}#[doc=" associative binary operation"]pub trait SemiGroup:Magma+Associative{}impl<S>SemiGroup for S where S:Magma+Associative{}#[doc=" $\\exists e \\in T, \\forall a \\in T, e \\circ a = a \\circ e = e$"]pub trait Unital:Magma{#[doc=" identity element: $e$"]fn unit()->Self::T;#[inline]fn is_unit(x:&Self::T)->bool where<Self as Magma>::T:PartialEq{x==&Self::unit()}#[inline]fn set_unit(x:&mut Self::T){*x=Self::unit();}}#[doc=" associative binary operation and an identity element"]pub trait Monoid:SemiGroup+Unital{#[doc=" binary exponentiation: $x^n = x\\circ\\ddots\\circ x$"]fn pow(mut x:Self::T,mut n:usize)->Self::T{let mut res=Self::unit();while n>0{if n&1==1{res=Self::operate(&res,&x);}x=Self::operate(&x,&x);n>>=1;}res}}impl<M>Monoid for M where M:SemiGroup+Unital{}#[doc=" $\\exists e \\in T, \\forall a \\in T, \\exists b,c \\in T, b \\circ a = a \\circ c = e$"]pub trait Invertible:Magma{#[doc=" $a$ where $a \\circ x = e$"]fn inverse(x:&Self::T)->Self::T;#[inline]fn rinv_operate(x:&Self::T,y:&Self::T)->Self::T{Self::operate(x,&Self::inverse(y))}}#[doc=" associative binary operation and an identity element and inverse elements"]pub trait Group:Monoid+Invertible{}impl<G>Group for G where G:Monoid+Invertible{}#[doc=" $\\forall a,\\forall b \\in T, a \\circ b = b \\circ a$"]pub trait Commutative{}#[doc=" commutative monoid"]pub trait AbelianMonoid:Monoid+Commutative{}impl<M>AbelianMonoid for M where M:Monoid+Commutative{}#[doc=" commutative group"]pub trait AbelianGroup:Group+Commutative{}impl<G>AbelianGroup for G where G:Group+Commutative{}#[doc=" $\\forall a \\in T, a \\circ a = a$"]pub trait Idempotent{}#[doc=" idempotent monoid"]pub trait IdempotentMonoid:Monoid+Idempotent{}impl<M>IdempotentMonoid for M where M:Monoid+Idempotent{}#[macro_export]macro_rules!monoid_fold{($m:ty)=>{<$m as Unital>::unit()};($m:ty,)=>{<$m as Unital>::unit()};($m:ty,$f:expr)=>{$f};($m:ty,$f:expr,$($ff:expr),*)=>{<$m as Magma>::operate(&($f),&monoid_fold!($m,$($ff),*))};}#[macro_export]macro_rules!define_monoid{($Name:ident,$t:ty,|$x:ident,$y:ident|$op:expr,$unit:expr)=>{struct$Name;impl Magma for$Name{type T=$t;fn operate($x:&Self::T,$y:&Self::T)->Self::T{$op}}impl Unital for$Name{fn unit()->Self::T{$unit}}impl Associative for$Name{}};}}
pub use self::bounded::Bounded;
mod bounded{#[doc=" Trait for max/min bounds"]pub trait Bounded:Sized+PartialOrd{fn maximum()->Self;fn minimum()->Self;fn is_maximum(&self)->bool{self==&Self::maximum()}fn is_minimum(&self)->bool{self==&Self::minimum()}fn set_maximum(&mut self){*self=Self::maximum()}fn set_minimum(&mut self){*self=Self::minimum()}}macro_rules!bounded_num_impls{($($t:ident)*)=>{$(impl Bounded for$t{fn maximum()->Self{std::$t::MAX}fn minimum()->Self{std::$t::MIN}})*};}bounded_num_impls!(u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize f32 f64);macro_rules!bounded_tuple_impls{(@impl$($T:ident)*)=>{impl<$($T:Bounded),*>Bounded for($($T,)*){fn maximum()->Self{($(<$T as Bounded>::maximum(),)*)}fn minimum()->Self{($(<$T as Bounded>::minimum(),)*)}}};(@inner$($T:ident)*,)=>{bounded_tuple_impls!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{bounded_tuple_impls!(@impl$($T)*);bounded_tuple_impls!(@inner$($T)*$U,$($Rest)*);};($T:ident$($Rest:ident)*)=>{bounded_tuple_impls!(@inner$T,$($Rest)*);};}bounded_tuple_impls!(A B C D E F G H I J);impl Bounded for(){fn maximum()->Self{}fn minimum()->Self{}}impl Bounded for bool{fn maximum()->Self{true}fn minimum()->Self{false}}impl<T>Bounded for Option<T>where T:Bounded{fn maximum()->Self{Some(<T as Bounded>::maximum())}fn minimum()->Self{None}}impl<T>Bounded for std::cmp::Reverse<T>where T:Bounded{fn maximum()->Self{std::cmp::Reverse(<T as Bounded>::minimum())}fn minimum()->Self{std::cmp::Reverse(<T as Bounded>::maximum())}}}
pub use self::ring::*;
mod ring{use super::*;use std::{marker::PhantomData,ops::{Add,Mul}};pub trait SemiRing{type T:Clone;type Additive:AbelianMonoid<T=Self::T>;type Multiplicative:Monoid<T=Self::T>;#[doc=" additive identity: $0$"]fn zero()->Self::T{<Self::Additive as Unital>::unit()}#[doc=" multiplicative identity: $1$"]fn one()->Self::T{<Self::Multiplicative as Unital>::unit()}#[doc=" additive operaion: $+$"]fn add(x:&Self::T,y:&Self::T)->Self::T{<Self::Additive as Magma>::operate(x,y)}#[doc=" multiplicative operaion: $+$"]fn mul(x:&Self::T,y:&Self::T)->Self::T{<Self::Multiplicative as Magma>::operate(x,y)}}pub trait Ring:SemiRing where Self::Additive:Invertible{#[doc=" additive inverse: $-$"]fn neg(x:&Self::T)->Self::T{<Self::Additive as Invertible>::inverse(x)}#[doc=" additive right inversed operaion: $-$"]fn sub(x:&Self::T,y:&Self::T)->Self::T{Self::add(x,&Self::neg(y))}}impl<R>Ring for R where R:SemiRing,R::Additive:Invertible{}pub trait Field:Ring where Self::Additive:Invertible,Self::Multiplicative:Invertible{#[doc=" multiplicative inverse: $-$"]fn inv(x:&Self::T)->Self::T{<Self::Additive as Invertible>::inverse(x)}#[doc=" multiplicative right inversed operaion: $-$"]fn div(x:&Self::T,y:&Self::T)->Self::T{Self::mul(x,&Self::inv(y))}}impl<F>Field for F where F:Ring,F::Additive:Invertible,F::Multiplicative:Invertible{}#[doc=" $+,\\times$"]pub struct AddMulOperation<T>where T:Clone+Zero+One+Add<Output=T>+Mul<Output=T>{_marker:PhantomData<fn()->T>}impl<T>SemiRing for AddMulOperation<T>where T:Clone+Zero+One+Add<Output=T>+Mul<Output=T>{type T=T;type Additive=AdditiveOperation<T>;type Multiplicative=MultiplicativeOperation<T>;}}
pub use self::zero_one::{One,Zero};
mod zero_one{pub trait Zero:Sized{fn zero()->Self;#[inline]fn is_zero(&self)->bool where Self:PartialEq{self==&Self::zero()}#[inline]fn set_zero(&mut self){*self=Self::zero();}}pub trait One:Sized{fn one()->Self;#[inline]fn is_one(&self)->bool where Self:PartialEq{self==&Self::one()}#[inline]fn set_one(&mut self){*self=Self::one();}}macro_rules!zero_one_impls{($({$Trait:ident$method:ident$($t:ty)*,$e:expr})*)=>{$($(impl$Trait for$t{fn$method()->Self{$e}})*)*};}zero_one_impls!({Zero zero u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128,0}{Zero zero f32 f64,0.}{One one u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128,1}{One one f32 f64,1.});}