pub fn main() {
    crate::prepare!();
    sc!(l, r);
    let solve1 = |n: usize| {
        let n = n.to_digit_sequence_radix_len(10, 13);
        let a = automaton!(<= n);
        let a = automaton!(=> (a)
            || 0usize,
            |_s, &a| Some(a),
            |_s| true
        );
        type A = AdditiveOperation<usize>;
        a.dp::<(A, A)>((0usize, 1usize))
            .run_effect(
                || 0..10,
                13,
                |x, &(_, s), &a, _| {
                    if s == 1 && a == 2 {
                        (x.0 + x.1, x.1)
                    } else {
                        *x
                    }
                },
            )
            .0
    };
    let solve2 = |n: usize| {
        let n = n.to_digit_sequence_radix_len(10, 13);
        let a = automaton!(<= n);
        let a = automaton!(=> (a)
            || (0usize, 0usize),
            |&(_, (s, _)), &a| Some((if s == 0 { a } else { s }, a)),
            |&(_, (x, y))| x == 2 && y == 1
        );
        type A = AdditiveOperation<usize>;
        a.dp::<A>(1usize).run(|| 0..10, 13)
    };
    let ans = solve1(r) - solve1(l - 1) + solve2(r - 1) - solve2(l - 1);
    pp!(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::automaton::*;
mod automaton{use super::Monoid;use std::{borrow::Borrow,cmp::Ordering,collections::HashMap,fmt::{self,Debug,Formatter},hash::Hash,marker::PhantomData,mem::swap};pub trait Automaton{type Alphabet;type State;fn initial(&self)->Self::State;fn next(&self,state:&Self::State,alph:&Self::Alphabet)->Option<Self::State>;fn accept(&self,state:&Self::State)->bool;fn dp<M>(&self,init:M::T)->Automatondp<M,&Self>where Self:Sized,Self::State:Eq+Hash,M:Monoid{Automatondp::new(self,init)}}impl<A>Automaton for&A where A:Automaton{type Alphabet=A::Alphabet;type State=A::State;fn initial(&self)->Self::State{A::initial(self)}fn next(&self,state:&Self::State,alph:&Self::Alphabet)->Option<Self::State>{A::next(self,state,alph)}fn accept(&self,state:&Self::State)->bool{A::accept(self,state)}}#[derive(Clone)]pub struct Automatondp<M,A>where M:Monoid,A:Automaton,A::State:Eq+Hash{dfa:A,pub dp:HashMap<A::State,M::T>,ndp:HashMap<A::State,M::T>}impl<M,A>Debug for Automatondp<M,A>where M:Monoid,A:Automaton+Debug,A::State:Eq+Hash+Debug,M::T:Debug{fn fmt(&self,f:&mut Formatter<'_>)->fmt::Result{f.debug_struct("Automatondp").field("dfa",&self.dfa).field("dp",&self.dp).field("ndp",&self.ndp).finish()}}impl<M,A>Automatondp<M,A>where M:Monoid,A:Automaton,A::State:Eq+Hash{pub fn new(dfa:A,init:M::T)->Self{let mut dp=HashMap::new();let ndp=HashMap::new();dp.insert(dfa.initial(),init);Self{dfa,dp,ndp}}pub fn step<S,I,B>(&mut self,mut sigma:S)where S:FnMut()->I,I:IntoIterator<Item=B>,B:Borrow<A::Alphabet>{for(state,value)in self.dp.drain(){for alph in sigma(){if let Some(nstate)=self.dfa.next(&state,alph.borrow()){self.ndp.entry(nstate).and_modify(|acc|*acc=M::operate(acc,&value)).or_insert_with(||value.clone());}}}swap(&mut self.dp,&mut self.ndp);}pub fn step_effect<S,I,B,F>(&mut self,mut sigma:S,mut effect:F)where S:FnMut()->I,I:IntoIterator<Item=B>,B:Borrow<A::Alphabet>,F:FnMut(&M::T,&A::State,&A::Alphabet,&A::State)->M::T{for(state,value)in self.dp.drain(){for alph in sigma(){if let Some(nstate)=self.dfa.next(&state,alph.borrow()){let nvalue=effect(&value,&state,alph.borrow(),&nstate);self.ndp.entry(nstate).and_modify(|acc|*acc=M::operate(acc,&nvalue)).or_insert(nvalue);}}}swap(&mut self.dp,&mut self.ndp);}pub fn fold_accept(&self)->M::T{let mut acc=M::unit();for(state,value)in self.dp.iter(){if self.dfa.accept(state){acc=M::operate(&acc,value);}}acc}pub fn map_fold_accept<U,F>(&self,mut f:F)->HashMap<U,M::T>where U:Eq+Hash,F:FnMut(&A::State)->U{let mut map=HashMap::new();for(state,value)in self.dp.iter(){if self.dfa.accept(state){map.entry(f(state)).and_modify(|acc|*acc=M::operate(acc,value)).or_insert_with(||value.clone());}}map}pub fn run<S,I,B>(&mut self,mut sigma:S,len:usize)->M::T where S:FnMut()->I,I:IntoIterator<Item=B>,B:Borrow<A::Alphabet>{for _ in 0..len{self.step(&mut sigma);}self.fold_accept()}pub fn run_effect<S,I,B,F>(&mut self,mut sigma:S,len:usize,mut effect:F)->M::T where S:FnMut()->I,I:IntoIterator<Item=B>,B:Borrow<A::Alphabet>,F:FnMut(&M::T,&A::State,&A::Alphabet,&A::State)->M::T{for _ in 0..len{self.step_effect(&mut sigma,&mut effect);}self.fold_accept()}}#[derive(Debug,Clone)]pub struct IntersectionAutomaton<X,Y>(pub X,pub Y);impl<A,X,Y>Automaton for IntersectionAutomaton<X,Y>where X:Automaton<Alphabet=A>,Y:Automaton<Alphabet=A>{type Alphabet=A;type State=(X::State,Y::State);fn initial(&self)->Self::State{(self.0.initial(),self.1.initial())}fn next(&self,state:&Self::State,alph:&Self::Alphabet)->Option<Self::State>{match(self.0.next(&state.0,alph),self.1.next(&state.1,alph)){(Some(s0),Some(s1))=>Some((s0,s1)),_=>None,}}fn accept(&self,state:&Self::State)->bool{self.0.accept(&state.0)&&self.1.accept(&state.1)}}#[derive(Debug,Clone)]pub struct UnionAutomaton<X,Y>(pub X,pub Y);impl<A,X,Y>Automaton for UnionAutomaton<X,Y>where X:Automaton<Alphabet=A>,Y:Automaton<Alphabet=A>{type Alphabet=A;type State=(X::State,Y::State);fn initial(&self)->Self::State{(self.0.initial(),self.1.initial())}fn next(&self,state:&Self::State,alph:&Self::Alphabet)->Option<Self::State>{match(self.0.next(&state.0,alph),self.1.next(&state.1,alph)){(Some(s0),Some(s1))=>Some((s0,s1)),_=>None,}}fn accept(&self,state:&Self::State)->bool{self.0.accept(&state.0)||self.1.accept(&state.1)}}#[derive(Debug,Clone)]pub struct ProductAutomaton<X,Y>(pub X,pub Y);impl<X,Y>Automaton for ProductAutomaton<X,Y>where X:Automaton,Y:Automaton{type Alphabet=(X::Alphabet,Y::Alphabet);type State=(X::State,Y::State);fn initial(&self)->Self::State{(self.0.initial(),self.1.initial())}fn next(&self,state:&Self::State,alph:&Self::Alphabet)->Option<Self::State>{match(self.0.next(&state.0,&alph.0),self.1.next(&state.1,&alph.1)){(Some(s0),Some(s1))=>Some((s0,s1)),_=>None,}}fn accept(&self,state:&Self::State)->bool{self.0.accept(&state.0)&&self.1.accept(&state.1)}}#[derive(Debug,Clone)]pub struct FunctionalAutomaton<A,S,F,G,H>where F:Fn()->S,G:Fn(&S,&A)->Option<S>,H:Fn(&S)->bool{fn_initial:F,fn_next:G,fn_accept:H,_marker:PhantomData<fn()->(A,S)>}impl<A,S,F,G,H>FunctionalAutomaton<A,S,F,G,H>where F:Fn()->S,G:Fn(&S,&A)->Option<S>,H:Fn(&S)->bool{pub fn new(fn_initial:F,fn_next:G,fn_accept:H)->Self{Self{fn_initial,fn_next,fn_accept,_marker:PhantomData}}}impl<A,S,F,G,H>Automaton for FunctionalAutomaton<A,S,F,G,H>where F:Fn()->S,G:Fn(&S,&A)->Option<S>,H:Fn(&S)->bool{type Alphabet=A;type State=S;fn initial(&self)->Self::State{(self.fn_initial)()}fn next(&self,state:&Self::State,alph:&Self::Alphabet)->Option<Self::State>{(self.fn_next)(state,alph)}fn accept(&self,state:&Self::State)->bool{(self.fn_accept)(state)}}#[derive(Debug,Clone)]pub struct MappingAutomaton<A,S,F,G,H>where A:Automaton,F:Fn()->S,G:Fn(&(A::State,S),&A::Alphabet)->Option<S>,H:Fn(&(A::State,S))->bool{dfa:A,fn_initial:F,fn_next:G,fn_accept:H,_marker:PhantomData<fn()->S>}impl<A,S,F,G,H>MappingAutomaton<A,S,F,G,H>where A:Automaton,F:Fn()->S,G:Fn(&(A::State,S),&A::Alphabet)->Option<S>,H:Fn(&(A::State,S))->bool{pub fn new(dfa:A,fn_initial:F,fn_next:G,fn_accept:H)->Self{Self{dfa,fn_initial,fn_next,fn_accept,_marker:PhantomData}}}impl<A,S,F,G,H>Automaton for MappingAutomaton<A,S,F,G,H>where A:Automaton,F:Fn()->S,G:Fn(&(A::State,S),&A::Alphabet)->Option<S>,H:Fn(&(A::State,S))->bool{type Alphabet=A::Alphabet;type State=(A::State,S);fn initial(&self)->Self::State{(self.dfa.initial(),(self.fn_initial)())}fn next(&self,state:&Self::State,alph:&Self::Alphabet)->Option<Self::State>{self.dfa.next(&state.0,alph).and_then(|s|(self.fn_next)(state,alph).map(|ss|(s,ss)))}fn accept(&self,state:&Self::State)->bool{self.dfa.accept(&state.0)&&(self.fn_accept)(state)}}#[derive(Debug,Clone)]pub struct AlphabetMappingAutomaton<A,S,B,F,G,H>where A:Automaton,F:Fn()->S,G:Fn(&S,&B)->Option<(S,A::Alphabet)>,H:Fn(&S)->bool{dfa:A,fn_initial:F,fn_next:G,fn_accept:H,_marker:PhantomData<fn()->(S,B)>}impl<A,S,B,F,G,H>AlphabetMappingAutomaton<A,S,B,F,G,H>where A:Automaton,F:Fn()->S,G:Fn(&S,&B)->Option<(S,A::Alphabet)>,H:Fn(&S)->bool{pub fn new(dfa:A,fn_initial:F,fn_next:G,fn_accept:H)->Self{Self{dfa,fn_initial,fn_next,fn_accept,_marker:PhantomData}}}impl<A,S,B,F,G,H>Automaton for AlphabetMappingAutomaton<A,S,B,F,G,H>where A:Automaton,F:Fn()->S,G:Fn(&S,&B)->Option<(S,A::Alphabet)>,H:Fn(&S)->bool{type Alphabet=B;type State=(A::State,S);fn initial(&self)->Self::State{(self.dfa.initial(),(self.fn_initial)())}fn next(&self,state:&Self::State,alph:&Self::Alphabet)->Option<Self::State>{(self.fn_next)(&state.1,alph).and_then(|(s1,a)|self.dfa.next(&state.0,&a).map(|s0|(s0,s1)))}fn accept(&self,state:&Self::State)->bool{self.dfa.accept(&state.0)&&(self.fn_accept)(&state.1)}}#[derive(Debug,Clone)]#[doc=" DFA to accept Less/Greater than (or equal to) the sequence"]pub struct LexicographicalAutomaton<'a,T>{sequence:&'a[T],ordering:Ordering,equal:bool}impl<'a,T>LexicographicalAutomaton<'a,T>{pub fn less_than(sequence:&'a[T])->Self{Self{sequence,ordering:Ordering::Less,equal:false}}pub fn less_than_or_equal(sequence:&'a[T])->Self{Self{sequence,ordering:Ordering::Less,equal:true}}pub fn greater_than(sequence:&'a[T])->Self{Self{sequence,ordering:Ordering::Greater,equal:false}}pub fn greater_than_or_equal(sequence:&'a[T])->Self{Self{sequence,ordering:Ordering::Greater,equal:true}}}impl<'a,T>Automaton for LexicographicalAutomaton<'a,T>where T:Ord{type Alphabet=T;#[doc=" (next position of sequence, is equal)"]type State=(usize,bool);fn initial(&self)->Self::State{(0,true)}fn next(&self,state:&Self::State,alph:&Self::Alphabet)->Option<Self::State>{self.sequence.get(state.0).and_then(|c|match(state.1,c.cmp(alph)){(true,Ordering::Equal)=>Some((state.0+1,true)),(true,ord)if ord==self.ordering=>None,_=>Some((state.0+1,false)),})}fn accept(&self,state:&Self::State)->bool{self.equal||!state.1}}#[derive(Debug,Clone)]#[doc=" DFA to accept Less/Greater than (or equal to) the reversed sequence"]pub struct RevLexicographicalAutomaton<'a,T>{sequence:&'a[T],ordering:Ordering,equal:bool}impl<'a,T>RevLexicographicalAutomaton<'a,T>{pub fn less_than(sequence:&'a[T])->Self{Self{sequence,ordering:Ordering::Less,equal:false}}pub fn less_than_or_equal(sequence:&'a[T])->Self{Self{sequence,ordering:Ordering::Less,equal:true}}pub fn greater_than(sequence:&'a[T])->Self{Self{sequence,ordering:Ordering::Greater,equal:false}}pub fn greater_than_or_equal(sequence:&'a[T])->Self{Self{sequence,ordering:Ordering::Greater,equal:true}}}impl<'a,T>Automaton for RevLexicographicalAutomaton<'a,T>where T:Ord{type Alphabet=T;#[doc=" (next position of sequence, is equal)"]type State=(usize,Ordering);fn initial(&self)->Self::State{(self.sequence.len(),Ordering::Equal)}fn next(&self,state:&Self::State,alph:&Self::Alphabet)->Option<Self::State>{let index=state.0.wrapping_add(!0);self.sequence.get(index).map(|c|(index,alph.cmp(c).then(state.1)))}fn accept(&self,state:&Self::State)->bool{state.1==self.ordering||self.equal&&matches!(state.1,Ordering::Equal)}}#[derive(Debug,Clone)]pub struct MonoidalAutomaton<M>(PhantomData<fn()->M>)where M:Monoid;impl<M>MonoidalAutomaton<M>where M:Monoid{pub fn new()->Self{Default::default()}}impl<M>Default for MonoidalAutomaton<M>where M:Monoid{fn default()->Self{Self(PhantomData)}}impl<M>Automaton for MonoidalAutomaton<M>where M:Monoid{type Alphabet=M::T;type State=M::T;fn initial(&self)->Self::State{M::unit()}fn next(&self,state:&Self::State,alph:&Self::Alphabet)->Option<Self::State>{Some(M::operate(state,alph))}fn accept(&self,_state:&Self::State)->bool{true}}#[derive(Debug,Clone)]pub struct AlwaysAcceptingAutomaton<A>(PhantomData<fn()->A>);impl<A>AlwaysAcceptingAutomaton<A>{pub fn new()->Self{Default::default()}}impl<A>Default for AlwaysAcceptingAutomaton<A>{fn default()->Self{Self(PhantomData)}}impl<A>Automaton for AlwaysAcceptingAutomaton<A>{type Alphabet=A;type State=();fn initial(&self)->Self::State{}fn next(&self,_state:&Self::State,_alph:&Self::Alphabet)->Option<Self::State>{Some(())}fn accept(&self,_state:&Self::State)->bool{true}}pub trait ToDigitSequence:Sized{fn to_digit_sequence(&self)->Vec<Self>;fn to_digit_sequence_radix(&self,radix:Self)->Vec<Self>;fn to_digit_sequence_len(&self,len:usize)->Vec<Self>;fn to_digit_sequence_radix_len(&self,radix:Self,len:usize)->Vec<Self>;}macro_rules!impl_to_digit_sequence{($($t:ty)*)=>{$(impl ToDigitSequence for$t{fn to_digit_sequence(&self)->Vec<$t>{self.to_digit_sequence_radix(10)}fn to_digit_sequence_radix(&self,radix:Self)->Vec<$t>{let mut x=*self;let mut res:Vec<$t> =vec![];while x>0{res.push(x%radix);x/=radix;}res.reverse();res}fn to_digit_sequence_len(&self,len:usize)->Vec<$t>{self.to_digit_sequence_radix_len(10,len)}fn to_digit_sequence_radix_len(&self,radix:Self,len:usize)->Vec<$t>{let mut x=*self;let mut res:Vec<$t> =vec![0;len];for r in res.iter_mut().rev(){if x==0{break;}*r=x%radix;x/=radix;}res}})*};}impl_to_digit_sequence!(u8 u16 u32 u64 u128 usize);#[doc=" build automaton"]#[doc=""]#[doc=" - `automaton!(A)`"]#[doc=" - `<= seq`: `LexicographicalAutomaton::less_than_or_equal(seq)`"]#[doc=" - `>= seq`: `LexicographicalAutomaton::greater_than_or_equal(seq)`"]#[doc=" - `< seq`: `LexicographicalAutomaton::greater_than(seq)`"]#[doc=" - `> seq`: `LexicographicalAutomaton::greater_than(seq)`"]#[doc=" - `!<= seq`: `RevLexicographicalAutomaton::less_than_or_equal(seq)`"]#[doc=" - `!>= seq`: `RevLexicographicalAutomaton::greater_than_or_equal(seq)`"]#[doc=" - `!< seq`: `RevLexicographicalAutomaton::greater_than(seq)`"]#[doc=" - `!> seq`: `RevLexicographicalAutomaton::greater_than(seq)`"]#[doc=" - `=> f g h`: `FunctionalAutomaton::new(f, g, h)`"]#[doc=" - `=> (A) f g h`: `MappingAutomaton::new(A, f, g, h)`"]#[doc=" - `=> f g h (A)`: `AlphabetMappingAutomaton::new(A, f, g, h)`"]#[doc=" - `@`: `AlwaysAcceptingAutomaton::new()`"]#[doc=" - `(A) * (B)`: `ProductAutomaton(A, B)`"]#[doc=" - `(A) & (B)`: `IntersectionAutomaton(A, B)`"]#[doc=" - `(A) | (B)`: `UnionAutomaton(A, B)`"]#[macro_export]macro_rules!automaton{(@inner($($t:tt)*))=>{$crate::automaton!(@inner$($t)*)};(@inner<=$e:expr)=>{LexicographicalAutomaton::less_than_or_equal(&$e)};(@inner>=$e:expr)=>{LexicographicalAutomaton::greater_than_or_equal(&$e)};(@inner<$e:expr)=>{LexicographicalAutomaton::less_than(&$e)};(@inner>$e:expr)=>{LexicographicalAutomaton::greater_than(&$e)};(@inner!<=$e:expr)=>{RevLexicographicalAutomaton::less_than_or_equal(&$e)};(@inner!>=$e:expr)=>{RevLexicographicalAutomaton::greater_than_or_equal(&$e)};(@inner!<$e:expr)=>{RevLexicographicalAutomaton::less_than(&$e)};(@inner!>$e:expr)=>{RevLexicographicalAutomaton::greater_than(&$e)};(@inner=>$f:expr,$g:expr,$h:expr,($($t:tt)*)$(,)?)=>{AlphabetMappingAutomaton::new($crate::automaton!(@inner$($t)*),$f,$g,$h)};(@inner=>($($t:tt)*)$f:expr,$g:expr,$h:expr$(,)?)=>{MappingAutomaton::new($crate::automaton!(@inner$($t)*),$f,$g,$h)};(@inner=>$f:expr,$g:expr,$h:expr$(,)?)=>{FunctionalAutomaton::new($f,$g,$h)};(@inner($($h:tt)*)$($op:tt($($t:tt)*))*)=>{$crate::automaton!(@union[]($($h)*)$($op($($t)*))*)};(@inner@)=>{AlwaysAcceptingAutomaton::new()};(@inner$($t:tt)*)=>{$($t)*};(@union[]($($h:tt)*)$($t:tt)*)=>{$crate::automaton!(@union[($($h)*)]$($t)*)};(@union[$($h:tt)*]|($($x:tt)*)$($t:tt)*)=>{UnionAutomaton($crate::automaton!(@inner$($h)*),$crate::automaton!(@inner($($x)*)$($t)*))};(@union[$($h:tt)*]$op:tt($($x:tt)*)$($t:tt)*)=>{$crate::automaton!(@union[$($h)*$op($($x)*)]$($t)*)};(@union[$($h:tt)*])=>{$crate::automaton!(@inter[]$($h)*)};(@inter[]($($h:tt)*)$($t:tt)*)=>{$crate::automaton!(@inter[($($h)*)]$($t)*)};(@inter[$($h:tt)*]&($($x:tt)*)$($t:tt)*)=>{IntersectionAutomaton($crate::automaton!(@inner$($h)*),$crate::automaton!(@inner($($x)*)$($t)*))};(@inter[$($h:tt)*]$op:tt($($x:tt)*)$($t:tt)*)=>{$crate::automaton!(@inter[$($h)*$op($($x)*)]$($t)*)};(@inter[$($h:tt)*])=>{$crate::automaton!(@prod[]$($h)*)};(@prod[]($($h:tt)*)$($t:tt)*)=>{$crate::automaton!(@prod[($($h)*)]$($t)*)};(@prod[$($h:tt)*]*($($x:tt)*)$($t:tt)*)=>{ProductAutomaton($crate::automaton!(@inner$($h)*),$crate::automaton!(@inner($($x)*)$($t)*))};(@prod[$($h:tt)*]$op:tt($($x:tt)*)$($t:tt)*)=>{$crate::automaton!(@prod[$($h)*$op($($x)*)]$($t)*)};(@prod[$($h:tt)*])=>{$crate::automaton!(@inner$($h)*)};($($t:tt)*)=>{$crate::automaton!(@inner$($t)*)};}}
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::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::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.});}
mod tuple_operation_impl{#![allow(unused_variables,clippy::unused_unit)]use super::*;macro_rules!impl_tuple_operation{(@impl$($T:ident)*,$($i:tt)*)=>{impl<$($T:Magma),*>Magma for($($T,)*){type T=($(<$T as Magma>::T,)*);#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{($(<$T as Magma>::operate(&x.$i,&y.$i),)*)}}impl<$($T:Unital),*>Unital for($($T,)*){#[inline]fn unit()->Self::T{($(<$T as Unital>::unit(),)*)}}impl<$($T:Associative),*>Associative for($($T,)*){}impl<$($T:Commutative),*>Commutative for($($T,)*){}impl<$($T:Idempotent),*>Idempotent for($($T,)*){}impl<$($T:Invertible),*>Invertible for($($T,)*){#[inline]fn inverse(x:&Self::T)->Self::T{($(<$T as Invertible>::inverse(&x.$i),)*)}}};(@inner[$($T:ident)*][][$($i:tt)*][])=>{impl_tuple_operation!(@impl$($T)*,$($i)*);};(@inner[$($T:ident)*][$U:ident$($Rest:ident)*][$($i:tt)*][$j:tt$($rest:tt)*])=>{impl_tuple_operation!(@impl$($T)*,$($i)*);impl_tuple_operation!(@inner[$($T)*$U][$($Rest)*][$($i)*$j][$($rest)*]);};($($T:ident)*,$($i:tt)*)=>{impl_tuple_operation!(@inner[][$($T)*][][$($i)*]);};}impl_tuple_operation!(A B C D E F G H I J,0 1 2 3 4 5 6 7 8 9);}