pub fn main() { crate::prepare!(); sc!(n, s: [@CharsWithBase('a'); n], q); let cap = s.iter().map(|s| s.len()).sum::() + q; let mut trie = Trie::with_capacity(26, cap); let mut edges = vec![]; let mut last = vec![0usize; n]; let mut dp = Vec::with_capacity(cap); dp.push(0i64); for (i, s) in s.iter().enumerate() { let ss = trie.insert(s.iter().cloned()); let k = dp.len(); for w in ss.windows(2) { if w[1] >= k { edges.push((w[0], w[1])); } if dp.len() <= w[1] { dp.resize_with(w[1] + 1, Default::default); } dp[w[1]] += 1; } last[i] = ss.last().cloned().unwrap(); } let mut query = vec![]; for _ in 0..q { sc!(ty); if ty == 1 { sc!(x: Usize1, c: @CharWithBase('a')); let ss = trie.insert_at(last[x], once(c)); if ss[1] >= dp.len() { edges.push((ss[0], ss[1])); } last[x] = ss[1]; if dp.len() <= ss[1] { dp.resize_with(ss[1] + 1, Default::default); } query.push((ty, x, ss[1])); } else { sc!(x: Usize1); query.push((ty, x, last[x])); } } let g = UndirectedSparseGraph::from_edges(dp.len(), edges); let mut et = EulerTourForVertex::new(&g); et.path_vertex_tour(0, !0); let mut ep = vec![0i64; dp.len() * 2]; for i in 0..dp.len() { ep[et.vidx[i].0] += dp[i]; ep[et.vidx[i].1] -= dp[i]; } let mut bit = BinaryIndexedTree::>::from_slice(&ep); for (ty, _x, k) in query { if ty == 1 { bit.update(et.vidx[k].0, 1); bit.update(et.vidx[k].1, -1); } else { let ans = et.path_query(0, k, |l, r| bit.fold(l, r)); pp!(ans); } } } use std::iter::once; #[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(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display;}macro_rules!iter_print_tuple_impl{(@impl$($A:ident$a:ident)?,$($B:ident$b:ident)*)=>{impl<$($A,)?$($B),*>IterPrint for($($A,)?$($B),*)where$($A:Display,)?$($B:Display),*{#[allow(unused_variables)]fn iter_print(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display{let($($a,)?$($b,)*)=self;$(if is_head{::std::write!(writer,"{}",$a)?;}else{::std::write!(writer,"{}{}",sep,$a)?;})?$(::std::write!(writer,"{}{}",sep,$b)?;)*Ok(())}}};(@inc,,$C:ident$c:ident$($D:ident$d:ident)*)=>{iter_print_tuple_impl!(@impl,);iter_print_tuple_impl!(@inc$C$c,,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,$C:ident$c:ident$($D:ident$d:ident)*)=>{iter_print_tuple_impl!(@impl$A$a,$($B$b)*);iter_print_tuple_impl!(@inc$A$a,$($B$b)*$C$c,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,)=>{iter_print_tuple_impl!(@impl$A$a,$($B$b)*);};($($t:tt)*)=>{iter_print_tuple_impl!(@inc,,$($t)*);};}iter_print_tuple_impl!(A a B b C c D d E e F f G g H h I i J j K k);#[doc=" Print expressions with a separator."]#[doc=" - `iter_print!(writer, args...)`"]#[doc=" - `@sep $expr`: set separator (default: `' '`)"]#[doc=" - `@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>(iter:&mut I)->Option;}pub trait MarkedIterScan:Sized{type Output;fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option;}#[derive(Clone,Debug)]pub struct Scanner<'a>{iter:std::str::SplitAsciiWhitespace<'a>}impl<'a>Scanner<'a>{#[inline]pub fn new(s:&'a str)->Self{let iter=s.split_ascii_whitespace();Self{iter}}#[inline]pub fn scan(&mut self)->::Output where T:IterScan{::scan(&mut self.iter).expect("scan error")}#[inline]pub fn mscan(&mut self,marker:T)->::Output where T:MarkedIterScan{marker.mscan(&mut self.iter).expect("scan error")}#[inline]pub fn scan_vec(&mut self,size:usize)->Vec<::Output>where T:IterScan{(0..size).map(|_|::scan(&mut self.iter).expect("scan error")).collect()}#[inline]pub fn iter<'b,T>(&'b mut self)->ScannerIter<'a,'b,T>where T:IterScan{ScannerIter{inner:self,_marker:std::marker::PhantomData}}}macro_rules!iter_scan_impls{($($t:ty)*)=>{$(impl IterScan for$t{type Output=Self;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{iter.next()?.parse::<$t>().ok()}})*};}iter_scan_impls!(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String);macro_rules!iter_scan_tuple_impl{(@impl$($T:ident)*)=>{impl<$($T:IterScan),*>IterScan for($($T,)*){type Output=($(<$T as IterScan>::Output,)*);#[inline]fn scan<'a,It:Iterator>(_iter:&mut It)->Option{Some(($(<$T as IterScan>::scan(_iter)?,)*))}}};(@inner$($T:ident)*,)=>{iter_scan_tuple_impl!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{iter_scan_tuple_impl!(@impl$($T)*);iter_scan_tuple_impl!(@inner$($T)*$U,$($Rest)*);};($($T:ident)*)=>{iter_scan_tuple_impl!(@inner,$($T)*);};}iter_scan_tuple_impl!(A B C D E F G H I J K);pub struct ScannerIter<'a,'b,T>{inner:&'b mut Scanner<'a>,_marker:std::marker::PhantomDataT>}impl<'a,'b,T>Iterator for ScannerIter<'a,'b,T>where T:IterScan{type Item=::Output;#[inline]fn next(&mut self)->Option{::scan(&mut self.inner.iter)}}#[doc=" - `scan_value!(scanner, ELEMENT)`"]#[doc=""]#[doc=" ELEMENT :="]#[doc=" - `$ty`: IterScan"]#[doc=" - `@$expr`: MarkedIterScan"]#[doc=" - `[ELEMENT; $expr]`: vector"]#[doc=" - `[ELEMENT]`: iterator"]#[doc=" - `($(ELEMENT)*,)`: tuple"]#[macro_export]macro_rules!scan_value{(@repeat$scanner:expr,[$($t:tt)*]$($len:expr)?)=>{::std::iter::repeat_with(||$crate::scan_value!(@inner$scanner,[]$($t)*))$(.take($len).collect::>())?};(@tuple$scanner:expr,[$([$($args:tt)*])*])=>{($($($args)*,)*)};(@$tag:ident$scanner:expr,[[$($args:tt)*]])=>{$($args)*};(@$tag:ident$scanner:expr,[$($args:tt)*]@$e:expr)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.mscan($e)]])};(@$tag:ident$scanner:expr,[$($args:tt)*]@$e:expr,$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.mscan($e)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*]($($tuple:tt)*)$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@tuple$scanner,[]$($tuple)*)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][@$e:expr;$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[@$e]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][[$($tt:tt)*];$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[[$($tt)*]]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][($($tt:tt)*);$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[($($tt)*)]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][$ty:ty;$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[$ty]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[$($tt)*])]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*]$ty:ty)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.scan::<$ty>()]])};(@$tag:ident$scanner:expr,[$($args:tt)*]$ty:ty,$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.scan::<$ty>()]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*],$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*])=>{::std::compile_error!(::std::stringify!($($args)*))};($scanner:expr,$($t:tt)*)=>{$crate::scan_value!(@inner$scanner,[]$($t)*)}}#[doc=" - `scan!(scanner, $($pat $(: ELEMENT)?),*)`"]#[macro_export]macro_rules!scan{(@assert$p:pat)=>{};(@assert$($p:tt)*)=>{::std::compile_error!(::std::concat!("expected pattern, found `",::std::stringify!($($p)*),"`"));};(@pat$scanner:expr,[][])=>{};(@pat$scanner:expr,[][],$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]$x:ident$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*$x][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]::$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*::][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]&$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*&][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]($($x:tt)*)$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*($($x)*)][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][][$($x:tt)*]$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*[$($x)*]][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]{$($x:tt)*}$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*{$($x)*}][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]:$($t:tt)*)=>{$crate::scan!(@ty$scanner,[$($p)*][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][usize]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]@$e:expr)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*@$e])};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]@$e:expr,$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*@$e],$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]($($x:tt)*)$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*($($x)*)]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*][$($x:tt)*]$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*[$($x)*]]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]$ty:ty)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*$ty])};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]$ty:ty,$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*$ty],$($t)*)};(@let$scanner:expr,[$($p:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::scan!{@assert$($p)*}let$($p)* =$crate::scan_value!($scanner,$($tt)*);$crate::scan!(@pat$scanner,[][]$($t)*)};($scanner:expr,$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)}}#[derive(Debug,Copy,Clone)]pub enum Usize1{}impl IterScan for Usize1{type Output=usize;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{::scan(iter)?.checked_sub(1)}}#[derive(Debug,Copy,Clone)]pub struct CharWithBase(pub char);impl MarkedIterScan for CharWithBase{type Output=usize;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{Some((::scan(iter)?as u8-self.0 as u8)as usize)}}#[derive(Debug,Copy,Clone)]pub enum Chars{}impl IterScan for Chars{type Output=Vec;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{Some(iter.next()?.chars().collect())}}#[derive(Debug,Copy,Clone)]pub struct CharsWithBase(pub char);impl MarkedIterScan for CharsWithBase{type Output=Vec;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{Some(iter.next()?.chars().map(|c|(c as u8-self.0 as u8)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub struct ByteWithBase(pub u8);impl MarkedIterScan for ByteWithBase{type Output=usize;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{Some((::scan(iter)?as u8-self.0)as usize)}}#[derive(Debug,Copy,Clone)]pub enum Bytes{}impl IterScan for Bytes{type Output=Vec;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{Some(iter.next()?.bytes().collect())}}#[derive(Debug,Copy,Clone)]pub struct BytesWithBase(pub u8);impl MarkedIterScan for BytesWithBase{type Output=Vec;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{Some(iter.next()?.bytes().map(|c|(c-self.0)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub struct Collect::Output>>where T:IterScan,B:FromIterator<::Output>{size:usize,_marker:PhantomData(T,B)>}implCollectwhere T:IterScan,B:FromIterator<::Output>{pub fn new(size:usize)->Self{Self{size,_marker:PhantomData}}}implMarkedIterScan for Collectwhere T:IterScan,B:FromIterator<::Output>{type Output=B;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{repeat_with(||::scan(iter)).take(self.size).collect()}}#[derive(Debug,Copy,Clone)]pub struct SizedCollect::Output>>where T:IterScan,B:FromIterator<::Output>{_marker:PhantomData(T,B)>}implIterScan for SizedCollectwhere T:IterScan,B:FromIterator<::Output>{type Output=B;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{let size=usize::scan(iter)?;repeat_with(||::scan(iter)).take(size).collect()}}#[derive(Debug,Copy,Clone)]pub struct Splittedwhere T:IterScan{pat:P,_marker:PhantomDataT>}implSplittedwhere T:IterScan{pub fn new(pat:P)->Self{Self{pat,_marker:PhantomData}}}implMarkedIterScan for Splittedwhere T:IterScan{type Output=Vec<::Output>;fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{let mut iter=iter.next()?.split(self.pat);Some(from_fn(||::scan(&mut iter)).collect())}}implMarkedIterScan for Splittedwhere T:IterScan{type Output=Vec<::Output>;fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{let mut iter=iter.next()?.split(self.pat);Some(from_fn(||::scan(&mut iter)).collect())}}implMarkedIterScan for F where F:Fn(&str)->Option{type Output=T;fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{self(iter.next()?)}}} pub use self::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=PhantomDataT>;#[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{vsize:usize,pub start:Vec,pub elist:Vec,pub edges:Vec<(usize,usize)>,_marker:Marker}implSparseGraph{#[doc=" Return the number of vertices."]pub fn vertices_size(&self)->usize{self.vsize}#[doc=" Return the number of edges."]pub fn edges_size(&self)->usize{self.edges.len()}#[doc=" Return an iterator over graph vertices."]pub fn vertices(&self)->ops::Range{0..self.vertices_size()}#[doc=" Return a slice of adjacency vertices."]pub fn adjacencies(&self,v:usize)->slice::Iter<'_,Adjacency>{self.elist[self.start[v]..self.start[v+1]].iter()}pub fn builder(vsize:usize)->SparseGraphBuilder{SparseGraphBuilder::new(vsize)}pub fn builder_with_esize(vsize:usize,esize:usize)->SparseGraphBuilder{SparseGraphBuilder::new_with_esize(vsize,esize)}}pub trait SparseGraphConstruction:Sized{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph;}implSparseGraphwhere 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{let mut start:Vec<_>=vec![0usize;vsize+1];for(from,_)in edges.iter().cloned(){start[from]+=1;}for i in 1..=vsize{start[i]+=start[i-1];}let mut elist=Vec::::with_capacity(edges.len());let ptr=elist.as_mut_ptr();for(id,(from,to))in edges.iter().cloned().enumerate(){start[from]-=1;unsafe{ptr.add(start[from]).write(Adjacency::new(id,to))};}unsafe{elist.set_len(edges.len())};SparseGraph{vsize,start,elist,edges,_marker:PhantomData}}}impl SparseGraphConstruction for UndirectedEdge{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph{let mut start:Vec<_>=vec![0usize;vsize+1];for(from,to)in edges.iter().cloned(){start[to]+=1;start[from]+=1;}for i in 1..=vsize{start[i]+=start[i-1];}let mut elist=Vec::::with_capacity(edges.len()*2);let ptr=elist.as_mut_ptr();for(id,(from,to))in edges.iter().cloned().enumerate(){start[from]-=1;unsafe{ptr.add(start[from]).write(Adjacency::new(id,to))};start[to]-=1;unsafe{ptr.add(start[to]).write(Adjacency::new(id,from))};}unsafe{elist.set_len(edges.len()*2)};SparseGraph{vsize,start,elist,edges,_marker:PhantomData}}}impl SparseGraphConstruction for BidirectionalEdge{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph{let mut start:Vec<_>=vec![0usize;vsize+1];for(from,to)in edges.iter().cloned(){start[to]+=1;start[from]+=1;}for i in 1..=vsize{start[i]+=start[i-1];}let mut elist=Vec::::with_capacity(edges.len()*2);let ptr=elist.as_mut_ptr();for(id,(from,to))in edges.iter().cloned().enumerate(){start[from]-=1;unsafe{ptr.add(start[from]).write(Adjacency::new(id*2,to))};start[to]-=1;unsafe{ptr.add(start[to]).write(Adjacency::new(id*2+1,from))};}unsafe{elist.set_len(edges.len()*2)};SparseGraph{vsize,start,elist,edges,_marker:PhantomData}}}pub type DirectedSparseGraph=SparseGraph;pub type UndirectedSparseGraph=SparseGraph;pub type BidirectionalSparseGraph=SparseGraph;pub struct SparseGraphBuilder{vsize:usize,edges:Vec<(usize,usize)>,rest:Vec,_marker:Marker}implSparseGraphBuilder{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);}}implSparseGraphBuilderwhere D:SparseGraphConstruction{pub fn build(self)->(SparseGraph,Vec){let graph=SparseGraph::from_edges(self.vsize,self.edges);(graph,self.rest)}}pub struct SparseGraphScannerwhere U:IterScan,T:IterScan{vsize:usize,esize:usize,_marker:Marker<(U,T,D)>}implSparseGraphScannerwhere U:IterScan,T:IterScan{pub fn new(vsize:usize,esize:usize)->Self{Self{vsize,esize,_marker:PhantomData}}}implMarkedIterScan for SparseGraphScannerwhere U:IterScan,T:IterScan,D:SparseGraphConstruction{type Output=(SparseGraph,Vec<::Output>);fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{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=SparseGraphScanner;pub type UndirectedGraphScanner=SparseGraphScanner;pub type BidirectionalGraphScanner=SparseGraphScanner;pub struct TreeGraphScannerwhere U:IterScan,T:IterScan{vsize:usize,_marker:Marker<(U,T)>}implTreeGraphScannerwhere U:IterScan,T:IterScan{pub fn new(vsize:usize)->Self{Self{vsize,_marker:PhantomData}}}implMarkedIterScan for TreeGraphScannerwhere U:IterScan,T:IterScan{type Output=(UndirectedSparseGraph,Vec<::Output>);fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{UndirectedGraphScanner::::new(self.vsize,self.vsize-1).mscan(iter)}}implGraphBase<'_>for SparseGraph{type VIndex=usize;}implEIndexedGraph<'_>for SparseGraph{type EIndex=usize;}implVertexSize<'_>for SparseGraph{fn vsize(&self)->usize{self.vsize}}implEdgeSize<'_>for SparseGraph{fn esize(&self)->usize{self.edges.len()}}implVertices<'_>for SparseGraph{type VIter=ops::Range;fn vertices(&self)->Self::VIter{0..self.vsize}}impl<'g,D>Adjacencies<'g>for SparseGraph{type AIndex=Adjacency;type AIter=Cloned>;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{type AIndex=Adjacency;type AIter=Cloned>;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}}implVertexMap<'_,T>for SparseGraph{type Vmap=Vec;fn construct_vmap(&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,map:&'a mut Self::Vmap,vid:Self::VIndex)->&'a mut T{assert!(vidVertexView<'_,Vec,T>for SparseGraphwhere T:Clone{fn vview(&self,map:&Vec,vid:Self::VIndex)->T{self.vmap_get(map,vid).clone()}}implVertexView<'_,[T],T>for SparseGraphwhere T:Clone{fn vview(&self,map:&[T],vid:Self::VIndex)->T{assert!(vidEdgeMap<'_,T>for SparseGraph{type Emap=Vec;fn construct_emap(&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(&self,map:&'a mut Self::Emap,eid:Self::EIndex)->&'a mut T{let esize=self.edges.len();assert!(eidEdgeView<'_,Vec,T>for SparseGraphwhere T:Clone{fn eview(&self,map:&Vec,eid:Self::EIndex)->T{self.emap_get(map,eid).clone()}}implEdgeView<'_,[T],T>for SparseGraphwhere T:Clone{fn eview(&self,map:&[T],eid:Self::EIndex)->T{let esize=self.edges.len();assert!(eidAdjacencyView<'g,'a,M,T>for SparseGraphwhere 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;fn vertices(&'g self)->Self::VIter;}pub trait Edges<'g>:EIndexedGraph<'g>{type EIter:'g+Iterator;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;type AIter:'g+Iterator;fn adjacencies(&'g self,vid:Self::VIndex)->Self::AIter;}pub trait AdjacenciesWithEindex<'g>:EIndexedGraph<'g>{type AIndex:'g+AdjacencyIndexWithEindex;type AIter:'g+Iterator;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;type AIter:'g+Iterator;fn adjacencies_with_value(&'g self,vid:Self::VIndex)->Self::AIter;}impl AdjacencyIndex for usize{type VIndex=usize;fn vindex(&self)->Self::VIndex{*self}}implAdjacencyIndex for(V,E)where V:Copy+Eq,E:Copy+Eq{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}implAdjacencyIndexWithEindex 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);#[derive(Debug,Clone,Copy,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct VIndexWithEIndex(V,E);#[derive(Debug,Clone,Copy,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct VIndexWithValue(V,T);#[derive(Debug,Clone,Copy,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct VIndexWithEIndexValue(V,E,T);implAdjacencyIndex for VIndexwhere V:Eq+Copy{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}implAdjacencyIndex for VIndexWithEIndexwhere V:Eq+Copy{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}implAdjacencyIndexWithEindex for VIndexWithEIndexwhere V:Eq+Copy,E:Eq+Copy{type EIndex=E;fn eindex(&self)->Self::EIndex{self.1}}implAdjacencyIndex for VIndexWithValuewhere V:Eq+Copy{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}implAdjacencyIndexWithValue for VIndexWithValuewhere V:Eq+Copy,T:Clone{type AValue=T;fn avalue(&self)->Self::AValue{self.1.clone()}}implAdjacencyIndex for VIndexWithEIndexValuewhere V:Eq+Copy{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}implAdjacencyIndexWithEindex for VIndexWithEIndexValuewhere V:Eq+Copy,E:Eq+Copy{type EIndex=E;fn eindex(&self)->Self::EIndex{self.1}}implAdjacencyIndexWithValue for VIndexWithEIndexValuewhere V:Eq+Copy,T:Clone{type AValue=T;fn avalue(&self)->Self::AValue{self.2.clone()}}implFromfor VIndex{fn from(vid:V)->Self{VIndex(vid)}}implFrom<(V,E)>for VIndexWithEIndex{fn from((vid,eid):(V,E))->Self{VIndexWithEIndex(vid,eid)}}implFrom<(V,T)>for VIndexWithValue{fn from((vid,value):(V,T))->Self{VIndexWithValue(vid,value)}}implFrom<(V,E,T)>for VIndexWithEIndexValue{fn from((vid,eid,value):(V,E,T))->Self{VIndexWithEIndexValue(vid,eid,value)}}implVIndexWithValue{pub fn map(self,mut f:F)->VIndexWithValuewhere F:FnMut(T)->U{VIndexWithValue(self.0,f(self.1))}}implVIndexWithEIndexValue{pub fn map(self,mut f:F)->VIndexWithEIndexValuewhere F:FnMut(T)->U{VIndexWithEIndexValue(self.0,self.1,f(self.2))}}pub trait VertexMap<'g,T>:GraphBase<'g>{type Vmap;fn construct_vmap(&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(&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>;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:PhantomDataT>}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;fn next(&mut self)->Option{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:PhantomDataU>}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;fn next(&mut self)->Option{self.iter.next().map(|adj|(adj.vindex(),(self.map)(adj.avalue())).into())}}} #[derive(Clone,Debug)]pub struct EulerTourForVertex<'a>{graph:&'a UndirectedSparseGraph,pub vidx:Vec<(usize,usize)>,vpos:usize} impl<'a>EulerTourForVertex<'a>{pub fn new(graph:&'a UndirectedSparseGraph)->Self{Self{graph,vidx:vec![(0,0);graph.vertices_size()],vpos:0}}pub fn length(&self)->usize{self.vpos}pub fn subtree_vertex_tour(&mut self,u:usize,p:usize){self.vidx[u].0=self.vpos;self.vpos+=1;for a in self.graph.adjacencies(u).filter(|a|a.to!=p){self.subtree_vertex_tour(a.to,u);}self.vidx[u].1=self.vpos;}pub fn path_vertex_tour(&mut self,u:usize,p:usize){self.vidx[u].0=self.vpos;self.vpos+=1;for a in self.graph.adjacencies(u).filter(|a|a.to!=p){self.path_vertex_tour(a.to,u);}self.vidx[u].1=self.vpos;self.vpos+=1;}pub fn subtree_queryT>(&self,u:usize,mut f:F)->T{let(l,r)=self.vidx[u];f(l,r)}pub fn subtree_update(&self,u:usize,x:T,mut f:F){let(l,_r)=self.vidx[u];f(l,x);}pub fn path_queryT>(&self,u:usize,v:usize,mut f:F)->T{let(mut l,mut r)=(self.vidx[u].0,self.vidx[v].0);if l>r{std::mem::swap(&mut l,&mut r);}f(l,r+1)}pub fn path_update(&self,u:usize,x:T,invx:T,mut f:F){let(l,r)=self.vidx[u];f(l,x);f(r,invx);}} pub use self::binary_indexed_tree::BinaryIndexedTree; mod binary_indexed_tree{use super::{Group,Monoid};use std::fmt::{self,Debug,Formatter};pub struct BinaryIndexedTreewhere M:Monoid{n:usize,bit:Vec}implClone for BinaryIndexedTreewhere M:Monoid{fn clone(&self)->Self{Self{n:self.n,bit:self.bit.clone()}}}implDebug for BinaryIndexedTreewhere M:Monoid,M::T:Debug{fn fmt(&self,f:&mut Formatter<'_>)->fmt::Result{f.debug_struct("BinaryIndexedTree").field("n",&self.n).field("bit",&self.bit).finish()}}implBinaryIndexedTreewhere M:Monoid{#[inline]pub fn new(n:usize)->Self{let bit=vec![M::unit();n+1];Self{n,bit}}#[inline]pub fn from_slice(slice:&[M::T])->Self{let n=slice.len();let mut bit=vec![M::unit();n+1];for(i,x)in slice.iter().enumerate(){let k=i+1;M::operate_assign(&mut bit[k],x);let j=k+(k&(!k+1));if j<=n{bit[j]=M::operate(&bit[j],&bit[k]);}}Self{n,bit}}#[inline]#[doc=" fold [0, k)"]pub fn accumulate0(&self,mut k:usize)->M::T{debug_assert!(k<=self.n);let mut res=M::unit();while k>0{res=M::operate(&res,&self.bit[k]);k-=k&(!k+1);}res}#[inline]#[doc=" fold [0, k]"]pub fn accumulate(&self,k:usize)->M::T{self.accumulate0(k+1)}#[inline]pub fn update(&mut self,k:usize,x:M::T){debug_assert!(kBinaryIndexedTree{#[inline]pub fn fold(&self,l:usize,r:usize)->G::T{debug_assert!(l<=self.n&&r<=self.n);G::operate(&G::inverse(&self.accumulate0(l)),&self.accumulate0(r))}#[inline]pub fn get(&self,k:usize)->G::T{self.fold(k,k+1)}#[inline]pub fn set(&mut self,k:usize,x:G::T){self.update(k,G::operate(&G::inverse(&self.get(k)),&x));}}implBinaryIndexedTreewhere M::T:Ord{#[inline]pub fn lower_bound(&self,x:M::T)->usize{let n=self.n;let mut acc=M::unit();let mut pos=0;let mut k=n.next_power_of_two();while k>0{if k+pos<=n&&M::operate(&acc,&self.bit[k+pos])>=1;}pos}}} 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{}implSemiGroup 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::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}}implMonoid 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{}implGroup 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{}implAbelianMonoid for M where M:Monoid+Commutative{}#[doc=" commutative group"]pub trait AbelianGroup:Group+Commutative{}implAbelianGroup 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{}implIdempotentMonoid 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>{_marker:PhantomDataT>}impl>Magma for AdditiveOperation{type T=T;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{x.clone()+y.clone()}}impl>Unital for AdditiveOperation{#[inline]fn unit()->Self::T{Zero::zero()}}impl>Associative for AdditiveOperation{}impl>Commutative for AdditiveOperation{}impl+Sub+Neg>Invertible for AdditiveOperation{#[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.});} pub use self::trie::Trie; mod trie { #[derive(Debug, Clone)] pub struct Trie { child: Vec, accept: Vec, char_size: usize, } impl Trie { pub fn new(char_size: usize) -> Self { Self { child: vec![0; char_size], accept: vec![0], char_size, } } pub fn with_capacity(char_size: usize, capacity: usize) -> Self { let mut child = Vec::with_capacity(capacity * char_size); let mut accept = Vec::with_capacity(capacity); child.resize_with(char_size, Default::default); accept.push(0); Self { child, accept, char_size, } } pub fn insert_at( &mut self, mut node: usize, iter: impl IntoIterator, ) -> Vec { let mut path = Vec::new(); for ch in iter.into_iter() { path.push(node); if self.child[node * self.char_size + ch] == 0 { self.child[node * self.char_size + ch] = self.accept.len(); self.child .resize_with(self.child.len() + self.char_size, Default::default); self.accept.push(0); } node = self.child[node * self.char_size + ch]; } path.push(node); self.accept[node] += 1; path } pub fn insert(&mut self, iter: impl IntoIterator) -> Vec { self.insert_at(0, iter) } pub fn find_at( &self, mut node: usize, iter: impl IntoIterator, ) -> Result { for ch in iter.into_iter() { if let Some(&nnode) = self.child.get(node * self.char_size + ch) { node = nnode; } else { return Err(node); } } Ok(node) } pub fn find(&self, iter: impl IntoIterator) -> Result { self.find_at(0, iter) } pub fn next_node(&self, node: usize, ch: usize) -> Option { if self.child[node * self.char_size + ch] == 0 { None } else { Some(self.child[node * self.char_size + ch]) } } pub fn count(&self, node: usize) -> usize { self.accept[node] } pub fn next_count(&self, node: usize, ch: usize) -> usize { if let Some(node) = self.next_node(node, ch) { self.count(node) } else { 0 } } } }