pub fn main() {
    crate::prepare!();
    sc!(n, q, mut a: [usize; n]);
    a.sort_unstable();
    a.dedup();
    type L = EmptyLazy<AdditiveOperation<usize>>;
    let mut seq = [SplaySequence::<L>::new(), SplaySequence::<L>::new()];
    let mut l = a[0];
    let mut i = 0usize;
    while i < a.len() {
        if i > 0 {
            seq[1].insert(seq[1].len(), a[i] - a[i - 1] - 1);
        }
        let mut j = i + 1;
        while j < a.len() && a[j - 1] + 1 == a[j] {
            j += 1;
        }
        seq[0].insert(seq[0].len(), j - i);
        i = j;
    }
    for (k, x, m) in sv!([(usize, Usize1, usize)]).take(q) {
        for _ in 0..k.min(2) {
            l += seq[0].remove(0).unwrap();
            seq.swap(0, 1);
            while seq[0].fold(..) >= m {
                seq[1].remove(seq[1].len() - 1).unwrap();
                let cap = seq[0].fold(..) - m;
                if cap == 0 {
                    break;
                }
                seq[0].modify(seq[0].len() - 1, |q| q.saturating_sub(cap));
                if seq[0].get(seq[0].len() - 1).unwrap() == &0 {
                    seq[0].remove(seq[0].len() - 1);
                } else {
                    break;
                }
            }
            let cap = m - seq[0].fold(..);
            if cap > 0 {
                seq[0].insert(seq[0].len(), cap);
            }
        }
        {
            let cap = m - seq[1].fold(..);
            if cap > 0 {
                seq[1].insert(seq[1].len(), cap);
            }
            let k = k.saturating_sub(2);
            let f = seq[0].len() * 2;
            l += k / f * m * 2;
            let c0 = (k % f + 1) / 2;
            let c1 = k % f / 2;
            l += seq[0].fold(..c0);
            l += seq[1].fold(..c1);
            seq[0].rotate_left(c0);
            seq[1].rotate_left(c1);
            if c0 != c1 {
                seq.swap(0, 1);
            }
            seq[1].remove(seq[1].len() - 1);
        }
        l %= MOD;
        let i = seq[0].position_acc(.., |&s| s > x).unwrap();
        pp!((l + seq[1].fold(..i) + x) % MOD);
    }
}
const MOD: usize = 998244353;
pub struct EmptyLazy<M> {
    _marker: std::marker::PhantomData<fn() -> M>,
}
impl<M> MonoidAction for EmptyLazy<M>
where
    M: Monoid,
{
    type Key = M::T;
    type Agg = M::T;
    type Act = ();
    type AggMonoid = M;
    type ActMonoid = ();
    fn single_agg(key: &Self::Key) -> Self::Agg {
        key.clone()
    }
    fn act_key(x: &Self::Key, _a: &Self::Act) -> Self::Key {
        x.clone()
    }
    fn act_agg(x: &Self::Agg, _a: &Self::Act) -> Option<Self::Agg> {
        Some(x.clone())
    }
}
#[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::splay_tree::{SplayMap,SplaySequence};
mod splay_tree{use super::{Allocator,MemoryPool,MonoidAction};pub use sequence::SplaySequence;pub use sized_map::SplayMap;pub mod node{use super::Allocator;use std::{cmp::Ordering,fmt::{self,Debug},marker::PhantomData,mem::{replace,swap},ops::Bound,ptr::NonNull};pub trait SplaySpec:Sized{type T;fn has_bottom_up()->bool{false}fn top_down(_node:NodeRef<marker::DataMut<'_>,Self>){}fn bottom_up(_node:NodeRef<marker::DataMut<'_>,Self>){}}pub trait SplaySeeker{type S:SplaySpec;fn splay_seek(&mut self,_node:NodeRef<marker::Immut<'_>,Self::S>)->Ordering;}pub struct SeekLeft<S>{_marker:PhantomData<fn()->S>}impl<S>SeekLeft<S>{pub fn new()->Self{Self{_marker:PhantomData}}}impl<S>SplaySeeker for SeekLeft<S>where S:SplaySpec{type S=S;fn splay_seek(&mut self,_node:NodeRef<marker::Immut<'_>,Self::S>)->Ordering{Ordering::Less}}pub struct SeekRight<S>{_marker:PhantomData<fn()->S>}impl<S>SeekRight<S>{pub fn new()->Self{Self{_marker:PhantomData}}}impl<S>SplaySeeker for SeekRight<S>where S:SplaySpec{type S=S;fn splay_seek(&mut self,_node:NodeRef<marker::Immut<'_>,Self::S>)->Ordering{Ordering::Greater}}pub struct Node<T>{data:T,left:Option<NonNull<Node<T>>>,right:Option<NonNull<Node<T>>>}impl<T>Node<T>{pub fn new(data:T)->Self{Self{data,left:None,right:None}}}pub struct NodeRef<B,S>where S:SplaySpec{node:NonNull<Node<S::T>>,_marker:PhantomData<B>}pub struct Root<S>where S:SplaySpec{root:Option<NodeRef<marker::Owned,S>>}impl<S>Default for Root<S>where S:SplaySpec{fn default()->Self{Self{root:None}}}impl<'a,S>Copy for NodeRef<marker::Immut<'a>,S>where S:SplaySpec,S::T:'a{}impl<'a,S>Clone for NodeRef<marker::Immut<'a>,S>where S:SplaySpec,S::T:'a{fn clone(&self)->Self{*self}}impl<B,S>NodeRef<B,S>where S:SplaySpec{unsafe fn new_unchecked(node:NonNull<Node<S::T>>)->Self{Self{node,_marker:PhantomData}}fn reborrow(&self)->NodeRef<marker::Immut<'_>,S>{unsafe{NodeRef::new_unchecked(self.node)}}fn as_ptr(&self)->*mut Node<S::T>{self.node.as_ptr()}}impl<S>NodeRef<marker::Owned,S>where S:SplaySpec{pub fn new(node:NonNull<Node<S::T>>)->Self{unsafe{NodeRef::new_unchecked(node)}}pub unsafe fn from_data<A>(data:S::T,allocator:&mut A)->Self where A:Allocator<Node<S::T>>{Self::new(allocator.allocate(Node::new(data)))}pub fn borrow_mut(&mut self)->NodeRef<marker::Mut<'_>,S>{unsafe{NodeRef::new_unchecked(self.node)}}pub fn borrow_datamut(&mut self)->NodeRef<marker::DataMut<'_>,S>{unsafe{NodeRef::new_unchecked(self.node)}}pub fn into_dying(self)->NodeRef<marker::Dying,S>{unsafe{NodeRef::new_unchecked(self.node)}}}impl<'a,S>NodeRef<marker::Immut<'a>,S>where S:SplaySpec,S::T:'a{pub fn data(&self)->&'a S::T{unsafe{&(*self.as_ptr()).data}}pub fn left(&self)->Option<Self>{unsafe{(*self.as_ptr()).left.map(|node|NodeRef::new_unchecked(node))}}pub fn right(&self)->Option<Self>{unsafe{(*self.as_ptr()).right.map(|node|NodeRef::new_unchecked(node))}}pub fn traverse<F>(self,f:&mut F)where S::T:'a,F:FnMut(Self){if let Some(left)=self.clone().left(){left.traverse(f);}f(self);if let Some(right)=self.clone().right(){right.traverse(f);}}}impl<'a,S>NodeRef<marker::DataMut<'a>,S>where S:SplaySpec,S::T:'a{pub fn data(&self)->&'a S::T{unsafe{&(*self.as_ptr()).data}}pub fn data_mut(&self)->&'a mut S::T{unsafe{&mut(*self.as_ptr()).data}}pub fn left(&self)->Option<Self>{unsafe{(*self.as_ptr()).left.map(|node|NodeRef::new_unchecked(node))}}pub fn right(&self)->Option<Self>{unsafe{(*self.as_ptr()).right.map(|node|NodeRef::new_unchecked(node))}}pub fn reverse(&self){unsafe{let node=&mut(*self.as_ptr());swap(&mut node.left,&mut node.right);}}}impl<'a,S>NodeRef<marker::Mut<'a>,S>where S:SplaySpec,S::T:'a{pub fn data(self)->&'a S::T{unsafe{&(*self.as_ptr()).data}}pub fn data_mut(self)->&'a mut S::T{unsafe{&mut(*self.as_ptr()).data}}pub fn take_left(&mut self)->Option<NodeRef<marker::Owned,S>>{Some(NodeRef::new(unsafe{(*self.as_ptr()).left.take()?}))}pub fn take_right(&mut self)->Option<NodeRef<marker::Owned,S>>{Some(NodeRef::new(unsafe{(*self.as_ptr()).right.take()?}))}pub fn set_left(&mut self,node:Option<NodeRef<marker::Owned,S>>){unsafe{(*self.as_ptr()).left=node.map(|node|node.node)}}pub fn set_right(&mut self,node:Option<NodeRef<marker::Owned,S>>){unsafe{(*self.as_ptr()).right=node.map(|node|node.node)}}}impl<S>NodeRef<marker::Dying,S>where S:SplaySpec{pub unsafe fn into_inner(self)->NonNull<Node<S::T>>{let node=self.node;debug_assert!((*node.as_ptr()).left.is_none());debug_assert!((*node.as_ptr()).right.is_none());node}pub unsafe fn into_data<A>(self,allocator:&mut A)->S::T where A:Allocator<Node<S::T>>{let Node{data,left,right}=allocator.deallocate(self.node);debug_assert!(left.is_none());debug_assert!(right.is_none());data}}impl<S>NodeRef<marker::Owned,S>where S:SplaySpec{#[doc=" `cmp(key)`: [`Ordering`] between splaying and `key`"]pub fn splay_by<Seeker>(self,mut seeker:Seeker)->(Ordering,Self)where Seeker:SplaySeeker<S=S>{let mut x=self;let mut left_subtree:Option<NonNull<Node<S::T>>>=None;let mut right_subtree:Option<NonNull<Node<S::T>>>=None;let mut left_entry=&mut left_subtree;let mut right_entry=&mut right_subtree;let mut stack=vec![];macro_rules!add{(@left Some($ptr:ident))=>{add!(@inner Some($ptr.node),left_entry$ptr right);};(@right Some($ptr:ident))=>{add!(@inner Some($ptr.node),right_entry$ptr left);};(@inner$node:expr,$entry:ident$ptr:ident$dir:ident)=>{*$entry=$node;if S::has_bottom_up(){stack.push($ptr.node);}$entry=unsafe{&mut(*$entry.as_mut().unwrap().as_ptr()).$dir};};}let root_ord=loop{S::top_down(x.borrow_datamut());match seeker.splay_seek(unsafe{NodeRef::new_unchecked(x.node)}){Ordering::Less=>{if let Some(mut y)=x.borrow_mut().take_left(){S::top_down(y.borrow_datamut());match seeker.splay_seek(unsafe{NodeRef::new_unchecked(y.node)}){Ordering::Less=>{if let Some(mut z)=y.borrow_mut().take_left(){S::top_down(z.borrow_datamut());x.borrow_mut().set_left(y.borrow_mut().take_right());S::bottom_up(x.borrow_datamut());y.borrow_mut().set_right(Some(x));add!(@right Some(y));x=z;}else{add!(@right Some(x));x=y;break Ordering::Less;}}Ordering::Equal=>{add!(@right Some(x));x=y;break Ordering::Equal;}Ordering::Greater=>{if let Some(mut z)=y.borrow_mut().take_right(){S::top_down(z.borrow_datamut());add!(@right Some(x));add!(@left Some(y));x=z;}else{add!(@right Some(x));x=y;break Ordering::Greater;}}}}else{break Ordering::Less;}}Ordering::Equal=>break Ordering::Equal,Ordering::Greater=>{if let Some(mut y)=x.borrow_mut().take_right(){S::top_down(y.borrow_datamut());match seeker.splay_seek(unsafe{NodeRef::new_unchecked(y.node)}){Ordering::Less=>{if let Some(mut z)=y.borrow_mut().take_left(){S::top_down(z.borrow_datamut());add!(@left Some(x));add!(@right Some(y));x=z;}else{add!(@left Some(x));x=y;break Ordering::Less;}}Ordering::Equal=>{add!(@left Some(x));x=y;break Ordering::Equal;}Ordering::Greater=>{if let Some(mut z)=y.borrow_mut().take_right(){S::top_down(z.borrow_datamut());x.borrow_mut().set_right(y.borrow_mut().take_left());S::bottom_up(x.borrow_datamut());y.borrow_mut().set_left(Some(x));add!(@left Some(y));x=z;}else{add!(@left Some(x));x=y;break Ordering::Greater;}}}}else{break Ordering::Greater;}}}};*left_entry=x.borrow_mut().take_left().map(|node|node.node);*right_entry=x.borrow_mut().take_right().map(|node|node.node);unsafe{x.borrow_mut().set_left(left_subtree.map(|node|NodeRef::new_unchecked(node)));x.borrow_mut().set_right(right_subtree.map(|node|NodeRef::new_unchecked(node)));if S::has_bottom_up(){while let Some(node)=stack.pop(){S::bottom_up(NodeRef::new_unchecked(node));}}}S::bottom_up(x.borrow_datamut());(root_ord,x)}pub fn insert_left(mut self,mut node:Self)->Self{if let Some(left)=self.borrow_mut().take_left(){node.borrow_mut().set_left(Some(left));S::bottom_up(self.borrow_datamut());};node.borrow_mut().set_right(Some(self));S::bottom_up(node.borrow_datamut());node}pub fn insert_right(mut self,mut node:Self)->Self{if let Some(right)=self.borrow_mut().take_right(){node.borrow_mut().set_right(Some(right));S::bottom_up(self.borrow_datamut());}node.borrow_mut().set_left(Some(self));S::bottom_up(node.borrow_datamut());node}pub fn insert_first(self,mut node:Self)->Self{node.borrow_mut().set_right(Some(self));S::bottom_up(node.borrow_datamut());node}pub fn insert_last(self,mut node:Self)->Self{node.borrow_mut().set_left(Some(self));S::bottom_up(node.borrow_datamut());node}pub fn merge(mut self,mut other:Self)->Self{if other.reborrow().left().is_none(){S::top_down(other.borrow_datamut());other.borrow_mut().set_left(Some(self));S::bottom_up(other.borrow_datamut());other}else{self=self.splay_by(SeekRight::new()).1;self.borrow_mut().set_right(Some(other));S::bottom_up(self.borrow_datamut());self}}}impl<S>Root<S>where S:SplaySpec{pub fn new(root:Option<NodeRef<marker::Owned,S>>)->Self{Self{root}}pub fn is_empty(&self)->bool{self.root.is_none()}pub fn root(&self)->Option<NodeRef<marker::Immut<'_>,S>>{Some(self.root.as_ref()?.reborrow())}pub fn root_data_mut(&mut self)->Option<NodeRef<marker::DataMut<'_>,S>>{Some(self.root.as_mut()?.borrow_datamut())}pub fn splay_by<Seeker>(&mut self,seeker:Seeker)->Option<Ordering>where Seeker:SplaySeeker<S=S>{let(ord,root)=self.root.take()?.splay_by(seeker);self.root=Some(root);Some(ord)}pub fn insert_left(&mut self,mut node:NodeRef<marker::Owned,S>){self.root=Some(match self.root.take(){Some(root)=>root.insert_left(node),None=>{S::bottom_up(node.borrow_datamut());node}});}pub fn insert_right(&mut self,mut node:NodeRef<marker::Owned,S>){self.root=Some(match self.root.take(){Some(root)=>root.insert_right(node),None=>{S::bottom_up(node.borrow_datamut());node}});}pub fn insert_first(&mut self,mut node:NodeRef<marker::Owned,S>){self.root=Some(match self.root.take(){Some(root)=>root.insert_first(node),None=>{S::bottom_up(node.borrow_datamut());node}});}pub fn insert_last(&mut self,mut node:NodeRef<marker::Owned,S>){self.root=Some(match self.root.take(){Some(root)=>root.insert_last(node),None=>{S::bottom_up(node.borrow_datamut());node}});}pub fn take_root(&mut self)->Option<NodeRef<marker::Owned,S>>{let mut root=self.root.take()?;let right=root.borrow_mut().take_right();self.root=root.borrow_mut().take_left();self.append(&mut Self::new(right));Some(root)}pub fn take_first(&mut self)->Option<NodeRef<marker::Owned,S>>{let mut root=self.root.take()?.splay_by(SeekLeft::new()).1;let right=root.borrow_mut().take_right();self.root=right;Some(root)}pub fn take_last(&mut self)->Option<NodeRef<marker::Owned,S>>{let mut root=self.root.take()?.splay_by(SeekRight::new()).1;let left=root.borrow_mut().take_left();self.root=left;Some(root)}pub fn split_left(&mut self)->Option<NodeRef<marker::Owned,S>>{let root=self.root.as_mut()?;let left=root.borrow_mut().take_left();S::bottom_up(root.borrow_datamut());left}pub fn split_right(&mut self)->Option<NodeRef<marker::Owned,S>>{let root=self.root.as_mut()?;let right=root.borrow_mut().take_right();S::bottom_up(root.borrow_datamut());right}pub fn split_left_eq(&mut self)->Option<NodeRef<marker::Owned,S>>{let right=self.split_right();replace(&mut self.root,right)}pub fn split_right_eq(&mut self)->Option<NodeRef<marker::Owned,S>>{let left=self.split_left();replace(&mut self.root,left)}pub fn append(&mut self,other:&mut Self){self.root=match(self.root.take(),other.root.take()){(Some(node),None)|(None,Some(node))=>Some(node),(Some(left),Some(right))=>Some(left.merge(right)),(None,None)=>None,}}pub fn range<Seeker>(&mut self,start:Bound<Seeker>,end:Bound<Seeker>)->NodeRange<'_,S>where Seeker:SplaySeeker<S=S>{if self.is_empty(){return NodeRange::new(self);}let right=match end{Bound::Included(seeker)=>match self.splay_by(seeker).unwrap(){Ordering::Greater|Ordering::Equal=>self.split_right(),Ordering::Less=>self.split_right_eq(),},Bound::Excluded(seeker)=>match self.splay_by(seeker).unwrap(){Ordering::Greater=>self.split_right(),Ordering::Less|Ordering::Equal=>self.split_right_eq(),},Bound::Unbounded=>None,};if self.is_empty(){return NodeRange::three_way(None,self,right);}let left=match start{Bound::Included(seeker)=>match self.splay_by(seeker).unwrap(){Ordering::Less|Ordering::Equal=>self.split_left(),Ordering::Greater=>self.split_left_eq(),},Bound::Excluded(seeker)=>match self.splay_by(seeker).unwrap(){Ordering::Less=>self.split_left(),Ordering::Greater|Ordering::Equal=>self.split_left_eq(),},Bound::Unbounded=>None,};NodeRange::three_way(left,self,right)}}impl<S>Debug for Root<S>where S:SplaySpec,S::T:Debug{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{fn fmt_recurse<'a,S>(node:NodeRef<marker::Immut<'a>,S>,f:&mut fmt::Formatter<'_>)->fmt::Result where S:SplaySpec,S::T:'a+Debug{write!(f,"[")?;if let Some(left)=node.left(){fmt_recurse(left,f)?;}node.data().fmt(f)?;if let Some(right)=node.right(){fmt_recurse(right,f)?;}write!(f,"]")?;Ok(())}if let Some(root)=self.root.as_ref(){let root=root.reborrow();fmt_recurse(root,f)?;}Ok(())}}pub struct NodeRange<'a,S>where S:SplaySpec,S::T:'a{front:Root<S>,back:Root<S>,root:&'a mut Root<S>}impl<'a,S>Debug for NodeRange<'a,S>where S:SplaySpec,S::T:'a+Debug{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{f.debug_struct("NodeRange").field("front",&self.front).field("back",&self.back).field("root",&self.root).finish()}}impl<'a,S>NodeRange<'a,S>where S:SplaySpec,S::T:'a{pub fn new(root:&'a mut Root<S>)->Self{Self{front:Default::default(),back:Default::default(),root}}pub fn three_way(front:Option<NodeRef<marker::Owned,S>>,root:&'a mut Root<S>,back:Option<NodeRef<marker::Owned,S>>)->Self{Self{front:Root::new(front),back:Root::new(back),root}}pub fn next_checked(&mut self)->Option<NodeRef<marker::DataMut<'a>,S>>{let first=self.root.take_first()?;let noderef=unsafe{NodeRef::new_unchecked(first.node)};self.front.insert_last(first);Some(noderef)}pub fn next_back_checked(&mut self)->Option<NodeRef<marker::DataMut<'a>,S>>{let last=self.root.take_last()?;let noderef=unsafe{NodeRef::new_unchecked(last.node)};self.back.insert_first(last);Some(noderef)}pub fn root(&self)->&Root<S>{self.root}pub fn root_mut(&mut self)->&mut Root<S>{self.root}pub fn front(&self)->&Root<S>{&self.front}pub fn drop_rotate_left(mut self){self.root.append(&mut self.back);self.root.append(&mut self.front);}}impl<'a,S>Drop for NodeRange<'a,S>where S:SplaySpec,S::T:'a{fn drop(&mut self){swap(self.root,&mut self.front);self.root.append(&mut self.front);self.root.append(&mut self.back);}}pub mod marker{use std::marker::PhantomData;pub enum Owned{}pub enum Dying{}pub struct Immut<'a>(PhantomData<&'a()>);pub struct Mut<'a>(PhantomData<&'a mut()>);pub struct DataMut<'a>(PhantomData<&'a mut()>);}}pub mod sequence{use super::{node::{marker,Node,NodeRange,NodeRef,Root,SplaySeeker,SplaySpec},Allocator,MemoryPool,MonoidAction};use std::{cmp::Ordering,fmt::{self,Debug},marker::PhantomData,mem::{replace,ManuallyDrop},ops::{Bound,DerefMut,RangeBounds}};pub struct LazyAggElement<T>where T:MonoidAction{key:T::Key,agg:T::Agg,lazy:T::Act,size:usize,rev:bool}impl<T>Debug for LazyAggElement<T>where T:MonoidAction,T::Key:Debug,T::Agg:Debug,T::Act:Debug{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{f.debug_struct("LazyAggElement").field("key",&self.key).field("agg",&self.agg).field("lazy",&self.lazy).field("size",&self.size).finish()}}pub struct LazyAggSplay<T>{_marker:PhantomData<fn()->T>}impl<T>LazyAggSplay<T>where T:MonoidAction{pub fn update_lazy(mut node:NodeRef<marker::DataMut<'_>,Self>,lazy:&T::Act){T::act_operate_assign(&mut node.data_mut().lazy,lazy);node.data_mut().key=T::act_key(&node.data().key,lazy);if let Some(nxlazy)=T::act_agg(&node.data().agg,lazy){node.data_mut().agg=nxlazy;}else{node=Self::propagate(node);Self::recalc(node);}}pub fn reverse(node:NodeRef<marker::DataMut<'_>,Self>){node.reverse();T::toggle(&mut node.data_mut().agg);node.data_mut().rev^=true;}fn propagate(node:NodeRef<marker::DataMut<'_>,Self>)->NodeRef<marker::DataMut<'_>,Self>{let lazy=replace(&mut node.data_mut().lazy,T::act_unit());if let Some(left)=node.left(){Self::update_lazy(left,&lazy);}if let Some(right)=node.right(){Self::update_lazy(right,&lazy);}if replace(&mut node.data_mut().rev,false){if let Some(left)=node.left(){Self::reverse(left);}if let Some(right)=node.right(){Self::reverse(right);}}node}fn recalc(node:NodeRef<marker::DataMut<'_>,Self>)->NodeRef<marker::DataMut<'_>,Self>{let mut agg=T::single_agg(&node.data().key);let mut size=1;if let Some(left)=node.left(){let data=left.data();agg=T::agg_operate(&data.agg,&agg);size+=data.size;}if let Some(right)=node.right(){let data=right.data();agg=T::agg_operate(&agg,&data.agg);size+=data.size;}let data=node.data_mut();data.agg=agg;data.size=size;node}}impl<T>SplaySpec for LazyAggSplay<T>where T:MonoidAction{type T=LazyAggElement<T>;fn has_bottom_up()->bool{true}fn top_down(node:NodeRef<marker::DataMut<'_>,Self>){Self::propagate(node);}fn bottom_up(node:NodeRef<marker::DataMut<'_>,Self>){Self::recalc(node);}}struct SeekBySize<T>{index:usize,_marker:PhantomData<fn()->T>}impl<T>SeekBySize<T>{fn new(index:usize)->Self{Self{index,_marker:PhantomData}}}impl<T>SplaySeeker for SeekBySize<T>where T:MonoidAction{type S=LazyAggSplay<T>;fn splay_seek(&mut self,node:NodeRef<marker::Immut<'_>,Self::S>)->Ordering{let lsize=node.left().map(|l|l.data().size).unwrap_or_default();let ord=self.index.cmp(&lsize);if matches!(ord,Ordering::Greater){self.index-=lsize+1;}ord}}struct SeekByAccCond<F,T>where T:MonoidAction{acc:T::Agg,f:F,_marker:PhantomData<fn()->T>}impl<F,T>SeekByAccCond<F,T>where T:MonoidAction{fn new(f:F)->Self{Self{acc:T::agg_unit(),f,_marker:PhantomData}}}impl<F,T>SplaySeeker for SeekByAccCond<F,T>where F:FnMut(&T::Agg)->bool,T:MonoidAction{type S=LazyAggSplay<T>;fn splay_seek(&mut self,node:NodeRef<marker::Immut<'_>,Self::S>)->Ordering{if let Some(lagg)=node.left().map(|l|&l.data().agg){let nacc=T::agg_operate(&self.acc,lagg);if(self.f)(&nacc){return Ordering::Less;}self.acc=nacc;};self.acc=T::agg_operate(&self.acc,&T::single_agg(&node.data().key));if(self.f)(&self.acc){Ordering::Equal}else{Ordering::Greater}}}struct SeekByRaccCond<F,T>where T:MonoidAction{acc:T::Agg,f:F,_marker:PhantomData<fn()->T>}impl<F,T>SeekByRaccCond<F,T>where T:MonoidAction{fn new(f:F)->Self{Self{acc:T::agg_unit(),f,_marker:PhantomData}}}impl<F,T>SplaySeeker for SeekByRaccCond<F,T>where F:FnMut(&T::Agg)->bool,T:MonoidAction{type S=LazyAggSplay<T>;fn splay_seek(&mut self,node:NodeRef<marker::Immut<'_>,Self::S>)->Ordering{if let Some(lagg)=node.right().map(|r|&r.data().agg){let nacc=T::agg_operate(lagg,&self.acc);if(self.f)(&nacc){return Ordering::Greater;}self.acc=nacc;};self.acc=T::agg_operate(&T::single_agg(&node.data().key),&self.acc);if(self.f)(&self.acc){Ordering::Equal}else{Ordering::Less}}}pub struct SplaySequence<T,A=MemoryPool<Node<LazyAggElement<T>>>>where T:MonoidAction,A:Allocator<Node<LazyAggElement<T>>>{root:Root<LazyAggSplay<T>>,length:usize,alloc:ManuallyDrop<A>}impl<T,A>Debug for SplaySequence<T,A>where T:MonoidAction,T::Key:Debug,T::Agg:Debug,T::Act:Debug,A:Allocator<Node<LazyAggElement<T>>>{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{f.debug_struct("SplayMap").field("root",&self.root).field("length",&self.length).finish()}}impl<T,A>Drop for SplaySequence<T,A>where T:MonoidAction,A:Allocator<Node<LazyAggElement<T>>>{fn drop(&mut self){unsafe{while let Some(node)=self.root.take_first(){self.alloc.deallocate(node.into_dying().into_inner());}ManuallyDrop::drop(&mut self.alloc);}}}impl<T,A>Default for SplaySequence<T,A>where T:MonoidAction,A:Allocator<Node<LazyAggElement<T>>>+Default{fn default()->Self{Self{root:Root::default(),length:0,alloc:Default::default()}}}impl<T>SplaySequence<T>where T:MonoidAction{pub fn new()->Self{Default::default()}pub fn with_capacity(capacity:usize)->Self{Self{root:Root::default(),length:0,alloc:ManuallyDrop::new(MemoryPool::with_capacity(capacity))}}pub fn len(&self)->usize{self.length}pub fn is_empty(&self)->bool{self.length==0}}impl<T,A>SplaySequence<T,A>where T:MonoidAction,A:Allocator<Node<LazyAggElement<T>>>{fn range<R>(&mut self,range:R)->NodeRange<'_,LazyAggSplay<T>>where R:RangeBounds<usize>{let start=match range.start_bound(){Bound::Included(&index)=>Bound::Included(SeekBySize::new(index)),Bound::Excluded(&index)=>Bound::Excluded(SeekBySize::new(index)),Bound::Unbounded=>Bound::Unbounded,};let end=match range.end_bound(){Bound::Included(&index)=>Bound::Included(SeekBySize::new(index)),Bound::Excluded(&index)=>Bound::Excluded(SeekBySize::new(index)),Bound::Unbounded=>Bound::Unbounded,};self.root.range(start,end)}pub fn update<R>(&mut self,range:R,x:T::Act)where R:RangeBounds<usize>{if let Some(root)=self.range(range).root_mut().root_data_mut(){LazyAggSplay::<T>::update_lazy(root,&x);}}pub fn fold<R>(&mut self,range:R)->T::Agg where R:RangeBounds<usize>{if let Some(root)=self.range(range).root().root(){root.data().agg.clone()}else{T::agg_unit()}}pub fn reverse<R>(&mut self,range:R)where R:RangeBounds<usize>{if let Some(root)=self.range(range).root_mut().root_data_mut(){LazyAggSplay::<T>::reverse(root);}}pub fn get(&mut self,index:usize)->Option<&T::Key>{self.root.splay_by(SeekBySize::new(index))?;self.root.root().map(|root|&root.data().key)}pub fn modify<F>(&mut self,index:usize,f:F)where F:FnOnce(&T::Key)->T::Key{self.root.splay_by(SeekBySize::new(index)).unwrap();let data=self.root.root_data_mut().unwrap().data_mut();data.key=f(&data.key);LazyAggSplay::<T>::bottom_up(self.root.root_data_mut().unwrap());}pub fn insert(&mut self,index:usize,x:T::Key){assert!(index<=self.length);self.root.splay_by(SeekBySize::new(index));let agg=T::single_agg(&x);unsafe{let node=NodeRef::from_data(LazyAggElement{key:x,agg,lazy:T::act_unit(),size:1,rev:false},self.alloc.deref_mut());if index==self.length{self.root.insert_right(node);}else{self.root.insert_left(node);}}self.length+=1;}pub fn remove(&mut self,index:usize)->Option<T::Key>{if index>=self.length{return None;}self.root.splay_by(SeekBySize::new(index));self.length-=1;let node=self.root.take_root().unwrap().into_dying();unsafe{Some(node.into_data(self.alloc.deref_mut()).key)}}pub fn position_acc<R,F>(&mut self,range:R,f:F)->Option<usize>where R:RangeBounds<usize>,F:FnMut(&T::Agg)->bool{let mut range=self.range(range);let ord=range.root_mut().splay_by(SeekByAccCond::new(f));if!matches!(ord,Some(Ordering::Equal)){return None;}let front_size=range.front().size();let left_size=range.root().left_size();Some(front_size+left_size)}pub fn rposition_acc<R,F>(&mut self,range:R,f:F)->Option<usize>where R:RangeBounds<usize>,F:FnMut(&T::Agg)->bool{let mut range=self.range(range);let ord=range.root_mut().splay_by(SeekByRaccCond::new(f));if!matches!(ord,Some(Ordering::Equal)){return None;}let front_size=range.front().size();let left_size=range.root().left_size();Some(front_size+left_size)}pub fn rotate_left(&mut self,mid:usize){assert!(mid<=self.length);if mid!=0||mid!=self.length{self.range(mid..).drop_rotate_left()}}pub fn rotate_right(&mut self,k:usize){assert!(k<=self.length);self.rotate_left(self.length-k);}}impl<T>Root<LazyAggSplay<T>>where T:MonoidAction{fn size(&self)->usize{self.root().map(|root|root.data().size).unwrap_or_default()}fn left_size(&self)->usize{self.root().and_then(|root|root.left().map(|left|left.data().size)).unwrap_or_default()}}}pub mod sized_map{use super::{node::{marker,Node,NodeRange,NodeRef,Root,SplaySeeker,SplaySpec},Allocator,MemoryPool};use std::{borrow::Borrow,cmp::Ordering,fmt::{self,Debug},iter::FusedIterator,marker::PhantomData,mem::{replace,ManuallyDrop},ops::{Bound,DerefMut,RangeBounds}};struct SizedSplay<T>{_marker:PhantomData<fn()->T>}impl<T>SplaySpec for SizedSplay<T>{type T=(T,usize);fn has_bottom_up()->bool{true}fn bottom_up(node:NodeRef<marker::DataMut<'_>,Self>){let l=node.left().map(|p|p.data().1).unwrap_or_default();let r=node.right().map(|p|p.data().1).unwrap_or_default();node.data_mut().1=l+r+1;}}struct SeekByKey<'a,K,V,Q>where Q:?Sized{key:&'a Q,_marker:PhantomData<fn()->(K,V)>}impl<'a,K,V,Q>SeekByKey<'a,K,V,Q>where Q:?Sized{fn new(key:&'a Q)->Self{Self{key,_marker:PhantomData}}}impl<'a,K,V,Q>SplaySeeker for SeekByKey<'a,K,V,Q>where K:Borrow<Q>,Q:Ord+?Sized{type S=SizedSplay<(K,V)>;fn splay_seek(&mut self,node:NodeRef<marker::Immut<'_>,Self::S>)->Ordering{self.key.cmp((node.data().0).0.borrow())}}struct SeekBySize<K,V>{index:usize,_marker:PhantomData<fn()->(K,V)>}impl<K,V>SeekBySize<K,V>{fn new(index:usize)->Self{Self{index,_marker:PhantomData}}}impl<K,V>SplaySeeker for SeekBySize<K,V>{type S=SizedSplay<(K,V)>;fn splay_seek(&mut self,node:NodeRef<marker::Immut<'_>,Self::S>)->Ordering{let lsize=node.left().map(|l|l.data().1).unwrap_or_default();let ord=self.index.cmp(&lsize);if matches!(ord,Ordering::Greater){self.index-=lsize+1;}ord}}pub struct SplayMap<K,V,A=MemoryPool<Node<((K,V),usize)>>>where A:Allocator<Node<((K,V),usize)>>{root:Root<SizedSplay<(K,V)>>,length:usize,alloc:ManuallyDrop<A>}impl<K,V,A>Debug for SplayMap<K,V,A>where K:Debug,V:Debug,A:Allocator<Node<((K,V),usize)>>{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{f.debug_struct("SplayMap").field("root",&self.root).field("length",&self.length).finish()}}impl<K,V,A>Drop for SplayMap<K,V,A>where A:Allocator<Node<((K,V),usize)>>{fn drop(&mut self){unsafe{while let Some(node)=self.root.take_first(){self.alloc.deallocate(node.into_dying().into_inner());}ManuallyDrop::drop(&mut self.alloc);}}}impl<K,V,A>Default for SplayMap<K,V,A>where A:Allocator<Node<((K,V),usize)>>+Default{fn default()->Self{Self{root:Root::default(),length:0,alloc:Default::default()}}}impl<K,V>SplayMap<K,V>{pub fn new()->Self{Default::default()}pub fn with_capacity(capacity:usize)->Self{Self{root:Root::default(),length:0,alloc:ManuallyDrop::new(MemoryPool::with_capacity(capacity))}}}impl<K,V,A>SplayMap<K,V,A>where A:Allocator<Node<((K,V),usize)>>{pub fn get<Q>(&mut self,key:&Q)->Option<&V>where K:Borrow<Q>,Q:Ord+?Sized{self.get_key_value(key).map(|(_,v)|v)}fn splay_by_key<Q>(&mut self,key:&Q)->Option<Ordering>where K:Borrow<Q>,Q:Ord+?Sized{self.root.splay_by(SeekByKey::new(key))}pub fn get_key_value<Q>(&mut self,key:&Q)->Option<(&K,&V)>where K:Borrow<Q>,Q:Ord+?Sized{if!matches!(self.splay_by_key(key)?,Ordering::Equal){return None;}self.root.root().map(|node|{let((k,v),_)=node.data();(k,v)})}fn splay_at(&mut self,index:usize)->Option<Ordering>{self.root.splay_by(SeekBySize::new(index))}pub fn get_key_value_at(&mut self,index:usize)->Option<(&K,&V)>{if index>=self.length{return None;}self.splay_at(index);self.root.root().map(|node|{let((k,v),_)=node.data();(k,v)})}pub fn insert(&mut self,key:K,value:V)->Option<V>where K:Ord{let ord=self.splay_by_key(&key);self.length+=(ord!=Some(Ordering::Equal))as usize;match ord{Some(Ordering::Equal)=>{return Some(replace(&mut(self.root.root_data_mut().unwrap().data_mut().0).1,value))}Some(Ordering::Less)=>unsafe{self.root.insert_left(NodeRef::from_data(((key,value),1),self.alloc.deref_mut()));},_=>unsafe{self.root.insert_right(NodeRef::from_data(((key,value),1),self.alloc.deref_mut()));},}None}pub fn remove<Q>(&mut self,key:&Q)->Option<V>where K:Borrow<Q>,Q:Ord+?Sized{if!matches!(self.splay_by_key(key)?,Ordering::Equal){return None;}self.length-=1;let node=self.root.take_root().unwrap().into_dying();unsafe{Some((node.into_data(self.alloc.deref_mut()).0).1)}}pub fn remove_at(&mut self,index:usize)->Option<(K,V)>{if index>=self.length{return None;}self.splay_at(index);self.length-=1;let node=self.root.take_root().unwrap().into_dying();unsafe{Some(node.into_data(self.alloc.deref_mut()).0)}}pub fn len(&self)->usize{self.length}pub fn is_empty(&self)->bool{self.len()==0}pub fn iter(&mut self)->Iter<'_,K,V>{Iter{iter:NodeRange::new(&mut self.root)}}pub fn range<Q,R>(&mut self,range:R)->Iter<'_,K,V>where K:Borrow<Q>,Q:Ord+?Sized,R:RangeBounds<Q>{let start=match range.start_bound(){Bound::Included(key)=>Bound::Included(SeekByKey::new(key)),Bound::Excluded(key)=>Bound::Excluded(SeekByKey::new(key)),Bound::Unbounded=>Bound::Unbounded,};let end=match range.end_bound(){Bound::Included(key)=>Bound::Included(SeekByKey::new(key)),Bound::Excluded(key)=>Bound::Excluded(SeekByKey::new(key)),Bound::Unbounded=>Bound::Unbounded,};Iter{iter:self.root.range(start,end)}}pub fn range_at<R>(&mut self,range:R)->Iter<'_,K,V>where R:RangeBounds<usize>{let start=match range.start_bound(){Bound::Included(&index)=>Bound::Included(SeekBySize::new(index)),Bound::Excluded(&index)=>Bound::Excluded(SeekBySize::new(index)),Bound::Unbounded=>Bound::Unbounded,};let end=match range.end_bound(){Bound::Included(&index)=>Bound::Included(SeekBySize::new(index)),Bound::Excluded(&index)=>Bound::Excluded(SeekBySize::new(index)),Bound::Unbounded=>Bound::Unbounded,};Iter{iter:self.root.range(start,end)}}}#[derive(Debug)]pub struct Iter<'a,K,V>{iter:NodeRange<'a,SizedSplay<(K,V)>>}impl<'a,K,V>Iterator for Iter<'a,K,V>where K:Clone,V:Clone{type Item=(K,V);fn next(&mut self)->Option<Self::Item>{self.iter.next_checked().map(|node|node.data().0.clone())}fn last(mut self)->Option<Self::Item>{self.next_back()}fn min(mut self)->Option<Self::Item>{self.next()}fn max(mut self)->Option<Self::Item>{self.next_back()}}impl<K,V>FusedIterator for Iter<'_,K,V>where K:Clone,V:Clone{}impl<'a,K,V>DoubleEndedIterator for Iter<'a,K,V>where K:Clone,V:Clone{fn next_back(&mut self)->Option<Self::Item>{self.iter.next_back_checked().map(|node|node.data().0.clone())}}}}
pub use self::allocator::{Allocator,MemoryPool};
mod allocator{use std::{marker::PhantomData,mem::{replace,size_of,take},ptr::{self,read,write,NonNull}};pub trait Allocator<T>{fn allocate(&mut self,value:T)->NonNull<T>;fn deallocate(&mut self,ptr:NonNull<T>)->T;}#[derive(Debug)]pub struct MemoryPool<T>{pool:Vec<T>,chunks:Vec<Vec<T>>,unused:Vec<NonNull<T>>}impl<T>Default for MemoryPool<T>{fn default()->Self{Self::with_capacity(CAP/1usize.max(size_of::<T>()))}}const CAP:usize=1024;impl<T>MemoryPool<T>{pub fn new()->Self{Default::default()}pub fn with_capacity(capacity:usize)->Self{let pool=Vec::with_capacity(capacity.max(1));Self{pool,chunks:Vec::new(),unused:Vec::new()}}}impl<T>Drop for MemoryPool<T>{fn drop(&mut self){self.chunks.push(take(&mut self.pool));let mut removed=vec![vec![];self.chunks.len()];for p in self.unused.iter(){let p=p.as_ptr();for(chunk,removed)in self.chunks.iter().zip(&mut removed).rev(){let ptr=chunk.as_ptr()as*mut _;let len=chunk.len();if ptr<=p&&p<ptr.wrapping_add(len){removed.push(p);}}}for(chunk,removed)in self.chunks.iter_mut().zip(&mut removed){removed.sort_unstable();for&p in removed.iter(){unsafe{let len=chunk.len();let base_ptr=chunk.as_mut_ptr();ptr::copy(base_ptr.add(len-1),p,1);chunk.set_len(len-1);}}}}}impl<T>Allocator<T>for MemoryPool<T>{fn allocate(&mut self,value:T)->NonNull<T>{if let Some(mut ptr)=self.unused.pop(){unsafe{write(ptr.as_mut(),value)};ptr}else{let len=self.pool.len();if len>=self.pool.capacity(){let new_capacity=self.pool.capacity()*2;let new_pool=Vec::with_capacity(new_capacity);self.chunks.push(replace(&mut self.pool,new_pool));}let len=self.pool.len();debug_assert!(len<self.pool.capacity());self.pool.push(value);unsafe{NonNull::new_unchecked(self.pool.as_mut_ptr().add(len))}}}fn deallocate(&mut self,ptr:NonNull<T>)->T{self.unused.push(ptr);unsafe{read(ptr.as_ptr())}}}#[derive(Debug,Default)]pub struct BoxAllocator<T>(PhantomData<fn()->T>);impl<T>Allocator<T>for BoxAllocator<T>{fn allocate(&mut self,value:T)->NonNull<T>{unsafe{NonNull::new_unchecked(Box::leak(Box::new(value)))}}fn deallocate(&mut self,ptr:NonNull<T>)->T{unsafe{*Box::from_raw(ptr.as_ptr())}}}}
pub trait MonoidAction{type Key;type Agg:Clone;type Act:Clone;type AggMonoid:Monoid<T=Self::Agg>;type ActMonoid:Monoid<T=Self::Act>;fn single_agg(key:&Self::Key)->Self::Agg;fn act_key(x:&Self::Key,a:&Self::Act)->Self::Key;fn act_agg(x:&Self::Agg,a:&Self::Act)->Option<Self::Agg>;fn toggle(_x:&mut Self::Agg){}#[inline]fn agg_unit()->Self::Agg{<Self::AggMonoid as Unital>::unit()}#[inline]fn act_unit()->Self::Act{<Self::ActMonoid as Unital>::unit()}#[inline]fn agg_operate(x:&Self::Agg,y:&Self::Agg)->Self::Agg{<Self::AggMonoid as Magma>::operate(x,y)}#[inline]fn act_operate(x:&Self::Act,y:&Self::Act)->Self::Act{<Self::ActMonoid as Magma>::operate(x,y)}#[inline]fn agg_operate_assign(x:&mut Self::Agg,y:&Self::Agg){*x=<Self::AggMonoid as Magma>::operate(x,y);}#[inline]fn act_operate_assign(x:&mut Self::Act,y:&Self::Act){*x=<Self::ActMonoid as Magma>::operate(x,y);}}
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);}