pub fn solve() {
    crate::prepare!();
    sc!(n, a: [u64; n]);
    let bit_len = a
        .iter()
        .cloned()
        .max()
        .map_or(0, |x| (u64::BITS - x.leading_zeros()) as usize);
    let mut trie = BinaryTrie::<X>::with_capacity(bit_len, n + 1);
    let mut ans = 0usize;
    for x in a.into_iter().rev() {
        trie.modify_or_insert(0, |agg| agg.0 += 1);
        if x == 1 {
            trie.update(.., ((1, 1, 0), (1, -1)));
        } else {
            trie.update(.., ((2, 1, -1), (0, 0)));
        }
        trie.update(..x, ((1, 0, 0), (0, 0)));
        ans += trie.fold(..).1 as usize;
        trie.xor_all(x);
    }
    pp!(ans);
}
struct X;
impl Magma for X {
    type T = ((i64, i64, i64), (i64, i64));

    fn operate(f: &Self::T, g: &Self::T) -> Self::T {
        let ((a0, b0, c0), (d0, e0)) = *f;
        let ((a1, b1, c1), (d1, e1)) = *g;
        (
            (a1 + b1 * a0 + c1 * d0, b1 * b0, b1 * c0 + c1 * e0),
            (d1 + e1 * d0, e1 * e0),
        )
    }
}
impl Unital for X {
    fn unit() -> Self::T {
        ((0, 1, 0), (0, 1))
    }
}
impl Associative for X {}
impl MonoidAct for X {
    type Key = u64;
    type Act = ((i64, i64, i64), (i64, i64));
    type ActMonoid = X;

    fn act(x: &Self::Key, _a: &Self::Act) -> Self::Key {
        *x
    }
}
impl LazyMapMonoid for X {
    type Key = u64;
    type Agg = (i64, i64, i64);
    type Act = ((i64, i64, i64), (i64, i64));
    type AggMonoid = (
        AdditiveOperation<i64>,
        AdditiveOperation<i64>,
        AdditiveOperation<i64>,
    );
    type ActMonoid = X;
    type KeyAct = X;

    fn single_agg(_key: &Self::Key) -> Self::Agg {
        (1, 0, 0)
    }

    fn act_agg(
        &(size, sum, cnt_one): &Self::Agg,
        &((a, b, c), (d, e)): &Self::Act,
    ) -> Option<Self::Agg> {
        Some((
            size,
            size * a + sum * b + cnt_one * c,
            size * d + cnt_one * e,
        ))
    }
}
crate::main!();
#[allow(unused_imports)]use std::{cmp::{Ordering,Reverse},collections::{BTreeMap,BTreeSet,BinaryHeap,HashMap,HashSet,VecDeque}};
mod main_macros{#[doc=" Prepare useful macros."]#[doc=" - `prepare!();`: default (all input scanner (`sc!`, `sv!`) + buf print (`pp!`, `dg!`))"]#[doc=" - `prepare!(?);`: interactive (line scanner (`scln!`) + buf print (`pp!`, `dg!`))"]#[macro_export]#[allow(clippy::crate_in_macro_def)]macro_rules!prepare{(@output($dol:tt))=>{#[allow(unused_imports)]use std::io::Write as _;let __out=std::io::stdout();#[allow(unused_mut,unused_variables)]let mut __out=std::io::BufWriter::new(__out.lock());#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stdout."]macro_rules!pp{($dol($dol t:tt)*)=>{$dol crate::iter_print!(__out,$dol($dol t)*)}}#[cfg(debug_assertions)]#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stderr. Do nothing in release mode."]macro_rules!dg{($dol($dol t:tt)*)=>{{#[allow(unused_imports)]use std::io::Write as _;let __err=std::io::stderr();#[allow(unused_mut,unused_variables)]let mut __err=std::io::BufWriter::new(__err.lock());$dol crate::iter_print!(__err,$dol($dol t)*);let _=__err.flush();}}}#[cfg(not(debug_assertions))]#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stderr. Do nothing in release mode."]macro_rules!dg{($dol($dol t:tt)*)=>{}}};(@normal($dol:tt))=>{let __in_buf=read_stdin_all_unchecked();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);#[allow(unused_macros)]macro_rules!sc{($dol($dol t:tt)*)=>{$dol crate::scan!(__scanner,$dol($dol t)*)}}#[allow(unused_macros)]macro_rules!sv{($dol($dol t:tt)*)=>{$dol crate::scan_value!(__scanner,$dol($dol t)*)}}};(@interactive($dol:tt))=>{#[allow(unused_macros)]#[doc=" Scan a line, and previous line will be truncated in the next call."]macro_rules!scln{($dol($dol t:tt)*)=>{let __in_buf=read_stdin_line();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);$dol crate::scan!(__scanner,$dol($dol t)*)}}#[allow(unused_macros)]#[doc=" Scan a line, and previous line will be truncated in the next call."]macro_rules!svln{($dol($dol t:tt)*)=>{{let __in_buf=read_stdin_line();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);$dol crate::scan_value!(__scanner,$dol($dol t)*)}}}};()=>{$crate::prepare!(@output($));$crate::prepare!(@normal($))};(?)=>{$crate::prepare!(@output($));$crate::prepare!(@interactive($))};}#[macro_export]macro_rules!main{()=>{fn main(){solve();}};(avx2)=>{fn main(){#[target_feature(enable="avx2")]unsafe fn solve_avx2(){solve();}unsafe{solve_avx2()}}};(large_stack)=>{fn main(){const STACK_SIZE:usize=512*1024*1024;::std::thread::Builder::new().stack_size(STACK_SIZE).spawn(solve).unwrap().join().unwrap();}};}}
pub use self::iter_print::IterPrint;
mod iter_print{use std::{fmt::Display,io::{Error,Write}};pub trait IterPrint{fn iter_print<W,S>(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display;}macro_rules!impl_iter_print_tuple{(@impl,)=>{impl IterPrint for(){fn iter_print<W,S>(self,_writer:&mut W,_sep:S,_is_head:bool)->Result<(),Error>where W:Write,S:Display{Ok(())}}};(@impl$($A:ident$a:ident)?,$($B:ident$b:ident)*)=>{impl<$($A,)?$($B),*>IterPrint for($($A,)?$($B),*)where$($A:Display,)?$($B:Display),*{fn iter_print<W,S>(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display{let($($a,)?$($b,)*)=self;$(if is_head{::std::write!(writer,"{}",$a)?;}else{::std::write!(writer,"{}{}",sep,$a)?;})?$(::std::write!(writer,"{}{}",sep,$b)?;)*Ok(())}}};(@inc,,$C:ident$c:ident$($D:ident$d:ident)*)=>{impl_iter_print_tuple!(@impl,);impl_iter_print_tuple!(@inc$C$c,,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,$C:ident$c:ident$($D:ident$d:ident)*)=>{impl_iter_print_tuple!(@impl$A$a,$($B$b)*);impl_iter_print_tuple!(@inc$A$a,$($B$b)*$C$c,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,)=>{impl_iter_print_tuple!(@impl$A$a,$($B$b)*);};($($t:tt)*)=>{impl_iter_print_tuple!(@inc,,$($t)*);};}impl_iter_print_tuple!(A a B b C c D d E e F f G g H h I i J j K k);#[doc=" Print expressions with a separator."]#[doc=" - `iter_print!(writer, args...)`"]#[doc=" - `@sep $expr`: set separator (default: `' '`)"]#[doc=" - `@ns`: alias for `@sep \"\"`"]#[doc=" - `@lf`: alias for `@sep '\\n'`"]#[doc=" - `@sp`: alias for `@sep ' '`"]#[doc=" - `@fmt ($lit, $($expr),*)`: print `format!($lit, $($expr),*)`"]#[doc=" - `@flush`: flush writer (auto insert `!`)"]#[doc=" - `@it $expr`: print iterator"]#[doc=" - `@it1 $expr`: print iterator as 1-indexed"]#[doc=" - `@cw ($char $expr)`: print iterator as `(elem as u8 + $char as u8) as char`"]#[doc=" - `@bw ($byte $expr)`: print iterator as `(elem as u8 + $byte) as char`"]#[doc=" - `@it2d $expr`: print 2d-iterator"]#[doc=" - `@tup $expr`: print tuple (need to import [`IterPrint`])"]#[doc=" - `@ittup $expr`: print iterative tuple (need to import [`IterPrint`])"]#[doc=" - `$expr`: print expr"]#[doc=" - `{ args... }`: scoped"]#[doc=" - `;`: print `'\\n'`"]#[doc=" - `!`: not print `'\\n'` at the end"]#[macro_export]macro_rules!iter_print{(@@fmt$writer:expr,$sep:expr,$is_head:expr,($lit:literal$(,$e:expr)*$(,)?))=>{if!$is_head{::std::write!($writer,"{}",$sep).expect("io error");}::std::write!($writer,$lit,$($e),*).expect("io error");};(@@item$writer:expr,$sep:expr,$is_head:expr,$e:expr)=>{$crate::iter_print!(@@fmt$writer,$sep,$is_head,("{}",$e));};(@@line_feed$writer:expr$(,)?)=>{::std::writeln!($writer).expect("io error");};(@@it$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,item);}}};(@@it1$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,item+1);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,item+1);}}};(@@cw$writer:expr,$sep:expr,$is_head:expr,($ch:literal$iter:expr))=>{{let mut iter=$iter.into_iter();let b=$ch as u8;if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,(item as u8+b)as char);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,(item as u8+b)as char);}}};(@@bw$writer:expr,$sep:expr,$is_head:expr,($b:literal$iter:expr))=>{{let mut iter=$iter.into_iter();let b:u8=$b;if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,(item as u8+b)as char);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,(item as u8+b)as char);}}};(@@it2d$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@it$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@it$writer,$sep,true,item);}};(@@tup$writer:expr,$sep:expr,$is_head:expr,$tuple:expr)=>{IterPrint::iter_print($tuple,&mut$writer,$sep,$is_head).expect("io error");};(@@ittup$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@tup$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@tup$writer,$sep,true,item);}};(@@assert_tag item)=>{};(@@assert_tag it)=>{};(@@assert_tag it1)=>{};(@@assert_tag it2d)=>{};(@@assert_tag tup)=>{};(@@assert_tag ittup)=>{};(@@assert_tag$tag:ident)=>{::std::compile_error!(::std::concat!("invalid tag in `iter_print!`: `",std::stringify!($tag),"`"));};(@@inner$writer:expr,$sep:expr,$is_head:expr,@sep$e:expr,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$e,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@ns$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,"",$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@lf$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,'\n',$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@sp$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,' ',$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@flush$($t:tt)*)=>{$writer.flush().expect("io error");$crate::iter_print!(@@inner$writer,$sep,$is_head,!$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@fmt$arg:tt$($t:tt)*)=>{$crate::iter_print!(@@fmt$writer,$sep,$is_head,$arg);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@cw$arg:tt$($t:tt)*)=>{$crate::iter_print!(@@cw$writer,$sep,$is_head,$arg);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@bw$arg:tt$($t:tt)*)=>{$crate::iter_print!(@@bw$writer,$sep,$is_head,$arg);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr,$($t:tt)*)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@inner$writer,$sep,false,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr;$($t:tt)*)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@inner$writer,$sep,true,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@inner$writer,$sep,false,);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$($t:tt)*)=>{::std::compile_error!(::std::concat!("invalid expr in `iter_print!`: `",std::stringify!($($t)*),"`"));};(@@inner$writer:expr,$sep:expr,$is_head:expr,,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,;$($t:tt)*)=>{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,!$(,)?)=>{};(@@inner$writer:expr,$sep:expr,$is_head:expr,!$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,)=>{$crate::iter_print!(@@line_feed$writer);};(@@inner$writer:expr,$sep:expr,$is_head:expr,{$($t:tt)*}$($rest:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*,!);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($rest)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,@item$($t)*);};($writer:expr,$($t:tt)*)=>{{$crate::iter_print!(@@inner$writer,' ',true,$($t)*);}};}}
mod array{#[macro_export]macro_rules!array{[@inner$data:ident=[$init:expr;$len:expr]]=>{{use::std::mem::{ManuallyDrop,MaybeUninit};let mut$data:[MaybeUninit<_>;$len]=unsafe{MaybeUninit::uninit().assume_init()};$init;#[repr(C)]union __Transmuter<const N:usize,T:Clone>{src:ManuallyDrop<[MaybeUninit<T>;N]>,dst:ManuallyDrop<[T;N]>,}ManuallyDrop::into_inner(unsafe{__Transmuter{src:ManuallyDrop::new($data)}.dst})}};[||$e:expr;$len:expr]=>{$crate::array![@inner data=[data.iter_mut().for_each(|item|*item=MaybeUninit::new($e));$len]]};[|$i:pat_param|$e:expr;$len:expr]=>{$crate::array![@inner data=[data.iter_mut().enumerate().for_each(|($i,item)|*item=MaybeUninit::new($e));$len]]};[$e:expr;$len:expr]=>{{let e=$e;$crate::array![||Clone::clone(&e);$len]}};}}
pub use self::scanner::*;
mod scanner{use std::{iter::{FromIterator,from_fn,repeat_with},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,I:Iterator<Item=&'a str>=std::str::SplitAsciiWhitespace<'a>>{iter:I}impl<'a>Scanner<'a>{pub fn new(s:&'a str)->Self{let iter=s.split_ascii_whitespace();Self{iter}}}impl<'a,I:Iterator<Item=&'a str>>Scanner<'a,I>{pub fn new_from_iter(iter:I)->Self{Self{iter}}pub fn scan<T>(&mut self)-><T as IterScan>::Output where T:IterScan{<T as IterScan>::scan(&mut self.iter).expect("scan error")}pub fn mscan<T>(&mut self,marker:T)-><T as MarkedIterScan>::Output where T:MarkedIterScan{marker.mscan(&mut self.iter).expect("scan error")}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,I,T>where T:IterScan{ScannerIter{inner:self,_marker:std::marker::PhantomData}}}macro_rules!impl_iter_scan{($($t:ty)*)=>{$(impl IterScan for$t{type Output=Self;fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self>{iter.next()?.parse::<$t>().ok()}})*};}impl_iter_scan!(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String);macro_rules!impl_iter_scan_tuple{(@impl$($T:ident)*)=>{impl<$($T:IterScan),*>IterScan for($($T,)*){type Output=($(<$T as IterScan>::Output,)*);fn scan<'a,It:Iterator<Item=&'a str>>(_iter:&mut It)->Option<Self::Output>{Some(($(<$T as IterScan>::scan(_iter)?,)*))}}};(@inner$($T:ident)*,)=>{impl_iter_scan_tuple!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{impl_iter_scan_tuple!(@impl$($T)*);impl_iter_scan_tuple!(@inner$($T)*$U,$($Rest)*);};($($T:ident)*)=>{impl_iter_scan_tuple!(@inner,$($T)*);};}impl_iter_scan_tuple!(A B C D E F G H I J K);pub struct ScannerIter<'a,'b,I:Iterator<Item=&'a str>,T>{inner:&'b mut Scanner<'a,I>,_marker:std::marker::PhantomData<fn()->T>}impl<'a,I,T>Iterator for ScannerIter<'a,'_,I,T>where I:Iterator<Item=&'a str>,T:IterScan{type Item=<T as IterScan>::Output;#[inline]fn next(&mut self)->Option<Self::Item>{<T as IterScan>::scan(&mut self.inner.iter)}}#[doc=" scan a value with Scanner"]#[doc=""]#[doc=" - `scan_value!(scanner, ELEMENT)`"]#[doc=""]#[doc=" ELEMENT :="]#[doc=" - `$ty`: IterScan"]#[doc=" - `@$expr`: MarkedIterScan"]#[doc=" - `$ty = $expr`: MarkedIterScan"]#[doc=" - `[ELEMENT; $expr]`: vector"]#[doc=" - `[ELEMENT; const $expr]`: array"]#[doc=" - `[ELEMENT]`: iterator"]#[doc=" - `($(ELEMENT)*,)`: tuple"]#[macro_export]macro_rules!scan_value{(@repeat$scanner:expr,[$($t:tt)*]$($len:expr)?)=>{::std::iter::repeat_with(||$crate::scan_value!(@inner$scanner,[]$($t)*))$(.take($len).collect::<Vec<_>>())?};(@array$scanner:expr,[$($t:tt)*]$len:expr)=>{$crate::array![||$crate::scan_value!(@inner$scanner,[]$($t)*);$len]};(@tuple$scanner:expr,[$([$($args:tt)*])*])=>{($($($args)*,)*)};(@sparen$scanner:expr,[]@$e:expr;$($t:tt)*)=>{$crate::scan_value!(@sparen$scanner,[@$e]$($t)*)};(@sparen$scanner:expr,[]($($tt:tt)*);$($t:tt)*)=>{$crate::scan_value!(@sparen$scanner,[($($tt)*)]$($t)*)};(@sparen$scanner:expr,[][$($tt:tt)*];$($t:tt)*)=>{$crate::scan_value!(@sparen$scanner,[[$($tt)*]]$($t)*)};(@sparen$scanner:expr,[]$ty:ty=$e:expr;$($t:tt)*)=>{$crate::scan_value!(@sparen$scanner,[$ty=$e]$($t)*)};(@sparen$scanner:expr,[]$ty:ty;$($t:tt)*)=>{$crate::scan_value!(@sparen$scanner,[$ty]$($t)*)};(@sparen$scanner:expr,[]$($args:tt)*)=>{$crate::scan_value!(@repeat$scanner,[$($args)*])};(@sparen$scanner:expr,[$($args:tt)+]const$len:expr)=>{$crate::scan_value!(@array$scanner,[$($args)+]$len)};(@sparen$scanner:expr,[$($args:tt)+]$len:expr)=>{$crate::scan_value!(@repeat$scanner,[$($args)+]$len)};(@$tag:ident$scanner:expr,[[$($args:tt)*]])=>{$($args)*};(@$tag:ident$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$scanner:expr,[$($args:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@sparen$scanner,[]$($tt)*)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*]$ty:ty=$e:expr$(,$($t:tt)*)?)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[{let _tmp:$ty=$scanner.mscan($e);_tmp}]]$(,$($t)*)?)};(@$tag:ident$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$scanner:expr,[$($args:tt)*])=>{::std::compile_error!(::std::stringify!($($args)*))};(src=$src:expr,$($t:tt)*)=>{{let mut __scanner=Scanner::new($src);$crate::scan_value!(@inner __scanner,[]$($t)*)}};(iter=$iter:expr,$($t:tt)*)=>{{let mut __scanner=Scanner::new_from_iter($iter);$crate::scan_value!(@inner __scanner,[]$($t)*)}};($scanner:expr,$($t:tt)*)=>{$crate::scan_value!(@inner$scanner,[]$($t)*)}}#[doc=" scan and bind values with Scanner"]#[doc=""]#[doc=" - `scan!(scanner, $($pat $(: ELEMENT)?),*)`"]#[macro_export]macro_rules!scan{(@assert$p:pat)=>{};(@assert$($p:tt)*)=>{::std::compile_error!(::std::concat!("expected pattern, found `",::std::stringify!($($p)*),"`"));};(@pat$scanner:expr,[][])=>{};(@pat$scanner:expr,[][],$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]$x:ident$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*$x][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]::$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*::][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]&$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*&][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]($($x:tt)*)$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*($($x)*)][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][][$($x:tt)*]$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*[$($x)*]][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]{$($x:tt)*}$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*{$($x)*}][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]:$($t:tt)*)=>{$crate::scan!(@ty$scanner,[$($p)*][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][usize]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]@$e:expr$(,$($t:tt)*)?)=>{$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)*]$ty:ty=$e:expr$(,$($t:tt)*)?)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*$ty=$e]$(,$($t)*)?)};(@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$scanner,[][]$($t)*)};(src=$src:expr,$($t:tt)*)=>{let mut __scanner=Scanner::new($src);$crate::scan!(@pat __scanner,[][]$($t)*)};(iter=$iter:expr,$($t:tt)*)=>{let mut __scanner=Scanner::new_from_iter($iter);$crate::scan!(@pat __scanner,[][]$($t)*)};($scanner:expr,$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)}}#[doc=" define enum scan rules"]#[doc=""]#[doc=" # Example"]#[doc=" ```rust"]#[doc=" # use competitive::{define_enum_scan, tools::{CharsWithBase, IterScan, Scanner, Usize1}};"]#[doc=" define_enum_scan! {"]#[doc="   enum Query: u8 {"]#[doc="     0 => Noop,"]#[doc="     1 => Args { i: Usize1, s: char },"]#[doc="     9 => Complex { n: usize, c: [(usize, Vec<usize> = CharsWithBase('a')); n] },"]#[doc="   }"]#[doc=" }"]#[doc=" ```"]#[macro_export]macro_rules!define_enum_scan{(@field_ty@repeat[$($t:tt)*]$($len:expr)?)=>{Vec<$crate::define_enum_scan!(@field_ty$($t)*)>};(@field_ty@array[$($t:tt)*]$len:expr)=>{[$crate::define_enum_scan!(@field_ty$($t)*);$len]};(@field_ty@tuple[$([$($args:tt)*])*])=>{($($($args)*,)*)};(@field_ty@sparen[]($($tt:tt)*);$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@sparen[($($tt)*)]$($t)*)};(@field_ty@sparen[][$($tt:tt)*];$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@sparen[[$($tt)*]]$($t)*)};(@field_ty@sparen[]$ty:ty=$e:expr;$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@sparen[$ty=$e]$($t)*)};(@field_ty@sparen[]$ty:ty;$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@sparen[$ty]$($t)*)};(@field_ty@sparen[]$($args:tt)*)=>{$crate::define_enum_scan!(@field_ty@repeat[$($args)*])};(@field_ty@sparen[$($args:tt)+]const$len:expr)=>{$crate::define_enum_scan!(@field_ty@array[$($args)+]$len)};(@field_ty@sparen[$($args:tt)+]$len:expr)=>{$crate::define_enum_scan!(@field_ty@repeat[$($args)+]$len)};(@field_ty@$tag:ident[$($args:tt)*]($($tuple:tt)*)$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@$tag[$($args)*[$crate::define_enum_scan!(@field_ty@tuple[]$($tuple)*)]]$($t)*)};(@field_ty@$tag:ident[$($args:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@$tag[$($args)*[$crate::define_enum_scan!(@field_ty@sparen[]$($tt)*)]]$($t)*)};(@field_ty@$tag:ident[$($args:tt)*]$ty:ty=$e:expr$(,$($t:tt)*)?)=>{$crate::define_enum_scan!(@field_ty@$tag[$($args)*[$ty]]$(,$($t)*)?)};(@field_ty@$tag:ident[$($args:tt)*]$ty:ty$(,$($t:tt)*)?)=>{$crate::define_enum_scan!(@field_ty@$tag[$($args)*[<$ty as IterScan>::Output]]$(,$($t)*)?)};(@field_ty@$tag:ident[$($args:tt)*],$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@$tag[$($args)*]$($t)*)};(@field_ty@$tag:ident[[$($args:tt)*]])=>{$($args)*};(@field_ty@$tag:ident[$($args:tt)*])=>{::std::compile_error!(::std::stringify!($($args)*))};(@field_ty$($t:tt)*)=>{$crate::define_enum_scan!(@field_ty@inner[]$($t)*)};(@tag_expr raw,$iter:ident)=>{$iter.next()?};(@tag_expr$d:ty,$iter:ident)=>{<$d as IterScan>::scan($iter)?};(@variant([$($attr:tt)*]$vis:vis$T:ident$d:tt)[$($vars:tt)*])=>{$crate::define_enum_scan!{@def$($attr)*$vis enum$T:$d{$($vars)*}}};(@variant$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident{$($fs:tt)*}$($rest:tt)*)=>{$crate::define_enum_scan!{@field$ctx[$($vars)*]$p=>$v[]$($fs)*;$($rest)*}};(@variant$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident$($rest:tt)*)=>{$crate::define_enum_scan!{@variant$ctx[$($vars)*$p=>$v,]$($rest)*}};(@variant$ctx:tt[$($vars:tt)*],$($rest:tt)*)=>{$crate::define_enum_scan!{@variant$ctx[$($vars)*]$($rest)*}};(@endfield$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*][$f:ident:$($spec:tt)*],$($rest:tt)*)=>{$crate::define_enum_scan!{@field$ctx[$($vars)*]$p=>$v[$($fs)*[$f:$($spec)*]]$($rest)*}};(@endfield$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*][$f:ident:$($spec:tt)*];$($rest:tt)*)=>{$crate::define_enum_scan!{@variant$ctx[$($vars)*$p=>$v{$($fs)*[$f:$($spec)*]},]$($rest)*}};(@field$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*];$($rest:tt)*)=>{$crate::define_enum_scan!{@variant$ctx[$($vars)*$p=>$v{$($fs)*},]$($rest)*}};(@field$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*]$f:ident:($($tuple:tt)*)$sep:tt$($rest:tt)*)=>{$crate::define_enum_scan!{@endfield$ctx[$($vars)*]$p=>$v[$($fs)*][$f:($($tuple)*)]$sep$($rest)*}};(@field$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*]$f:ident:[$($x:tt)*]$sep:tt$($rest:tt)*)=>{$crate::define_enum_scan!{@endfield$ctx[$($vars)*]$p=>$v[$($fs)*][$f:[$($x)*]]$sep$($rest)*}};(@field$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*]$f:ident:$ty:ty=$e:expr,$($rest:tt)*)=>{$crate::define_enum_scan!{@endfield$ctx[$($vars)*]$p=>$v[$($fs)*][$f:$ty=$e],$($rest)*}};(@field$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*]$f:ident:$ty:ty;$($rest:tt)*)=>{$crate::define_enum_scan!{@endfield$ctx[$($vars)*]$p=>$v[$($fs)*][$f:$ty];$($rest)*}};(@field$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*]$f:ident:$ty:ty=$e:expr;$($rest:tt)*)=>{$crate::define_enum_scan!{@endfield$ctx[$($vars)*]$p=>$v[$($fs)*][$f:$ty=$e];$($rest)*}};(@field$ctx:tt[$($vars:tt)*]$p:pat=>$v:ident[$($fs:tt)*]$f:ident:$ty:ty,$($rest:tt)*)=>{$crate::define_enum_scan!{@endfield$ctx[$($vars)*]$p=>$v[$($fs)*][$f:$ty],$($rest)*}};(@def$(#[$attr:meta])*$vis:vis enum$T:ident:$d:tt{$($p:pat=>$v:ident$({$([$f:ident:$($spec:tt)*])*})?,)*})=>{$(#[$attr])*$vis enum$T{$($v$({$($f:$crate::define_enum_scan!(@field_ty$($spec)*)),*})?),*}impl IterScan for$T{type Output=Self;fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self>{let tag=$crate::define_enum_scan!(@tag_expr$d,iter);match tag{$($p=>{$($(let$f=$crate::scan_value!(iter=&mut*iter,$($spec)*);)*)?Some($T::$v$({$($f),*})?)}),*_=>None,}}}};($(#[$attr:meta])*$vis:vis enum$T:ident:raw{$($body:tt)*})=>{$crate::define_enum_scan!{@variant([$(#[$attr])*]$vis$T raw)[]$($body)*}};($(#[$attr:meta])*$vis:vis enum$T:ident:$d:ty{$($body:tt)*})=>{$crate::define_enum_scan!{@variant([$(#[$attr])*]$vis$T$d)[]$($body)*}};}#[derive(Debug,Copy,Clone)]pub enum Usize1{}impl IterScan for Usize1{type Output=usize;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;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>;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>;fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{Some(iter.next()?.chars().map(|c|(c as u8-self.0 as u8)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub enum Byte1{}impl IterScan for Byte1{type Output=u8;fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{let bytes=iter.next()?.as_bytes();assert_eq!(bytes.len(),1);Some(bytes[0])}}#[derive(Debug,Copy,Clone)]pub struct ByteWithBase(pub u8);impl MarkedIterScan for ByteWithBase{type Output=usize;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>;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>;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;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;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::binary_trie::BinaryTrie;
mod binary_trie{use super::{AbelianMonoid,LazyMapMonoid};use std::{mem::replace,ops::{Bound,RangeBounds}};struct Node<M>where M:LazyMapMonoid{child:[usize;2],parent:usize,agg:M::Agg,lazy:M::Act}impl<M>Node<M>where M:LazyMapMonoid{fn new(parent:usize)->Self{Self{child:[usize::MAX;2],parent,agg:M::agg_unit(),lazy:M::act_unit()}}}pub struct BinaryTrie<M>where M:LazyMapMonoid{bit_len:usize,max_key:u64,len:usize,xor_mask:u64,nodes:Vec<Node<M>>}impl<M>BinaryTrie<M>where M:LazyMapMonoid{pub fn new(bit_len:usize)->Self{Self::with_capacity(bit_len,0)}pub fn with_capacity(bit_len:usize,capacity:usize)->Self{assert!(bit_len<=64);let max_key=if bit_len==64{u64::MAX}else{(1u64<<bit_len)-1};let mut nodes=Vec::with_capacity(capacity.saturating_mul(bit_len.saturating_add(1)).saturating_add(1));nodes.push(Node::new(usize::MAX));Self{bit_len,max_key,len:0,xor_mask:0,nodes}}pub fn len(&self)->usize{self.len}pub fn is_empty(&self)->bool{self.len()==0}pub fn clear(&mut self){self.len=0;self.xor_mask=0;self.nodes.clear();self.nodes.push(Node::new(usize::MAX));}pub fn set(&mut self,key:u64,value:M::Agg){self.modify_or_insert(key,|x|*x=value);}pub fn modify_or_insert(&mut self,key:u64,f:impl FnOnce(&mut M::Agg)){assert!(key<=self.max_key);if self.bit_len==0{if self.is_empty(){self.len=1;}f(&mut self.nodes[0].agg);return;}let key=key^self.xor_mask;let mut inserted=false;let mut node=0;for d in(0..self.bit_len).rev(){self.push_at(node,d+1);let bit=((key>>d)&1)as usize;if self.nodes[node].child[bit]==usize::MAX{inserted=true;let next=self.nodes.len();self.nodes[node].child[bit]=next;self.nodes.push(Node::new(node));}node=self.nodes[node].child[bit];}if inserted{self.len+=1;}self.nodes[node].lazy=M::act_unit();f(&mut self.nodes[node].agg);self.recalc_up(node);}pub fn get(&mut self,key:u64)->Option<M::Agg>{assert!(key<=self.max_key);if self.is_empty(){return None;}if self.bit_len==0{return Some(self.nodes[0].agg.clone());}let key=key^self.xor_mask;let mut node=0;for d in(0..self.bit_len).rev(){let bit=((key>>d)&1)as usize;let next=self.nodes[node].child[bit];if next==usize::MAX{return None;}self.push_at(node,d+1);node=next;}Some(self.nodes[node].agg.clone())}pub fn update<R>(&mut self,range:R,act:M::Act)where R:RangeBounds<u64>{let Some(range)=self.range_to_bounds(range)else{return;};if self.is_empty(){return;}let(ql,qr)=range;if ql==0&&qr==self.max_key{self.apply_at(0,self.bit_len,&act);return;}let mut l=ql;loop{let depth=(l.trailing_zeros()as usize).min(self.bit_len).min(63-(qr-l+1).leading_zeros()as usize);let r=l|((1u64<<depth)-1);let mut node=0;for d in(depth..self.bit_len).rev(){self.push_at(node,d+1);node=self.nodes[node].child[(((l^self.xor_mask)>>d)&1)as usize];if node==usize::MAX{break;}}if node!=usize::MAX{self.apply_at(node,depth,&act);self.recalc_up(node);}if r==qr{break;}l=r+1;}}pub fn fold<R>(&mut self,range:R)->M::Agg where R:RangeBounds<u64>{let Some(range)=self.range_to_bounds(range)else{return M::agg_unit();};let(ql,qr)=range;if ql==0&&qr==self.max_key{return self.nodes[0].agg.clone();}let mut res=M::agg_unit();let mut l=ql;loop{let depth=(l.trailing_zeros()as usize).min(self.bit_len).min(63-(qr-l+1).leading_zeros()as usize);let r=l|((1u64<<depth)-1);let mut node=0;for d in(depth..self.bit_len).rev(){self.push_at(node,d+1);node=self.nodes[node].child[(((l^self.xor_mask)>>d)&1)as usize];if node==usize::MAX{break;}}if node!=usize::MAX{res=M::agg_operate(&res,&self.nodes[node].agg);}if r==qr{break;}l=r+1;}res}fn apply_at(&mut self,node:usize,depth:usize,act:&M::Act){if let Some(agg)=M::act_agg(&self.nodes[node].agg,act){self.nodes[node].agg=agg;if depth>0{M::act_operate_assign(&mut self.nodes[node].lazy,act);}}else if depth==0{panic!("act failed on leaf");}else{self.push_at(node,depth);for child in self.nodes[node].child{if child!=usize::MAX{self.apply_at(child,depth-1,act);}}self.recalc_at(node);}}fn push_at(&mut self,node:usize,depth:usize){let act=replace(&mut self.nodes[node].lazy,M::act_unit());let child=self.nodes[node].child;for child in child{if child!=usize::MAX{self.apply_at(child,depth-1,&act);}}}fn recalc_at(&mut self,node:usize){let mut agg=M::agg_unit();for child in self.nodes[node].child{if child!=usize::MAX{agg=M::agg_operate(&agg,&self.nodes[child].agg);}}self.nodes[node].agg=agg;}fn recalc_up(&mut self,mut node:usize){while self.nodes[node].parent!=usize::MAX{node=self.nodes[node].parent;self.recalc_at(node);}}fn range_to_bounds<R>(&self,range:R)->Option<(u64,u64)>where R:RangeBounds<u64>{let start=match range.start_bound(){Bound::Included(&x)=>{assert!(x<=self.max_key||(self.bit_len<64&&x==self.max_key+1));if x<=self.max_key{Some(x)}else{None}}Bound::Excluded(&x)=>{assert!(x<=self.max_key);(x<self.max_key).then_some(x+1)}Bound::Unbounded=>Some(0),};let end=match range.end_bound(){Bound::Included(&x)=>{assert!(x<=self.max_key);Some(x)}Bound::Excluded(&x)=>{if x==0{None}else{assert!(self.bit_len==64||x<=self.max_key+1);Some((x-1).min(self.max_key))}}Bound::Unbounded=>Some(self.max_key),};if let(Some(start),Some(end))=(start,end){(start<=end).then_some((start,end))}else{None}}}impl<M>BinaryTrie<M>where M:LazyMapMonoid,M::AggMonoid:AbelianMonoid{pub fn xor_all(&mut self,mask:u64){assert!(mask<=self.max_key);self.xor_mask^=mask;}}}
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>where T:Clone+Zero+Add<Output=T>{_marker:PhantomData<fn()->T>}impl<T>Magma for AdditiveOperation<T>where T:Clone+Zero+Add<Output=T>{type T=T;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{x.clone()+y.clone()}}impl<T>Unital for AdditiveOperation<T>where T:Clone+Zero+Add<Output=T>{#[inline]fn unit()->Self::T{Zero::zero()}}impl<T>Associative for AdditiveOperation<T>where T:Clone+Zero+Add<Output=T>{}impl<T>Commutative for AdditiveOperation<T>where T:Clone+Zero+Add<Output=T>{}impl<T>Invertible for AdditiveOperation<T>where T:Clone+Zero+Add<Output=T>+Sub<Output=T>+Neg<Output=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::last_operation_impl::LastOperation;
mod last_operation_impl{use super::*;use std::marker::PhantomData;#[doc=" retain the last element"]pub struct LastOperation<T>where T:Clone{_marker:PhantomData<fn()->T>}impl<T>Magma for LastOperation<T>where T:Clone{type T=Option<T>;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{y.as_ref().or(x.as_ref()).cloned()}}impl<T>Unital for LastOperation<T>where T:Clone{#[inline]fn unit()->Self::T{None}}impl<T>Associative for LastOperation<T>where T:Clone{}impl<T>Idempotent for LastOperation<T>where T:Clone{}}
pub use self::lazy_map::*;
mod lazy_map{use super::*;use std::{cmp::Ordering,marker::PhantomData,ops::{Add,Mul,Sub}};pub trait LazyMapMonoid{type Key;type Agg:Clone;type Act:Clone;type AggMonoid:Monoid<T=Self::Agg>;type ActMonoid:Monoid<T=Self::Act>;type KeyAct:MonoidAct<Key=Self::Key,Act=Self::Act,ActMonoid=Self::ActMonoid>;fn single_agg(key:&Self::Key)->Self::Agg;fn toggle(_x:&mut Self::Agg){}fn act_agg(x:&Self::Agg,a:&Self::Act)->Option<Self::Agg>;fn act_key(x:&Self::Key,a:&Self::Act)->Self::Key{<Self::KeyAct as MonoidAct>::act(x,a)}#[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 struct EmptyActLazy<M>{_marker:PhantomData<fn()->M>}impl<M>LazyMapMonoid for EmptyActLazy<M>where M:Monoid{type Key=M::T;type Agg=M::T;type Act=();type AggMonoid=M;type ActMonoid=();type KeyAct=EmptyAct<M::T>;fn single_agg(key:&Self::Key)->Self::Agg{key.clone()}fn act_agg(x:&Self::Agg,_a:&Self::Act)->Option<Self::Agg>{Some(x.clone())}}pub struct EmptyAggActLazy<T>{_marker:PhantomData<fn()->T>}impl<T>LazyMapMonoid for EmptyAggActLazy<T>where T:Clone{type Key=T;type Agg=();type Act=();type AggMonoid=();type ActMonoid=();type KeyAct=EmptyAct<T>;fn single_agg(_key:&Self::Key)->Self::Agg{}fn act_agg(_x:&Self::Agg,_a:&Self::Act)->Option<Self::Agg>{Some(())}}pub struct FlattenLazy<M>{_marker:PhantomData<fn()->M>}impl<M>LazyMapMonoid for FlattenLazy<M>where M:Monoid{type Key=M::T;type Agg=M::T;type Act=M::T;type AggMonoid=M;type ActMonoid=M;type KeyAct=FlattenAct<M>;fn single_agg(key:&Self::Key)->Self::Agg{key.clone()}fn act_agg(x:&Self::Agg,a:&Self::Act)->Option<Self::Agg>{Some(M::operate(x,a))}}pub struct RangeSumRangeAdd<T>{_marker:PhantomData<fn()->T>}impl<T>LazyMapMonoid for RangeSumRangeAdd<T>where T:Copy+Zero+One+Add<Output=T>+Mul<Output=T>+PartialEq{type Key=T;type Agg=(T,T);type Act=T;type AggMonoid=(AdditiveOperation<T>,AdditiveOperation<T>);type ActMonoid=AdditiveOperation<T>;type KeyAct=FlattenAct<Self::ActMonoid>;fn single_agg(key:&Self::Key)->Self::Agg{(*key,T::one())}fn act_agg(&(x,y):&Self::Agg,&a:&Self::Act)->Option<Self::Agg>{Some(if<Self::ActMonoid as Unital>::is_unit(&a){(x,y)}else{(x+a*y,y)})}}pub struct RangeSumRangeLinear<T>{_marker:PhantomData<fn()->T>}impl<T>LazyMapMonoid for RangeSumRangeLinear<T>where T:Copy+Zero+One+Add<Output=T>+Mul<Output=T>+PartialEq{type Key=T;type Agg=(T,T);type Act=(T,T);type AggMonoid=(AdditiveOperation<T>,AdditiveOperation<T>);type ActMonoid=LinearOperation<T>;type KeyAct=LinearAct<T>;fn single_agg(key:&Self::Key)->Self::Agg{(*key,T::one())}fn act_agg(&(x,y):&Self::Agg,&(a,b):&Self::Act)->Option<Self::Agg>{Some(if<Self::ActMonoid as Unital>::is_unit(&(a,b)){(x,y)}else{(a*x+b*y,y)})}}pub struct RangeSumRangeUpdate<T>{_marker:PhantomData<fn()->T>}impl<T>LazyMapMonoid for RangeSumRangeUpdate<T>where T:Copy+Zero+One+Add<Output=T>+Mul<Output=T>+PartialEq{type Key=T;type Agg=(T,T);type Act=Option<T>;type AggMonoid=(AdditiveOperation<T>,AdditiveOperation<T>);type ActMonoid=LastOperation<T>;type KeyAct=UpdateAct<T>;fn single_agg(key:&Self::Key)->Self::Agg{(*key,T::one())}fn act_agg(&(x,y):&Self::Agg,a:&Self::Act)->Option<Self::Agg>{Some((a.map(|a|a*y).unwrap_or(x),y))}}pub struct RangeMaxRangeUpdate<T>{_marker:PhantomData<fn()->T>}impl<T>LazyMapMonoid for RangeMaxRangeUpdate<T>where T:Clone+PartialEq+Ord+Bounded{type Key=T;type Agg=T;type Act=Option<T>;type AggMonoid=MaxOperation<T>;type ActMonoid=LastOperation<T>;type KeyAct=UpdateAct<T>;fn single_agg(key:&Self::Key)->Self::Agg{key.clone()}fn act_agg(x:&Self::Agg,a:&Self::Act)->Option<Self::Agg>{Some(a.as_ref().unwrap_or(x).clone())}}pub struct RangeMinRangeUpdate<T>{_marker:PhantomData<fn()->T>}impl<T>LazyMapMonoid for RangeMinRangeUpdate<T>where T:Clone+PartialEq+Ord+Bounded{type Key=T;type Agg=T;type Act=Option<T>;type AggMonoid=MinOperation<T>;type ActMonoid=LastOperation<T>;type KeyAct=UpdateAct<T>;fn single_agg(key:&Self::Key)->Self::Agg{key.clone()}fn act_agg(x:&Self::Agg,a:&Self::Act)->Option<Self::Agg>{Some(a.as_ref().unwrap_or(x).clone())}}pub struct RangeMaxRangeAdd<T>{_marker:PhantomData<fn()->T>}impl<T>LazyMapMonoid for RangeMaxRangeAdd<T>where T:Clone+Ord+Bounded+Zero+Add<Output=T>{type Key=T;type Agg=T;type Act=T;type AggMonoid=MaxOperation<T>;type ActMonoid=AdditiveOperation<T>;type KeyAct=FlattenAct<Self::ActMonoid>;fn single_agg(key:&Self::Key)->Self::Agg{key.clone()}fn act_agg(x:&Self::Agg,a:&Self::Act)->Option<Self::Agg>{Some(if<Self::ActMonoid as Unital>::is_unit(a){x.clone()}else{x.clone()+a.clone()})}}pub struct RangeMinRangeAdd<T>{_marker:PhantomData<fn()->T>}impl<T>LazyMapMonoid for RangeMinRangeAdd<T>where T:Clone+Ord+Bounded+Zero+Add<Output=T>{type Key=T;type Agg=T;type Act=T;type AggMonoid=MinOperation<T>;type ActMonoid=AdditiveOperation<T>;type KeyAct=FlattenAct<Self::ActMonoid>;fn single_agg(key:&Self::Key)->Self::Agg{key.clone()}fn act_agg(x:&Self::Agg,a:&Self::Act)->Option<Self::Agg>{Some(if<Self::ActMonoid as Unital>::is_unit(a){x.clone()}else{x.clone()+a.clone()})}}#[derive(Debug,Clone,Copy,PartialEq,Eq)]pub struct RangeChminChmaxAdd<T>{lb:T,ub:T,bias:T}impl<T>RangeChminChmaxAdd<T>where T:Zero+Bounded{pub fn chmin(x:T)->Self{Self{lb:T::minimum(),ub:x,bias:T::zero()}}pub fn chmax(x:T)->Self{Self{lb:x,ub:T::maximum(),bias:T::zero()}}pub fn add(x:T)->Self{Self{lb:T::minimum(),ub:T::maximum(),bias:x}}}impl<T>Magma for RangeChminChmaxAdd<T>where T:Copy+Zero+One+Ord+Bounded+Add<Output=T>+Sub<Output=T>+Mul<Output=T>+PartialEq{type T=Self;fn operate(x:&Self::T,y:&Self::T)->Self::T{Self{lb:(x.lb+x.bias).min(y.ub).max(y.lb)-x.bias,ub:(x.ub+x.bias).max(y.lb).min(y.ub)-x.bias,bias:x.bias+y.bias}}}impl<T>Associative for RangeChminChmaxAdd<T>where T:Copy+Zero+One+Ord+Bounded+Add<Output=T>+Sub<Output=T>+Mul<Output=T>+PartialEq{}impl<T>Unital for RangeChminChmaxAdd<T>where T:Copy+Zero+One+Ord+Bounded+Add<Output=T>+Sub<Output=T>+Mul<Output=T>+PartialEq{fn unit()->Self::T{Self{lb:T::minimum(),ub:T::maximum(),bias:T::zero()}}}#[derive(Debug,Clone,PartialEq,Eq)]pub struct RangeSumRangeChminChmaxAdd<T>{min:T,max:T,min2:T,max2:T,pub sum:T,size:T,n_min:T,n_max:T}impl<T>RangeSumRangeChminChmaxAdd<T>where T:Copy+Zero+One+Ord+Bounded+Add<Output=T>+Sub<Output=T>+Mul<Output=T>+PartialEq{pub fn single(key:T,size:T)->Self{Self{min:key,max:key,min2:T::maximum(),max2:T::minimum(),sum:key*size,size,n_min:size,n_max:size}}}impl<T>Magma for RangeSumRangeChminChmaxAdd<T>where T:Copy+Zero+One+Ord+Bounded+Add<Output=T>+Sub<Output=T>+Mul<Output=T>+PartialEq{type T=Self;fn operate(x:&Self::T,y:&Self::T)->Self::T{Self{min:x.min.min(y.min),max:x.max.max(y.max),min2:if x.min==y.min{x.min2.min(y.min2)}else if x.min2<=y.min{x.min2}else if y.min2<=x.min{y.min2}else{x.min.max(y.min)},max2:if x.max==y.max{x.max2.max(y.max2)}else if x.max2>=y.max{x.max2}else if y.max2>=x.max{y.max2}else{x.max.min(y.max)},sum:x.sum+y.sum,size:x.size+y.size,n_min:match x.min.cmp(&y.min){Ordering::Less=>x.n_min,Ordering::Equal=>x.n_min+y.n_min,Ordering::Greater=>y.n_min,},n_max:match x.max.cmp(&y.max){Ordering::Less=>y.n_max,Ordering::Equal=>x.n_max+y.n_max,Ordering::Greater=>x.n_max,}}}}impl<T>Associative for RangeSumRangeChminChmaxAdd<T>where T:Copy+Zero+One+Ord+Bounded+Add<Output=T>+Sub<Output=T>+Mul<Output=T>+PartialEq{}impl<T>Unital for RangeSumRangeChminChmaxAdd<T>where T:Copy+Zero+One+Ord+Bounded+Add<Output=T>+Sub<Output=T>+Mul<Output=T>+PartialEq{fn unit()->Self::T{Self{min:T::maximum(),max:T::minimum(),min2:T::maximum(),max2:T::minimum(),sum:T::zero(),size:T::zero(),n_min:T::zero(),n_max:T::zero()}}}impl<T>MonoidAct for RangeChminChmaxAdd<T>where T:Copy+Zero+One+Ord+Bounded+Add<Output=T>+Sub<Output=T>+Mul<Output=T>+PartialEq{type Key=T;type Act=RangeChminChmaxAdd<T>;type ActMonoid=RangeChminChmaxAdd<T>;fn act(x:&Self::Key,a:&Self::Act)->Self::Key{(*x).max(a.lb).min(a.ub)+a.bias}}impl<T>LazyMapMonoid for RangeSumRangeChminChmaxAdd<T>where T:Copy+Zero+One+Ord+Bounded+Add<Output=T>+Sub<Output=T>+Mul<Output=T>+PartialEq{type Key=T;type Agg=Self;type Act=RangeChminChmaxAdd<T>;type AggMonoid=Self;type ActMonoid=RangeChminChmaxAdd<T>;type KeyAct=RangeChminChmaxAdd<T>;fn single_agg(&key:&Self::Key)->Self::Agg{Self::single(key,T::one())}fn act_agg(x:&Self::Agg,a:&Self::Act)->Option<Self::Agg>{Some(if<Self::ActMonoid as Unital>::is_unit(a){x.clone()}else if x.size.is_zero(){Self::unit()}else if x.min==x.max||a.lb==a.ub||a.lb>=x.max||a.ub<=x.min{Self::single(x.min.max(a.lb).min(a.ub)+a.bias,x.size)}else if x.min2==x.max{let mut x=x.clone();let min=x.min.max(a.lb)+a.bias;let max=x.max.min(a.ub)+a.bias;x.min=min;x.max2=min;x.max=max;x.min2=max;x.sum=min*x.n_min+max*x.n_max;x}else if a.lb<x.min2&&x.max2<a.ub{let mut x=x.clone();let min=x.min.max(a.lb);let max=x.max.min(a.ub);x.sum=x.sum+(min-x.min)*x.n_min+(max-x.max)*x.n_max+a.bias*x.size;x.min=min+a.bias;x.max=max+a.bias;x.min2=x.min2+a.bias;x.max2=x.max2+a.bias;x}else{return None;})}}}
pub use self::linear_operation_impl::LinearOperation;
mod linear_operation_impl{use super::*;use std::{marker::PhantomData,ops::{Add,Div,Mul,Neg,Sub}};#[doc=" $(a, b) \\circ (c, d) = \\lambda x. c \\times (a \\times x + b) + d$"]pub struct LinearOperation<T>where T:Clone+Zero+Add<Output=T>+One+Mul<Output=T>{_marker:PhantomData<fn()->T>}impl<T>LinearOperation<T>where T:Clone+Zero+Add<Output=T>+One+Mul<Output=T>{pub fn apply(f:&(T,T),x:&T)->T{f.0 .clone()*x.clone()+f.1 .clone()}}impl<T>Magma for LinearOperation<T>where T:Clone+Zero+One+Add<Output=T>+Mul<Output=T>{type T=(T,T);#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{(y.0 .clone()*x.0 .clone(),y.0 .clone()*x.1 .clone()+y.1 .clone())}}impl<T>Unital for LinearOperation<T>where T:Clone+Zero+One+Add<Output=T>+Mul<Output=T>{#[inline]fn unit()->Self::T{(One::one(),Zero::zero())}}impl<T>Associative for LinearOperation<T>where T:Clone+Zero+One+Add<Output=T>+Mul<Output=T>{}impl<T>Invertible for LinearOperation<T>where T:Clone+Zero+One+Add<Output=T>+Sub<Output=T>+Neg<Output=T>+Mul<Output=T>+Div<Output=T>{fn inverse(x:&Self::T)->Self::T{let y=<T as One>::one().div(x.0 .clone());(y.clone(),-y.mul(x.1 .clone()))}}}
pub use self::max_operation_impl::MaxOperation;
mod max_operation_impl{use super::*;use std::marker::PhantomData;#[doc=" binary operation to select larger element"]pub struct MaxOperation<T>where T:Clone+Ord+Bounded{_marker:PhantomData<fn()->T>}impl<T>Magma for MaxOperation<T>where T:Clone+Ord+Bounded{type T=T;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{x.max(y).clone()}}impl<T>Unital for MaxOperation<T>where T:Clone+Ord+Bounded{#[inline]fn unit()->Self::T{<T as Bounded>::minimum()}}impl<T>Associative for MaxOperation<T>where T:Clone+Ord+Bounded{}impl<T>Commutative for MaxOperation<T>where T:Clone+Ord+Bounded{}impl<T>Idempotent for MaxOperation<T>where T:Clone+Ord+Bounded{}}
pub use self::min_operation_impl::MinOperation;
mod min_operation_impl{use super::*;use std::marker::PhantomData;#[doc=" binary operation to select smaller element"]pub struct MinOperation<T>where T:Clone+Ord+Bounded{_marker:PhantomData<fn()->T>}impl<T>Magma for MinOperation<T>where T:Clone+Ord+Bounded{type T=T;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{x.min(y).clone()}}impl<T>Unital for MinOperation<T>where T:Clone+Ord+Bounded{#[inline]fn unit()->Self::T{<T as Bounded>::maximum()}}impl<T>Associative for MinOperation<T>where T:Clone+Ord+Bounded{}impl<T>Commutative for MinOperation<T>where T:Clone+Ord+Bounded{}impl<T>Idempotent for MinOperation<T>where T:Clone+Ord+Bounded{}}
pub use self::action::*;
mod action{use super::*;use std::{marker::PhantomData,ops::{Add,Mul}};pub trait MonoidAct{type Key;type Act:Clone;type ActMonoid:Monoid<T=Self::Act>;fn act(x:&Self::Key,a:&Self::Act)->Self::Key;fn act_assign(x:&mut Self::Key,a:&Self::Act){*x=Self::act(x,a);}fn unit()->Self::Act{<Self::ActMonoid as Unital>::unit()}fn operate(x:&Self::Act,y:&Self::Act)->Self::Act{<Self::ActMonoid as Magma>::operate(x,y)}fn operate_assign(x:&mut Self::Act,y:&Self::Act){*x=<Self::ActMonoid as Magma>::operate(x,y);}}pub struct EmptyAct<T>{_marker:PhantomData<fn()->T>}impl<T>MonoidAct for EmptyAct<T>where T:Clone{type Key=T;type Act=();type ActMonoid=();fn act(x:&Self::Key,_a:&Self::Act)->Self::Key{x.clone()}}pub struct FlattenAct<M>{_marker:PhantomData<fn()->M>}impl<M>MonoidAct for FlattenAct<M>where M:Monoid{type Key=M::T;type Act=M::T;type ActMonoid=M;fn act(x:&Self::Key,a:&Self::Act)->Self::Key{M::operate(x,a)}}pub struct LinearAct<T>{_marker:PhantomData<fn()->T>}impl<T>MonoidAct for LinearAct<T>where T:Clone+Zero+One+Add<Output=T>+Mul<Output=T>{type Key=T;type Act=(T,T);type ActMonoid=LinearOperation<T>;fn act(x:&Self::Key,(a,b):&Self::Act)->Self::Key{a.clone()*x.clone()+b.clone()}}pub struct UpdateAct<T>{_marker:PhantomData<fn()->T>}impl<T>MonoidAct for UpdateAct<T>where T:Clone{type Key=T;type Act=Option<T>;type ActMonoid=LastOperation<T>;fn act(x:&Self::Key,a:&Self::Act)->Self::Key{a.as_ref().unwrap_or(x).clone()}}}
mod tuple_operation_impl{use super::*;macro_rules!impl_tuple_operation{(@impl)=>{impl Magma for(){type T=();fn operate(_x:&Self::T,_y:&Self::T)->Self::T{}}impl Unital for(){fn unit()->Self::T{}}impl Associative for(){}impl Commutative for(){}impl Idempotent for(){}impl Invertible for(){fn inverse(_x:&Self::T)->Self::T{}}};(@impl$($T:ident$i:tt)*)=>{impl<$($T:Magma),*>Magma for($($T,)*){type T=($(<$T as Magma>::T,)*);fn operate(x:&Self::T,y:&Self::T)->Self::T{($(<$T as Magma>::operate(&x.$i,&y.$i),)*)}}impl<$($T:Unital),*>Unital for($($T,)*){fn unit()->Self::T{($(<$T as Unital>::unit(),)*)}}impl<$($T:Associative),*>Associative for($($T,)*){}impl<$($T:Commutative),*>Commutative for($($T,)*){}impl<$($T:Idempotent),*>Idempotent for($($T,)*){}impl<$($T:Invertible),*>Invertible for($($T,)*){fn inverse(x:&Self::T)->Self::T{($(<$T as Invertible>::inverse(&x.$i),)*)}}};(@inner$($T:ident$i:tt)*;$U:ident$j:tt$($t:tt)*)=>{impl_tuple_operation!(@impl$($T$i)*);impl_tuple_operation!(@inner$($T$i)*$U$j;$($t)*);};(@inner$($T:ident$i:tt)*;)=>{impl_tuple_operation!(@impl$($T$i)*);};($($t:tt)*)=>{impl_tuple_operation!(@inner;$($t)*);};}impl_tuple_operation!(A 0 B 1 C 2 D 3 E 4 F 5 G 6 H 7 I 8 J 9);}
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;fn reverse_operate(x:&Self::T,y:&Self::T)->Self::T{Self::operate(y,x)}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:Magma{#[cfg(test)]fn check_associative(a:&Self::T,b:&Self::T,c:&Self::T)->bool where Self::T:PartialEq{({let ab_c=Self::operate(&Self::operate(a,b),c);let a_bc=Self::operate(a,&Self::operate(b,c));ab_c==a_bc})&&({let ab_c=Self::reverse_operate(c,&Self::reverse_operate(b,a));let a_bc=Self::reverse_operate(&Self::reverse_operate(c,b),a);ab_c==a_bc})&&({let mut ab_c=a.clone();Self::operate_assign(&mut ab_c,b);Self::operate_assign(&mut ab_c,c);let mut bc=b.clone();Self::operate_assign(&mut bc,c);let mut a_bc=a.clone();Self::operate_assign(&mut a_bc,&bc);ab_c==a_bc})}}#[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;fn is_unit(x:&Self::T)->bool where Self::T:PartialEq{x==&Self::unit()}fn set_unit(x:&mut Self::T){*x=Self::unit();}#[cfg(test)]fn check_unital(x:&Self::T)->bool where Self::T:PartialEq{let u=Self::unit();let xu=Self::operate(x,&u);let ux=Self::operate(&u,x);let mut any=x.clone();Self::set_unit(&mut any);xu==*x&&ux==*x&&Self::is_unit(&u)&&Self::is_unit(&any)}}pub trait ExpBits{type Iter:Iterator<Item=bool>;fn bits(self)->Self::Iter;}pub trait SignedExpBits{type T:ExpBits;fn neg_and_bits(self)->(bool,Self::T);}pub struct Bits<T>{n:T}macro_rules!impl_exp_bits_for_uint{($($t:ty)*)=>{$(impl Iterator for Bits<$t>{type Item=bool;fn next(&mut self)->Option<bool>{if self.n==0{None}else{let bit=(self.n&1)==1;self.n>>=1;Some(bit)}}}impl ExpBits for$t{type Iter=Bits<$t>;fn bits(self)->Self::Iter{Bits{n:self}}}impl SignedExpBits for$t{type T=$t;fn neg_and_bits(self)->(bool,Self::T){(false,self)}})*};}impl_exp_bits_for_uint!(u8 u16 u32 u64 u128 usize);macro_rules!impl_signed_exp_bits_for_sint{($($s:ty,$u:ty;)*)=>{$(impl SignedExpBits for$s{type T=$u;fn neg_and_bits(self)->(bool,Self::T){(self<0,self.unsigned_abs())}})*};}impl_signed_exp_bits_for_sint!(i8,u8;i16,u16;i32,u32;i64,u64;i128,u128;isize,usize;);#[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<E>(mut x:Self::T,exp:E)->Self::T where E:ExpBits{let mut res=Self::unit();for bit in exp.bits(){if bit{res=Self::operate(&res,&x);}x=Self::operate(&x,&x);}res}fn fold<I>(iter:I)->Self::T where I:IntoIterator<Item=Self::T>{let mut iter=iter.into_iter();if let Some(item)=iter.next(){iter.fold(item,|acc,x|Self::operate(&acc,&x))}else{Self::unit()}}}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+Unital{#[doc=" $a$ where $a \\circ x = e$"]fn inverse(x:&Self::T)->Self::T;fn rinv_operate(x:&Self::T,y:&Self::T)->Self::T{Self::operate(x,&Self::inverse(y))}fn rinv_operate_assign(x:&mut Self::T,y:&Self::T){*x=Self::rinv_operate(x,y);}#[cfg(test)]fn check_invertible(x:&Self::T)->bool where Self::T:PartialEq{let i=Self::inverse(x);({let xi=Self::operate(x,&i);let ix=Self::operate(&i,x);Self::is_unit(&xi)&&Self::is_unit(&ix)})&&({let ii=Self::inverse(&i);ii==*x})&&({let mut xi=x.clone();Self::operate_assign(&mut xi,&i);let mut ix=i.clone();Self::operate_assign(&mut ix,x);Self::is_unit(&xi)&&Self::is_unit(&ix)})&&({let mut xi=x.clone();Self::rinv_operate_assign(&mut xi,x);let mut ix=i.clone();Self::rinv_operate_assign(&mut ix,&i);Self::is_unit(&xi)&&Self::is_unit(&ix)})}}#[doc=" associative binary operation and an identity element and inverse elements"]pub trait Group:Monoid+Invertible{fn signed_pow<E>(x:Self::T,exp:E)->Self::T where E:SignedExpBits{let(neg,exp)=E::neg_and_bits(exp);let res=Self::pow(x,exp);if neg{Self::inverse(&res)}else{res}}}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:Magma{#[cfg(test)]fn check_commutative(a:&Self::T,b:&Self::T)->bool where Self::T:PartialEq{Self::operate(a,b)==Self::operate(b,a)}}#[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:Magma{#[cfg(test)]fn check_idempotent(a:&Self::T)->bool where Self::T:PartialEq{Self::operate(a,a)==*a}}#[doc=" idempotent monoid"]pub trait IdempotentMonoid:Monoid+Idempotent{}impl<M>IdempotentMonoid for M where M:Monoid+Idempotent{}#[macro_export]macro_rules!monoid_fold{($m:ty)=>{<$m as Unital>::unit()};($m:ty,)=>{<$m as Unital>::unit()};($m:ty,$f:expr)=>{$f};($m:ty,$f:expr,$($ff:expr),*)=>{<$m as Magma>::operate(&($f),&monoid_fold!($m,$($ff),*))};}#[macro_export]macro_rules!define_monoid{($Name:ident,$t:ty,|$x:ident,$y:ident|$op:expr,$unit:expr)=>{struct$Name;impl Magma for$Name{type T=$t;fn operate($x:&Self::T,$y:&Self::T)->Self::T{$op}}impl Unital for$Name{fn unit()->Self::T{$unit}}impl Associative for$Name{}};}}
pub use self::bounded::Bounded;
mod bounded{#[doc=" Trait for max/min bounds"]pub trait Bounded:Sized+PartialOrd{fn maximum()->Self;fn minimum()->Self;fn is_maximum(&self)->bool{self==&Self::maximum()}fn is_minimum(&self)->bool{self==&Self::minimum()}fn set_maximum(&mut self){*self=Self::maximum()}fn set_minimum(&mut self){*self=Self::minimum()}}macro_rules!impl_bounded_num{($($t:ident)*)=>{$(impl Bounded for$t{fn maximum()->Self{$t::MAX}fn minimum()->Self{$t::MIN}})*};}impl_bounded_num!(u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize f32 f64);macro_rules!impl_bounded_tuple{(@impl$($T:ident)*)=>{impl<$($T:Bounded),*>Bounded for($($T,)*){fn maximum()->Self{($(<$T as Bounded>::maximum(),)*)}fn minimum()->Self{($(<$T as Bounded>::minimum(),)*)}}};(@inner$($T:ident)*,)=>{impl_bounded_tuple!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{impl_bounded_tuple!(@impl$($T)*);impl_bounded_tuple!(@inner$($T)*$U,$($Rest)*);};($T:ident$($Rest:ident)*)=>{impl_bounded_tuple!(@inner$T,$($Rest)*);};}impl_bounded_tuple!(A B C D E F G H I J);impl Bounded for(){fn maximum()->Self{}fn minimum()->Self{}}impl Bounded for bool{fn maximum()->Self{true}fn minimum()->Self{false}}impl<T>Bounded for Option<T>where T:Bounded{fn maximum()->Self{Some(<T as Bounded>::maximum())}fn minimum()->Self{None}}impl<T>Bounded for std::cmp::Reverse<T>where T:Bounded{fn maximum()->Self{std::cmp::Reverse(<T as Bounded>::minimum())}fn minimum()->Self{std::cmp::Reverse(<T as Bounded>::maximum())}}}
pub use self::zero_one::{One,Zero};
mod zero_one{pub trait Zero:Sized{fn zero()->Self;#[inline]fn is_zero(&self)->bool where Self:PartialEq{self==&Self::zero()}#[inline]fn set_zero(&mut self){*self=Self::zero();}}pub trait One:Sized{fn one()->Self;#[inline]fn is_one(&self)->bool where Self:PartialEq{self==&Self::one()}#[inline]fn set_one(&mut self){*self=Self::one();}}macro_rules!impl_zero_one{($({$Trait:ident$method:ident$($t:ty)*,$e:expr})*)=>{$($(impl$Trait for$t{fn$method()->Self{$e}})*)*};}impl_zero_one!({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.});}