pub fn solve() {
    crate::prepare!();
    sc!(n, m, ps: [P; n * 2], st: [[(Usize1, Usize1); const 2]; m]);
    let mut d = vec![vec![f64::INFINITY; n * 2]; n * 2];
    let dist = |p: P, q: P| ((p - q).norm() as f64).sqrt();
    let cross = |p: P, q: P| {
        ps.chunks_exact(2).any(|c| {
            p != c[0]
                && p != c[1]
                && q != c[0]
                && q != c[1]
                && LineSegment::new(p, q).intersect(&LineSegment::new(c[0], c[1]))
        })
    };
    for i in 0..n * 2 {
        for j in 0..n * 2 {
            if i == j || !cross(ps[i], ps[j]) {
                d[i][j] = dist(ps[i], ps[j]);
            }
        }
    }
    for k in 0..n * 2 {
        for i in 0..n * 2 {
            for j in 0..n * 2 {
                chmin!(d[i][j], d[i][k] + d[k][j]);
            }
        }
    }
    for [s, t] in st {
        let ans = d[s.0 * 2 + s.1][t.0 * 2 + t.1];
        pp!(ans);
    }
}
type P = Complex<i64>;
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]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)*)}}};()=>{$crate::prepare!(@output($));$crate::prepare!(@normal($))};(?)=>{$crate::prepare!(@output($));$crate::prepare!(@interactive($))};}#[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!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=" - `@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;$len:expr]]=>{{use::std::mem::{ManuallyDrop,MaybeUninit};const LEN:usize=$len;let mut$data:[MaybeUninit<_>;LEN]=unsafe{MaybeUninit::uninit().assume_init()};$init;#[repr(C)]union __Transmuter<T:Copy>{src:ManuallyDrop<[MaybeUninit<T>;LEN]>,dst:ManuallyDrop<[T;LEN]>,}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::{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)*$U,$($Rest)*);};($($T:ident)*)=>{iter_scan_tuple_impl!(@inner,$($T)*);};}iter_scan_tuple_impl!(A B C D E F G H I J K);pub struct ScannerIter<'a,'b,T>{inner:&'b mut Scanner<'a>,_marker:std::marker::PhantomData<fn()->T>}impl<'a,'b,T>Iterator for ScannerIter<'a,'b,T>where T:IterScan{type Item=<T as IterScan>::Output;#[inline]fn next(&mut self)->Option<Self::Item>{<T as IterScan>::scan(&mut self.inner.iter)}}#[doc=" scan a value with Scanner"]#[doc=""]#[doc=" - `scan_value!(scanner, ELEMENT)`"]#[doc=""]#[doc=" ELEMENT :="]#[doc=" - `$ty`: IterScan"]#[doc=" - `@$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)*,)*)};(@$tag:ident$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;const$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@array$scanner,[@$e]$len)]]$($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$scanner:expr,[$($args:tt)*][[$($tt:tt)*];const$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@array$scanner,[[$($tt)*]]$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$scanner:expr,[$($args:tt)*][($($tt:tt)*);const$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@array$scanner,[($($tt)*)]$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;const$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@array$scanner,[$ty]$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 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)=>{$crate::scan!(@let$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 enum Byte1{}impl IterScan for Byte1{type Output=u8;#[inline]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;#[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::complex::Complex;
mod complex{use super::{Float,IterScan,One,Zero};use std::{cmp::Ordering,iter::{Product,Sum},ops::{Add,AddAssign,Div,DivAssign,Mul,MulAssign,Neg,Sub,SubAssign}};#[derive(Clone,Copy,Debug,Default,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct Complex<T>{pub re:T,pub im:T}impl<T>Complex<T>{pub fn new(re:T,im:T)->Self{Complex{re,im}}pub fn transpose(self)->Self{Complex{re:self.im,im:self.re}}}impl<T>Zero for Complex<T>where T:Zero{fn zero()->Self{Self::new(T::zero(),T::zero())}}impl<T>One for Complex<T>where T:Zero+One{fn one()->Self{Self::new(T::one(),T::zero())}}impl<T>Complex<T>where T:Zero+One{pub fn i()->Self{Self::new(T::zero(),T::one())}}impl<T>Complex<T>where T:Neg<Output=T>{pub fn conjugate(self)->Self{Self::new(self.re,-self.im)}}impl<T>Complex<T>where T:Mul,<T as Mul>::Output:Add{pub fn dot(self,rhs:Self)-><<T as Mul>::Output as Add>::Output{self.re*rhs.re+self.im*rhs.im}}impl<T>Complex<T>where T:Mul,<T as Mul>::Output:Sub{pub fn cross(self,rhs:Self)-><<T as Mul>::Output as Sub>::Output{self.re*rhs.im-self.im*rhs.re}}impl<T>Complex<T>where T:Mul+Clone,<T as Mul>::Output:Add{pub fn norm(self)-><<T as Mul>::Output as Add>::Output{self.re.clone()*self.re+self.im.clone()*self.im}}impl<T>Complex<T>where T:Zero+Ord+Mul,<T as Mul>::Output:Ord{pub fn cmp_by_arg(self,other:Self)->Ordering{fn pos<T>(c:&Complex<T>)->bool where T:Zero+Ord{let zero=T::zero();c.im<zero||c.im<=zero&&c.re<zero}pos(&self).cmp(&pos(&other)).then_with(||(self.re*other.im).cmp(&(self.im*other.re)).reverse())}}impl<T>Complex<T>where T:Float{pub fn polar(r:T,theta:T)->Self{Self::new(r*theta.cos(),r*theta.sin())}pub fn primitive_nth_root_of_unity(n:T)->Self{let theta=T::TAU/n;Self::new(theta.cos(),theta.sin())}pub fn abs(self)->T{self.re.hypot(self.im)}pub fn unit(self)->Self{self/self.abs()}pub fn angle(self)->T{self.im.atan2(self.re)}}impl<T>Add for Complex<T>where T:Add{type Output=Complex<<T as Add>::Output>;fn add(self,rhs:Self)->Self::Output{Complex::new(self.re+rhs.re,self.im+rhs.im)}}impl<T>Add<T>for Complex<T>where T:Add<Output=T>{type Output=Self;fn add(self,rhs:T)->Self::Output{Self::new(self.re+rhs,self.im)}}impl<T>Sub for Complex<T>where T:Sub{type Output=Complex<<T as Sub>::Output>;fn sub(self,rhs:Self)->Self::Output{Complex::new(self.re-rhs.re,self.im-rhs.im)}}impl<T>Sub<T>for Complex<T>where T:Sub<Output=T>{type Output=Self;fn sub(self,rhs:T)->Self::Output{Self::new(self.re-rhs,self.im)}}impl<T,U>Mul for Complex<T>where T:Clone+Mul,<T as Mul>::Output:Add<Output=U>+Sub<Output=U>{type Output=Complex<U>;fn mul(self,rhs:Self)->Self::Output{Complex::new(self.re.clone()*rhs.re.clone()-self.im.clone()*rhs.im.clone(),self.re*rhs.im+self.im*rhs.re)}}impl<T>Mul<T>for Complex<T>where T:Clone+Mul{type Output=Complex<<T as Mul>::Output>;fn mul(self,rhs:T)->Self::Output{Complex::new(self.re*rhs.clone(),self.im*rhs)}}impl<T>Div for Complex<T>where T:Clone+Add<Output=T>+Sub<Output=T>+Mul<Output=T>+Div{type Output=Complex<<T as Div>::Output>;fn div(self,rhs:Self)->Self::Output{let d=rhs.re.clone()*rhs.re.clone()+rhs.im.clone()*rhs.im.clone();Complex::new((self.re.clone()*rhs.re.clone()+self.im.clone()*rhs.im.clone())/d.clone(),(self.im*rhs.re-self.re*rhs.im)/d)}}impl<T>Div<T>for Complex<T>where T:Clone+Div{type Output=Complex<<T as Div>::Output>;fn div(self,rhs:T)->Self::Output{Complex::new(self.re/rhs.clone(),self.im/rhs)}}impl<T>Neg for Complex<T>where T:Neg{type Output=Complex<<T as Neg>::Output>;fn neg(self)->Self::Output{Complex::new(-self.re,-self.im)}}macro_rules!impl_complex_ref_binop{(impl<$T:ident>$imp:ident$method:ident($l:ty,$r:ty)where$($w:ident)*)=>{impl<$T>$imp<$r>for&$l where$T:Clone$(+$w<Output=$T>)*,{type Output=<$l as$imp<$r>>::Output;fn$method(self,rhs:$r)-><$l as$imp<$r>>::Output{$imp::$method(self.clone(),rhs)}}impl<$T>$imp<&$r>for$l where$T:Clone$(+$w<Output=$T>)*,{type Output=<$l as$imp<$r>>::Output;fn$method(self,rhs:&$r)-><$l as$imp<$r>>::Output{$imp::$method(self,rhs.clone())}}impl<$T>$imp<&$r>for&$l where$T:Clone$(+$w<Output=$T>)*,{type Output=<$l as$imp<$r>>::Output;fn$method(self,rhs:&$r)-><$l as$imp<$r>>::Output{$imp::$method(self.clone(),rhs.clone())}}};}impl_complex_ref_binop!(impl<T>Add add(Complex<T>,Complex<T>)where Add);impl_complex_ref_binop!(impl<T>Add add(Complex<T>,T)where Add);impl_complex_ref_binop!(impl<T>Sub sub(Complex<T>,Complex<T>)where Sub);impl_complex_ref_binop!(impl<T>Sub sub(Complex<T>,T)where Sub);impl_complex_ref_binop!(impl<T>Mul mul(Complex<T>,Complex<T>)where Add Sub Mul);impl_complex_ref_binop!(impl<T>Mul mul(Complex<T>,T)where Mul);impl_complex_ref_binop!(impl<T>Div div(Complex<T>,Complex<T>)where Add Sub Mul Div);impl_complex_ref_binop!(impl<T>Div div(Complex<T>,T)where Div);macro_rules!impl_complex_ref_unop{(impl<$T:ident>$imp:ident$method:ident($t:ty)where$($w:ident)*)=>{impl<$T>$imp for&$t where$T:Clone$(+$w<Output=$T>)*,{type Output=<$t as$imp>::Output;fn$method(self)-><$t as$imp>::Output{$imp::$method(self.clone())}}};}impl_complex_ref_unop!(impl<T>Neg neg(Complex<T>)where Neg);macro_rules!impl_complex_op_assign{(impl<$T:ident>$imp:ident$method:ident($l:ty,$r:ty)$fromimp:ident$frommethod:ident where$($w:ident)*)=>{impl<$T>$imp<$r>for$l where$T:Clone$(+$w<Output=$T>)*,{fn$method(&mut self,rhs:$r){*self=$fromimp::$frommethod(self.clone(),rhs);}}impl<$T>$imp<&$r>for$l where$T:Clone$(+$w<Output=$T>)*,{fn$method(&mut self,rhs:&$r){$imp::$method(self,rhs.clone());}}};}impl_complex_op_assign!(impl<T>AddAssign add_assign(Complex<T>,Complex<T>)Add add where Add);impl_complex_op_assign!(impl<T>AddAssign add_assign(Complex<T>,T)Add add where Add);impl_complex_op_assign!(impl<T>SubAssign sub_assign(Complex<T>,Complex<T>)Sub sub where Sub);impl_complex_op_assign!(impl<T>SubAssign sub_assign(Complex<T>,T)Sub sub where Sub);impl_complex_op_assign!(impl<T>MulAssign mul_assign(Complex<T>,Complex<T>)Mul mul where Add Sub Mul);impl_complex_op_assign!(impl<T>MulAssign mul_assign(Complex<T>,T)Mul mul where Mul);impl_complex_op_assign!(impl<T>DivAssign div_assign(Complex<T>,Complex<T>)Div div where Add Sub Mul Div);impl_complex_op_assign!(impl<T>DivAssign div_assign(Complex<T>,T)Div div where Div);macro_rules!impl_complex_fold{(impl<$T:ident>$imp:ident$method:ident($t:ty)$identimp:ident$identmethod:ident$fromimp:ident$frommethod:ident where$($w:ident)*$(+$x:ident)*)=>{impl<$T>$imp for$t where$T:$identimp$(+$w<Output=$T>)*$(+$x)*,{fn$method<I:Iterator<Item=Self>>(iter:I)->Self{iter.fold(<Self as$identimp>::$identmethod(),$fromimp::$frommethod)}}impl<'a,$T:'a>$imp<&'a$t>for$t where$T:Clone+$identimp$(+$w<Output=$T>)*$(+$x)*,{fn$method<I:Iterator<Item=&'a$t>>(iter:I)->Self{iter.fold(<Self as$identimp>::$identmethod(),$fromimp::$frommethod)}}};}impl_complex_fold!(impl<T>Sum sum(Complex<T>)Zero zero Add add where Add);impl_complex_fold!(impl<T>Product product(Complex<T>)One one Mul mul where Add Sub Mul+Zero+Clone);impl<T:IterScan>IterScan for Complex<T>{type Output=Complex<<T as IterScan>::Output>;fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{Some(Complex::new(<T as IterScan>::scan(iter)?,<T as IterScan>::scan(iter)?))}}}
pub use self::bounded::Bounded;
mod bounded{#[doc=" Trait for max/min bounds"]pub trait Bounded:Sized+PartialOrd{fn maximum()->Self;fn minimum()->Self;fn is_maximum(&self)->bool{self==&Self::maximum()}fn is_minimum(&self)->bool{self==&Self::minimum()}fn set_maximum(&mut self){*self=Self::maximum()}fn set_minimum(&mut self){*self=Self::minimum()}}macro_rules!bounded_num_impls{($($t:ident)*)=>{$(impl Bounded for$t{fn maximum()->Self{std::$t::MAX}fn minimum()->Self{std::$t::MIN}})*};}bounded_num_impls!(u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize f32 f64);macro_rules!bounded_tuple_impls{(@impl$($T:ident)*)=>{impl<$($T:Bounded),*>Bounded for($($T,)*){fn maximum()->Self{($(<$T as Bounded>::maximum(),)*)}fn minimum()->Self{($(<$T as Bounded>::minimum(),)*)}}};(@inner$($T:ident)*,)=>{bounded_tuple_impls!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{bounded_tuple_impls!(@impl$($T)*);bounded_tuple_impls!(@inner$($T)*$U,$($Rest)*);};($T:ident$($Rest:ident)*)=>{bounded_tuple_impls!(@inner$T,$($Rest)*);};}bounded_tuple_impls!(A B C D E F G H I J);impl Bounded for(){fn maximum()->Self{}fn minimum()->Self{}}impl Bounded for bool{fn maximum()->Self{true}fn minimum()->Self{false}}impl<T>Bounded for Option<T>where T:Bounded{fn maximum()->Self{Some(<T as Bounded>::maximum())}fn minimum()->Self{None}}impl<T>Bounded for std::cmp::Reverse<T>where T:Bounded{fn maximum()->Self{std::cmp::Reverse(<T as Bounded>::minimum())}fn minimum()->Self{std::cmp::Reverse(<T as Bounded>::maximum())}}}
pub use self::float::{Float,Float32,Float64};
mod float{use super::{Bounded,One,Zero};use std::{cmp::Ordering,convert::TryInto,fmt::Display,num::FpCategory,ops::{Add,Div,Mul,Neg,Rem,Sub},str::FromStr};pub trait Float:Copy+Default+Display+FromStr+PartialEq+PartialOrd+Zero+One+Bounded+Add<Output=Self>+Sub<Output=Self>+Mul<Output=Self>+Div<Output=Self>+Neg<Output=Self>+Rem<Output=Self>{fn floor(self)->Self;fn ceil(self)->Self;fn round(self)->Self;fn trunc(self)->Self;fn fract(self)->Self;fn abs(self)->Self;fn signum(self)->Self;fn copysign(self,sign:Self)->Self;fn mul_add(self,a:Self,b:Self)->Self;fn div_euclid(self,rhs:Self)->Self;fn rem_euclid(self,rhs:Self)->Self;fn powi(self,n:i32)->Self;fn powf(self,n:Self)->Self;fn sqrt(self)->Self;fn exp(self)->Self;fn exp2(self)->Self;fn ln(self)->Self;fn log(self,base:Self)->Self;fn log2(self)->Self;fn log10(self)->Self;fn cbrt(self)->Self;fn hypot(self,other:Self)->Self;fn sin(self)->Self;fn cos(self)->Self;fn tan(self)->Self;fn asin(self)->Self;fn acos(self)->Self;fn atan(self)->Self;fn atan2(self,other:Self)->Self;fn sin_cos(self)->(Self,Self);fn exp_m1(self)->Self;fn ln_1p(self)->Self;fn sinh(self)->Self;fn cosh(self)->Self;fn tanh(self)->Self;fn asinh(self)->Self;fn acosh(self)->Self;fn atanh(self)->Self;fn is_nan(self)->bool;fn is_infinite(self)->bool;fn is_finite(self)->bool;fn is_normal(self)->bool;fn classify(self)->FpCategory;fn is_sign_positive(self)->bool;fn is_sign_negative(self)->bool;fn recip(self)->Self;fn to_degrees(self)->Self;fn to_radians(self)->Self;fn max(self,other:Self)->Self;fn min(self,other:Self)->Self;fn to_bits(self)->u64;fn from_bits(v:u64)->Self;fn total_cmp(&self,other:&Self)->Ordering;const RADIX:u32;const MANTISSA_DIGITS:u32;const DIGITS:u32;const EPSILON:Self;const MIN:Self;const MIN_POSITIVE:Self;const MAX:Self;const MIN_EXP:i32;const MAX_EXP:i32;const MIN_10_EXP:i32;const MAX_10_EXP:i32;const NAN:Self;const INFINITY:Self;const NEG_INFINITY:Self;const PI:Self;const TAU:Self;const FRAC_PI_2:Self;const FRAC_PI_3:Self;const FRAC_PI_4:Self;const FRAC_PI_6:Self;const FRAC_PI_8:Self;const FRAC_1_PI:Self;const FRAC_2_PI:Self;const FRAC_2_SQRT_PI:Self;const SQRT_2:Self;const FRAC_1_SQRT_2:Self;const E:Self;const LOG2_E:Self;const LOG10_E:Self;const LN_2:Self;const LN_10:Self;}macro_rules!primitive_float_impls{($({$t:ident$i:ident$u:ident$e:expr})*)=>{$(impl Float for$t{fn floor(self)->Self{$t::floor(self)}fn ceil(self)->Self{$t::ceil(self)}fn round(self)->Self{$t::round(self)}fn trunc(self)->Self{$t::trunc(self)}fn fract(self)->Self{$t::fract(self)}fn abs(self)->Self{$t::abs(self)}fn signum(self)->Self{$t::signum(self)}fn copysign(self,sign:Self)->Self{$t::copysign(self,sign)}fn mul_add(self,a:Self,b:Self)->Self{$t::mul_add(self,a,b)}fn div_euclid(self,rhs:Self)->Self{$t::div_euclid(self,rhs)}fn rem_euclid(self,rhs:Self)->Self{$t::rem_euclid(self,rhs)}fn powi(self,n:i32)->Self{$t::powi(self,n)}fn powf(self,n:Self)->Self{$t::powf(self,n)}fn sqrt(self)->Self{$t::sqrt(self)}fn exp(self)->Self{$t::exp(self)}fn exp2(self)->Self{$t::exp2(self)}fn ln(self)->Self{$t::ln(self)}fn log(self,base:Self)->Self{$t::log(self,base)}fn log2(self)->Self{$t::log2(self)}fn log10(self)->Self{$t::log10(self)}fn cbrt(self)->Self{$t::cbrt(self)}fn hypot(self,other:Self)->Self{$t::hypot(self,other)}fn sin(self)->Self{$t::sin(self)}fn cos(self)->Self{$t::cos(self)}fn tan(self)->Self{$t::tan(self)}fn asin(self)->Self{$t::asin(self)}fn acos(self)->Self{$t::acos(self)}fn atan(self)->Self{$t::atan(self)}fn atan2(self,other:Self)->Self{$t::atan2(self,other)}fn sin_cos(self)->(Self,Self){$t::sin_cos(self)}fn exp_m1(self)->Self{$t::exp_m1(self)}fn ln_1p(self)->Self{$t::ln_1p(self)}fn sinh(self)->Self{$t::sinh(self)}fn cosh(self)->Self{$t::cosh(self)}fn tanh(self)->Self{$t::tanh(self)}fn asinh(self)->Self{$t::asinh(self)}fn acosh(self)->Self{$t::acosh(self)}fn atanh(self)->Self{$t::atanh(self)}fn is_nan(self)->bool{$t::is_nan(self)}fn is_infinite(self)->bool{$t::is_infinite(self)}fn is_finite(self)->bool{$t::is_finite(self)}fn is_normal(self)->bool{$t::is_normal(self)}fn classify(self)->std::num::FpCategory{$t::classify(self)}fn is_sign_positive(self)->bool{$t::is_sign_positive(self)}fn is_sign_negative(self)->bool{$t::is_sign_negative(self)}fn recip(self)->Self{$t::recip(self)}fn to_degrees(self)->Self{$t::to_degrees(self)}fn to_radians(self)->Self{$t::to_radians(self)}fn max(self,other:Self)->Self{$t::max(self,other)}fn min(self,other:Self)->Self{$t::min(self,other)}fn to_bits(self)->u64{$t::to_bits(self).into()}fn from_bits(v:u64)->Self{$t::from_bits(v.try_into().unwrap())}fn total_cmp(&self,other:&Self)->Ordering{let mut left=self.to_bits()as$i;let mut right=other.to_bits()as$i;left^=(((left>>$e)as$u)>>1)as$i;right^=(((right>>$e)as$u)>>1)as$i;left.cmp(&right)}const RADIX:u32=std::$t::RADIX;const MANTISSA_DIGITS:u32=std::$t::MANTISSA_DIGITS;const DIGITS:u32=std::$t::DIGITS;const EPSILON:Self=std::$t::EPSILON;const MIN:Self=std::$t::MIN;const MIN_POSITIVE:Self=std::$t::MIN_POSITIVE;const MAX:Self=std::$t::MAX;const MIN_EXP:i32=std::$t::MIN_EXP;const MAX_EXP:i32=std::$t::MAX_EXP;const MIN_10_EXP:i32=std::$t::MIN_10_EXP;const MAX_10_EXP:i32=std::$t::MAX_10_EXP;const NAN:Self=std::$t::NAN;const INFINITY:Self=std::$t::INFINITY;const NEG_INFINITY:Self=std::$t::NEG_INFINITY;const PI:Self=std::$t::consts::PI;const TAU:Self=std::$t::consts::PI*2.0;const FRAC_PI_2:Self=std::$t::consts::FRAC_PI_2;const FRAC_PI_3:Self=std::$t::consts::FRAC_PI_3;const FRAC_PI_4:Self=std::$t::consts::FRAC_PI_4;const FRAC_PI_6:Self=std::$t::consts::FRAC_PI_6;const FRAC_PI_8:Self=std::$t::consts::FRAC_PI_8;const FRAC_1_PI:Self=std::$t::consts::FRAC_1_PI;const FRAC_2_PI:Self=std::$t::consts::FRAC_2_PI;const FRAC_2_SQRT_PI:Self=std::$t::consts::FRAC_2_SQRT_PI;const SQRT_2:Self=std::$t::consts::SQRT_2;const FRAC_1_SQRT_2:Self=std::$t::consts::FRAC_1_SQRT_2;const E:Self=std::$t::consts::E;const LOG2_E:Self=std::$t::consts::LOG2_E;const LOG10_E:Self=std::$t::consts::LOG10_E;const LN_2:Self=std::$t::consts::LN_2;const LN_10:Self=std::$t::consts::LN_10;})*};}primitive_float_impls!({f32 i32 u32 31}{f64 i64 u64 63});macro_rules!ord_float_impls{($({$t:ident$n:ident})*)=>{$(#[derive(Debug,Copy,Clone,PartialEq,Default)]#[repr(transparent)]pub struct$n(pub$t);impl std::fmt::Display for$n{fn fmt(&self,f:&mut std::fmt::Formatter<'_>)->std::fmt::Result{<$t as std::fmt::Display>::fmt(&self.0,f)}}impl std::str::FromStr for$n{type Err=std::num::ParseFloatError;fn from_str(s:&str)->Result<Self,Self::Err>{<$t as std::str::FromStr>::from_str(s).map(Self)}}impl From<$t>for$n{fn from(x:$t)->Self{Self(x)}}impl Zero for$n{fn zero()->Self{Self(<$t as Zero>::zero())}}impl One for$n{fn one()->Self{Self(<$t as One>::one())}}impl Bounded for$n{fn maximum()->Self{Self(<$t as Bounded>::maximum())}fn minimum()->Self{Self(<$t as Bounded>::minimum())}}impl Add for$n{type Output=Self;fn add(self,rhs:Self)->Self::Output{Self(<$t as Add>::add(self.0,rhs.0))}}impl Sub for$n{type Output=Self;fn sub(self,rhs:Self)->Self::Output{Self(<$t as Sub>::sub(self.0,rhs.0))}}impl Mul for$n{type Output=Self;fn mul(self,rhs:Self)->Self::Output{Self(<$t as Mul>::mul(self.0,rhs.0))}}impl Div for$n{type Output=Self;fn div(self,rhs:Self)->Self::Output{Self(<$t as Div>::div(self.0,rhs.0))}}impl Neg for$n{type Output=Self;fn neg(self)->Self::Output{Self(<$t as Neg>::neg(self.0))}}impl Rem for$n{type Output=Self;fn rem(self,rhs:Self)->Self::Output{Self(<$t as Rem>::rem(self.0,rhs.0))}}impl Eq for$n{}impl PartialOrd for$n{fn partial_cmp(&self,other:&Self)->Option<Ordering>{Some(self.total_cmp(other))}}impl Ord for$n{fn cmp(&self,other:&Self)->Ordering{self.partial_cmp(other).unwrap()}}impl Float for$n{fn floor(self)->Self{Self(<$t as Float>::floor(self.0))}fn ceil(self)->Self{Self(<$t as Float>::ceil(self.0))}fn round(self)->Self{Self(<$t as Float>::round(self.0))}fn trunc(self)->Self{Self(<$t as Float>::trunc(self.0))}fn fract(self)->Self{Self(<$t as Float>::fract(self.0))}fn abs(self)->Self{Self(<$t as Float>::abs(self.0))}fn signum(self)->Self{Self(<$t as Float>::signum(self.0))}fn copysign(self,sign:Self)->Self{Self(<$t as Float>::copysign(self.0,sign.0))}fn mul_add(self,a:Self,b:Self)->Self{Self(<$t as Float>::mul_add(self.0,a.0,b.0))}fn div_euclid(self,rhs:Self)->Self{Self(<$t as Float>::div_euclid(self.0,rhs.0))}fn rem_euclid(self,rhs:Self)->Self{Self(<$t as Float>::rem_euclid(self.0,rhs.0))}fn powi(self,n:i32)->Self{Self(<$t as Float>::powi(self.0,n))}fn powf(self,n:Self)->Self{Self(<$t as Float>::powf(self.0,n.0))}fn sqrt(self)->Self{Self(<$t as Float>::sqrt(self.0))}fn exp(self)->Self{Self(<$t as Float>::exp(self.0))}fn exp2(self)->Self{Self(<$t as Float>::exp2(self.0))}fn ln(self)->Self{Self(<$t as Float>::ln(self.0))}fn log(self,base:Self)->Self{Self(<$t as Float>::log(self.0,base.0))}fn log2(self)->Self{Self(<$t as Float>::log2(self.0))}fn log10(self)->Self{Self(<$t as Float>::log10(self.0))}fn cbrt(self)->Self{Self(<$t as Float>::cbrt(self.0))}fn hypot(self,other:Self)->Self{Self(<$t as Float>::hypot(self.0,other.0))}fn sin(self)->Self{Self(<$t as Float>::sin(self.0))}fn cos(self)->Self{Self(<$t as Float>::cos(self.0))}fn tan(self)->Self{Self(<$t as Float>::tan(self.0))}fn asin(self)->Self{Self(<$t as Float>::asin(self.0))}fn acos(self)->Self{Self(<$t as Float>::acos(self.0))}fn atan(self)->Self{Self(<$t as Float>::atan(self.0))}fn atan2(self,other:Self)->Self{Self(<$t as Float>::atan2(self.0,other.0))}fn sin_cos(self)->(Self,Self){let(sin,cos)=<$t as Float>::sin_cos(self.0);(Self(sin),Self(cos))}fn exp_m1(self)->Self{Self(<$t as Float>::exp_m1(self.0))}fn ln_1p(self)->Self{Self(<$t as Float>::ln_1p(self.0))}fn sinh(self)->Self{Self(<$t as Float>::sinh(self.0))}fn cosh(self)->Self{Self(<$t as Float>::cosh(self.0))}fn tanh(self)->Self{Self(<$t as Float>::tanh(self.0))}fn asinh(self)->Self{Self(<$t as Float>::asinh(self.0))}fn acosh(self)->Self{Self(<$t as Float>::acosh(self.0))}fn atanh(self)->Self{Self(<$t as Float>::atanh(self.0))}fn is_nan(self)->bool{<$t as Float>::is_nan(self.0)}fn is_infinite(self)->bool{<$t as Float>::is_infinite(self.0)}fn is_finite(self)->bool{<$t as Float>::is_finite(self.0)}fn is_normal(self)->bool{<$t as Float>::is_normal(self.0)}fn classify(self)->std::num::FpCategory{<$t as Float>::classify(self.0)}fn is_sign_positive(self)->bool{<$t as Float>::is_sign_positive(self.0)}fn is_sign_negative(self)->bool{<$t as Float>::is_sign_negative(self.0)}fn recip(self)->Self{Self(<$t as Float>::recip(self.0))}fn to_degrees(self)->Self{Self(<$t as Float>::to_degrees(self.0))}fn to_radians(self)->Self{Self(<$t as Float>::to_radians(self.0))}fn max(self,other:Self)->Self{Self(<$t as Float>::max(self.0,other.0))}fn min(self,other:Self)->Self{Self(<$t as Float>::min(self.0,other.0))}fn to_bits(self)->u64{<$t as Float>::to_bits(self.0)}fn from_bits(v:u64)->Self{Self(<$t as Float>::from_bits(v))}fn total_cmp(&self,other:&Self)->Ordering{<$t as Float>::total_cmp(&self.0,&other.0)}const RADIX:u32=<$t as Float>::RADIX;const MANTISSA_DIGITS:u32=<$t as Float>::MANTISSA_DIGITS;const DIGITS:u32=<$t as Float>::DIGITS;const EPSILON:Self=Self(<$t as Float>::EPSILON);const MIN:Self=Self(<$t as Float>::MIN);const MIN_POSITIVE:Self=Self(<$t as Float>::MIN_POSITIVE);const MAX:Self=Self(<$t as Float>::MAX);const MIN_EXP:i32=<$t as Float>::MIN_EXP;const MAX_EXP:i32=<$t as Float>::MAX_EXP;const MIN_10_EXP:i32=<$t as Float>::MIN_10_EXP;const MAX_10_EXP:i32=<$t as Float>::MAX_10_EXP;const NAN:Self=Self(<$t as Float>::NAN);const INFINITY:Self=Self(<$t as Float>::INFINITY);const NEG_INFINITY:Self=Self(<$t as Float>::NEG_INFINITY);const PI:Self=Self(<$t as Float>::PI);const TAU:Self=Self(<$t as Float>::TAU);const FRAC_PI_2:Self=Self(<$t as Float>::FRAC_PI_2);const FRAC_PI_3:Self=Self(<$t as Float>::FRAC_PI_3);const FRAC_PI_4:Self=Self(<$t as Float>::FRAC_PI_4);const FRAC_PI_6:Self=Self(<$t as Float>::FRAC_PI_6);const FRAC_PI_8:Self=Self(<$t as Float>::FRAC_PI_8);const FRAC_1_PI:Self=Self(<$t as Float>::FRAC_1_PI);const FRAC_2_PI:Self=Self(<$t as Float>::FRAC_2_PI);const FRAC_2_SQRT_PI:Self=Self(<$t as Float>::FRAC_2_SQRT_PI);const SQRT_2:Self=Self(<$t as Float>::SQRT_2);const FRAC_1_SQRT_2:Self=Self(<$t as Float>::FRAC_1_SQRT_2);const E:Self=Self(<$t as Float>::E);const LOG2_E:Self=Self(<$t as Float>::LOG2_E);const LOG10_E:Self=Self(<$t as Float>::LOG10_E);const LN_2:Self=Self(<$t as Float>::LN_2);const LN_10:Self=Self(<$t as Float>::LN_10);})*};}ord_float_impls!({f32 Float32}{f64 Float64});}
pub use self::zero_one::{One,Zero};
mod zero_one{pub trait Zero:Sized{fn zero()->Self;#[inline]fn is_zero(&self)->bool where Self:PartialEq{self==&Self::zero()}#[inline]fn set_zero(&mut self){*self=Self::zero();}}pub trait One:Sized{fn one()->Self;#[inline]fn is_one(&self)->bool where Self:PartialEq{self==&Self::one()}#[inline]fn set_one(&mut self){*self=Self::one();}}macro_rules!zero_one_impls{($({$Trait:ident$method:ident$($t:ty)*,$e:expr})*)=>{$($(impl$Trait for$t{fn$method()->Self{$e}})*)*};}zero_one_impls!({Zero zero u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128,0}{Zero zero f32 f64,0.}{One one u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128,1}{One one f32 f64,1.});}
pub use self::ord_tools::PartialOrdExt;
mod ord_tools{pub trait PartialOrdExt:Sized{fn chmin(&mut self,other:Self);fn chmax(&mut self,other:Self);fn minmax(self,other:Self)->(Self,Self);}impl<T>PartialOrdExt for T where T:PartialOrd{#[inline]fn chmin(&mut self,other:Self){if*self>other{*self=other;}}#[inline]fn chmax(&mut self,other:Self){if*self<other{*self=other;}}#[inline]fn minmax(self,other:Self)->(Self,Self){if self<other{(self,other)}else{(other,self)}}}#[macro_export]macro_rules!min{($l:expr)=>{$l};($l:expr,)=>{$crate::min!($l)};($l:expr,$r:expr)=>{($l).min($r)};($l:expr,$r:expr,)=>{$crate::min!($l,$r)};($l:expr,$r:expr,$($t:tt)*)=>{$crate::min!($crate::min!($l,$r),$($t)*)};}#[macro_export]macro_rules!chmin{($l:expr)=>{};($l:expr,)=>{};($l:expr,$r:expr)=>{{let r=$r;if$l>r{$l=r;}}};($l:expr,$r:expr,)=>{$crate::chmin!($l,$r)};($l:expr,$r:expr,$($t:tt)*)=>{$crate::chmin!($l,$r);$crate::chmin!($l,$($t)*)};}#[macro_export]macro_rules!max{($l:expr)=>{$l};($l:expr,)=>{$crate::max!($l)};($l:expr,$r:expr)=>{($l).max($r)};($l:expr,$r:expr,)=>{$crate::max!($l,$r)};($l:expr,$r:expr,$($t:tt)*)=>{$crate::max!($crate::max!($l,$r),$($t)*)};}#[macro_export]macro_rules!chmax{($l:expr)=>{};($l:expr,)=>{};($l:expr,$r:expr)=>{{let r=$r;if$l<r{$l=r;}}};($l:expr,$r:expr,)=>{$crate::chmax!($l,$r)};($l:expr,$r:expr,$($t:tt)*)=>{$crate::chmax!($l,$r);$crate::chmax!($l,$($t)*)};}#[macro_export]macro_rules!minmax{($($t:tt)*)=>{($crate::min!($($t)*),$crate::max!($($t)*))};}}
pub use self::line::{Line,LineSegment};
mod line{use super::{Approx,Ccw,Ccwable,Complex,Float};#[derive(Clone,Debug,PartialEq)]pub struct Line<T>{p1:Complex<T>,p2:Complex<T>}impl<T>Line<T>{pub fn new(p1:Complex<T>,p2:Complex<T>)->Self{Line{p1,p2}}}impl<T>Line<T>where T:Ccwable{pub fn dir(&self)->Complex<T>{self.p2-self.p1}pub fn ccw(&self,p:Complex<T>)->Ccw{Ccw::ccw(self.p1,self.p2,p)}pub fn is_parallel(&self,other:&Self)->bool{Approx(self.dir().cross(other.dir()))==Approx(T::zero())}pub fn is_orthogonal(&self,other:&Self)->bool{Approx(self.dir().dot(other.dir()))==Approx(T::zero())}}impl<T>Line<T>where T:Ccwable+Float{pub fn projection(&self,p:Complex<T>)->Complex<T>{let e=self.dir().unit();self.p1+e*(p-self.p1).dot(e)}pub fn reflection(&self,p:Complex<T>)->Complex<T>{let d=self.projection(p)-p;p+d+d}pub fn distance_point(&self,p:Complex<T>)->T{(p/self.dir().unit()).re}}#[derive(Clone,Debug,PartialEq)]pub struct LineSegment<T>{p1:Complex<T>,p2:Complex<T>}impl<T>LineSegment<T>{pub fn new(p1:Complex<T>,p2:Complex<T>)->Self{LineSegment{p1,p2}}}impl<T>LineSegment<T>where T:Ccwable{pub fn dir(&self)->Complex<T>{self.p2-self.p1}pub fn ccw(&self,p:Complex<T>)->Ccw{Ccw::ccw(self.p1,self.p2,p)}pub fn is_parallel(&self,other:&Self)->bool{Approx(self.dir().cross(other.dir()))==Approx(T::zero())}pub fn is_orthogonal(&self,other:&Self)->bool{Approx(self.dir().dot(other.dir()))==Approx(T::zero())}pub fn intersect(&self,other:&Self)->bool{self.ccw(other.p1)as i8*self.ccw(other.p2)as i8<=0&&other.ccw(self.p1)as i8*other.ccw(self.p2)as i8<=0}pub fn intersect_point(&self,p:Complex<T>)->bool{self.ccw(p)==Ccw::OnSegment}}impl<T>LineSegment<T>where T:Ccwable+Float{pub fn projection(&self,p:Complex<T>)->Complex<T>{let e=self.dir().unit();self.p1+e*(p-self.p1).dot(e)}pub fn reflection(&self,p:Complex<T>)->Complex<T>{let d=self.projection(p)-p;p+d+d}pub fn cross_point(&self,other:&Self)->Option<Complex<T>>{if self.intersect(other){let a=self.dir().cross(other.dir());let b=self.dir().cross(self.p2-other.p1);if Approx(a.abs())==Approx(T::zero())&&Approx(b.abs())==Approx(T::zero()){Some(other.p1)}else{Some(other.p1+(other.dir()*b/a))}}else{None}}pub fn distance_point(&self,p:Complex<T>)->T{let r=self.projection(p);if self.intersect_point(r){(r-p).abs()}else{(self.p1-p).abs().min((self.p2-p).abs())}}pub fn distance(&self,other:&Self)->T{if self.intersect(other){T::zero()}else{let d1=self.distance_point(other.p1);let d2=self.distance_point(other.p2);let d3=other.distance_point(self.p1);let d4=other.distance_point(self.p2);d1.min(d2).min(d3).min(d4)}}}}
pub use self::approx::{Approx,ApproxOrd};
mod approx{use std::cmp::Ordering;pub trait ApproxOrd{fn approx_eq(&self,other:&Self)->bool;fn approx_cmp(&self,other:&Self)->Ordering;}macro_rules!impl_approx_zero_for_int{($($t:ty)*)=>{$(impl ApproxOrd for$t{fn approx_eq(&self,other:&Self)->bool{self.eq(other)}fn approx_cmp(&self,other:&Self)->Ordering{self.cmp(other)}})*};}impl_approx_zero_for_int!(u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize);impl ApproxOrd for f32{fn approx_eq(&self,other:&Self)->bool{const EPS_F32:f32=1e-8;(self-other).abs()<EPS_F32}fn approx_cmp(&self,other:&Self)->Ordering{if self.approx_eq(other){Ordering::Equal}else{let mut left=self.to_bits()as i32;let mut right=other.to_bits()as i32;left^=(((left>>31)as u32)>>1)as i32;right^=(((right>>31)as u32)>>1)as i32;left.cmp(&right)}}}impl ApproxOrd for f64{fn approx_eq(&self,other:&Self)->bool{const EPS_F64:f64=1e-8;(self-other).abs()<EPS_F64}fn approx_cmp(&self,other:&Self)->Ordering{if self.approx_eq(other){Ordering::Equal}else{let mut left=self.to_bits()as i64;let mut right=other.to_bits()as i64;left^=(((left>>63)as u64)>>1)as i64;right^=(((right>>63)as u64)>>1)as i64;left.cmp(&right)}}}#[derive(Debug,Default,Clone,Copy)]#[repr(transparent)]pub struct Approx<T>(pub T)where T:ApproxOrd;impl<T>PartialEq for Approx<T>where T:ApproxOrd{fn eq(&self,other:&Self)->bool{self.0 .approx_eq(&other.0)}}impl<T>Eq for Approx<T>where T:ApproxOrd{}impl<T>PartialOrd for Approx<T>where T:ApproxOrd{fn partial_cmp(&self,other:&Self)->Option<Ordering>{Some(self.0 .approx_cmp(&other.0))}}impl<T>Ord for Approx<T>where T:ApproxOrd{fn cmp(&self,other:&Self)->Ordering{self.0 .approx_cmp(&other.0)}}}
pub use self::ccw::{Ccw,Ccwable};
mod ccw{use super::{Approx,ApproxOrd,Complex,Zero};use std::{cmp::Ordering,ops::{Add,Mul,Sub}};pub trait Ccwable:ApproxOrd+Copy+Zero+Add<Output=Self>+Sub<Output=Self>+Mul<Output=Self>{}impl Ccwable for i8{}impl Ccwable for i16{}impl Ccwable for i32{}impl Ccwable for i64{}impl Ccwable for i128{}impl Ccwable for isize{}impl Ccwable for f32{}impl Ccwable for f64{}#[derive(Clone,Copy,Debug,PartialEq,Eq,PartialOrd,Ord,Hash)]pub enum Ccw{#[doc=" a--b--c"]OnlineFront=-2,#[doc=" a--b-vc"]Clockwise=-1,#[doc=" a--c--b"]OnSegment=0,#[doc=" a--b-^c"]CounterClockwise=1,#[doc=" c--a--b"]OnlineBack=2}impl Ccw{pub fn ccw<T>(a:Complex<T>,b:Complex<T>,c:Complex<T>)->Self where T:Ccwable{let x=b-a;let y=c-a;let zero=T::zero();match x.cross(y).approx_cmp(&zero){Ordering::Less=>Self::Clockwise,Ordering::Greater=>Self::CounterClockwise,Ordering::Equal=>{if Approx(x.dot(y))<Approx(zero){Self::OnlineBack}else if Approx((a-b).dot(c-b))<Approx(zero){Self::OnlineFront}else{Self::OnSegment}}}}pub fn ccw_open<T>(a:Complex<T>,b:Complex<T>,c:Complex<T>)->Self where T:Ccwable{let x=b-a;let y=c-a;let zero=T::zero();match x.cross(y).approx_cmp(&zero){Ordering::Less=>Self::Clockwise,Ordering::Greater=>Self::CounterClockwise,Ordering::Equal=>{if Approx(x.dot(y))<=Approx(zero){Self::OnlineBack}else if Approx((a-b).dot(c-b))<=Approx(zero){Self::OnlineFront}else{Self::OnSegment}}}}}}