pub fn main() { crate::prepare!(); sc!(n, k, pc: [(P, Usize1); n]); let mut ps = vec![vec![]; 2]; for (p, c) in pc { ps[c].push(p); } for a in 0..2 { for &p in &ps[a] { let mut map = HashMap::<[i64; 3], [bool; 2]>::new(); for &q in &ps[a ^ 1] { let dir = q - p; let mut a = dir.re; let mut b = dir.im; let mut c = dir.dot(p.transpose()); let g = gcd(gcd(a.abs() as _, b.abs() as _), c.abs() as _) as i64; a /= g; b /= g; c /= g; let s = [a, b, c].iter().find(|&&a| a != 0).unwrap().signum(); a *= s; b *= s; c *= s; assert_ne!(s, 0); map.entry([a, b, c]).or_default()[(s < 0) as usize] = true; } if map.values().any(|t| t.iter().all(|&b| b)) { pp!("Yes"); return; } } } if k == 3 { pp!("No"); return; } let mut qs = vec![vec![]; 2]; for a in 0..2 { let qs = &mut qs[a]; { let ps = &mut ps[a]; ps.sort_by(|p1, p2| ((p1.re, p1.im).partial_cmp(&(p2.re, p2.im)).unwrap())); for &p in ps.iter().chain(ps.iter().rev().skip(1)) { while { let k = qs.len(); k > 1 && Ccw::ccw(qs[k - 2], qs[k - 1], p) == Ccw::Clockwise } { qs.pop(); } qs.push(p); } } qs.pop(); } if qs[0].len().min(qs[1].len()) >= 2 { for w0 in qs[0].windows(2) { let w = w0[0]; let x = w0[1]; for w1 in qs[1].windows(2) { let y = w1[0]; let z = w1[1]; let ccw0 = |p: P| Ccw::ccw(w, x, p); let ccw1 = |p: P| Ccw::ccw(y, z, p); if ccw0(y) as i8 * ccw0(z) as i8 <= 0 && ccw1(w) as i8 * ccw1(x) as i8 <= 0 { pp!("Yes"); return; } } } } pp!("No"); } type P = Complex; #[allow(unused_imports)]use std::{cmp::{Ordering,Reverse},collections::{BTreeMap,BTreeSet,BinaryHeap,HashMap,HashSet,VecDeque}}; mod main_macros{#[doc=" Prepare useful macros."]#[doc=" - `prepare!();`: default (all input scanner (`sc!`, `sv!`) + buf print (`pp!`, `dg!`))"]#[doc=" - `prepare!(?);`: interactive (line scanner (`scln!`) + buf print (`pp!`, `dg!`))"]#[macro_export]macro_rules!prepare{(@output($dol:tt))=>{#[allow(unused_imports)]use std::io::Write as _;let __out=std::io::stdout();#[allow(unused_mut,unused_variables)]let mut __out=std::io::BufWriter::new(__out.lock());#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stdout."]macro_rules!pp{($dol($dol t:tt)*)=>{$dol crate::iter_print!(__out,$dol($dol t)*)}}#[cfg(debug_assertions)]#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stderr. Do nothing in release mode."]macro_rules!dg{($dol($dol t:tt)*)=>{{#[allow(unused_imports)]use std::io::Write as _;let __err=std::io::stderr();#[allow(unused_mut,unused_variables)]let mut __err=std::io::BufWriter::new(__err.lock());$dol crate::iter_print!(__err,$dol($dol t)*);let _=__err.flush();}}}#[cfg(not(debug_assertions))]#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stderr. Do nothing in release mode."]macro_rules!dg{($dol($dol t:tt)*)=>{}}};(@normal($dol:tt))=>{let __in_buf=read_stdin_all_unchecked();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);#[allow(unused_macros)]macro_rules!sc{($dol($dol t:tt)*)=>{$dol crate::scan!(__scanner,$dol($dol t)*)}}#[allow(unused_macros)]macro_rules!sv{($dol($dol t:tt)*)=>{$dol crate::scan_value!(__scanner,$dol($dol t)*)}}};(@interactive($dol:tt))=>{#[allow(unused_macros)]#[doc=" Scan a line, and previous line will be truncated in the next call."]macro_rules!scln{($dol($dol t:tt)*)=>{let __in_buf=read_stdin_line();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);$dol crate::scan!(__scanner,$dol($dol t)*)}}};()=>{$crate::prepare!(@output($));$crate::prepare!(@normal($))};(?)=>{$crate::prepare!(@output($));$crate::prepare!(@interactive($))};}} pub use self::iter_print::IterPrint; mod iter_print{use std::{fmt::Display,io::{Error,Write}};pub trait IterPrint{fn iter_print(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display;}macro_rules!iter_print_tuple_impl{(@impl$($A:ident$a:ident)?,$($B:ident$b:ident)*)=>{impl<$($A,)?$($B),*>IterPrint for($($A,)?$($B),*)where$($A:Display,)?$($B:Display),*{#[allow(unused_variables)]fn iter_print(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display{let($($a,)?$($b,)*)=self;$(if is_head{::std::write!(writer,"{}",$a)?;}else{::std::write!(writer,"{}{}",sep,$a)?;})?$(::std::write!(writer,"{}{}",sep,$b)?;)*Ok(())}}};(@inc,,$C:ident$c:ident$($D:ident$d:ident)*)=>{iter_print_tuple_impl!(@impl,);iter_print_tuple_impl!(@inc$C$c,,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,$C:ident$c:ident$($D:ident$d:ident)*)=>{iter_print_tuple_impl!(@impl$A$a,$($B$b)*);iter_print_tuple_impl!(@inc$A$a,$($B$b)*$C$c,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,)=>{iter_print_tuple_impl!(@impl$A$a,$($B$b)*);};($($t:tt)*)=>{iter_print_tuple_impl!(@inc,,$($t)*);};}iter_print_tuple_impl!(A a B b C c D d E e F f G g H h I i J j K k);#[doc=" Print expressions with a separator."]#[doc=" - `iter_print!(writer, args...)`"]#[doc=" - `@sep $expr`: set separator (default: `' '`)"]#[doc=" - `@ns`: alias for `@sep \"\"`"]#[doc=" - `@lf`: alias for `@sep '\\n'`"]#[doc=" - `@sp`: alias for `@sep ' '`"]#[doc=" - `@fmt $lit => {$($expr),*}`: print `format!($lit, $($expr),*)`"]#[doc=" - `@flush`: flush writer (auto insert `!`)"]#[doc=" - `@it $expr`: print iterator"]#[doc=" - `@it2d $expr`: print 2d-iterator"]#[doc=" - `@tup $expr`: print tuple (need to import [`IterPrint`])"]#[doc=" - `@ittup $expr`: print iterative tuple (need to import [`IterPrint`])"]#[doc=" - `$expr`: print expr"]#[doc=" - `{ args... }`: scoped"]#[doc=" - `;`: print `'\\n'`"]#[doc=" - `!`: not print `'\\n'` at the end"]#[macro_export]macro_rules!iter_print{(@@fmt$writer:expr,$sep:expr,$is_head:expr,$lit:literal,$($e:expr),*)=>{if!$is_head{::std::write!($writer,"{}",$sep).expect("io error");}::std::write!($writer,$lit,$($e),*).expect("io error");};(@@item$writer:expr,$sep:expr,$is_head:expr,$e:expr)=>{$crate::iter_print!(@@fmt$writer,$sep,$is_head,"{}",$e);};(@@line_feed$writer:expr$(,)?)=>{::std::writeln!($writer).expect("io error");};(@@it$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,item);}}};(@@it2d$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@it$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@it$writer,$sep,true,item);}};(@@tup$writer:expr,$sep:expr,$is_head:expr,$tuple:expr)=>{IterPrint::iter_print($tuple,&mut$writer,$sep,$is_head).expect("io error");};(@@ittup$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@tup$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@tup$writer,$sep,true,item);}};(@@assert_tag item)=>{};(@@assert_tag it)=>{};(@@assert_tag it2d)=>{};(@@assert_tag tup)=>{};(@@assert_tag ittup)=>{};(@@assert_tag$tag:ident)=>{::std::compile_error!(::std::concat!("invalid tag in `iter_print!`: `",std::stringify!($tag),"`"));};(@@inner$writer:expr,$sep:expr,$is_head:expr,@sep$e:expr,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$e,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@ns$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,"",$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@lf$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,'\n',$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@sp$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,' ',$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@flush$($t:tt)*)=>{$writer.flush().expect("io error");$crate::iter_print!(@@inner$writer,$sep,$is_head,!$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@fmt$lit:literal=>{$($e:expr),*$(,)?}$($t:tt)*)=>{$crate::iter_print!(@@fmt$writer,$sep,$is_head,$lit,$($e),*);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr,$($t:tt)*)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@inner$writer,$sep,false,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr;$($t:tt)*)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@inner$writer,$sep,true,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@inner$writer,$sep,false,);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$($t:tt)*)=>{::std::compile_error!(::std::concat!("invalid expr in `iter_print!`: `",std::stringify!($($t)*),"`"));};(@@inner$writer:expr,$sep:expr,$is_head:expr,,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,;$($t:tt)*)=>{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,!$(,)?)=>{};(@@inner$writer:expr,$sep:expr,$is_head:expr,!$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,)=>{$crate::iter_print!(@@line_feed$writer);};(@@inner$writer:expr,$sep:expr,$is_head:expr,{$($t:tt)*}$($rest:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*,!);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($rest)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,@item$($t)*);};($writer:expr,$($t:tt)*)=>{{$crate::iter_print!(@@inner$writer,' ',true,$($t)*);}};}} pub use self::scanner::*; mod scanner{use std::{iter::{from_fn,repeat_with,FromIterator},marker::PhantomData};pub fn read_stdin_all()->String{use std::io::Read as _;let mut s=String::new();std::io::stdin().read_to_string(&mut s).expect("io error");s}pub fn read_stdin_all_unchecked()->String{use std::io::Read as _;let mut buf=Vec::new();std::io::stdin().read_to_end(&mut buf).expect("io error");unsafe{String::from_utf8_unchecked(buf)}}pub fn read_all(mut reader:impl std::io::Read)->String{let mut s=String::new();reader.read_to_string(&mut s).expect("io error");s}pub fn read_all_unchecked(mut reader:impl std::io::Read)->String{let mut buf=Vec::new();reader.read_to_end(&mut buf).expect("io error");unsafe{String::from_utf8_unchecked(buf)}}pub fn read_stdin_line()->String{let mut s=String::new();std::io::stdin().read_line(&mut s).expect("io error");s}pub trait IterScan:Sized{type Output;fn scan<'a,I:Iterator>(iter:&mut I)->Option;}pub trait MarkedIterScan:Sized{type Output;fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option;}#[derive(Clone,Debug)]pub struct Scanner<'a>{iter:std::str::SplitAsciiWhitespace<'a>}impl<'a>Scanner<'a>{#[inline]pub fn new(s:&'a str)->Self{let iter=s.split_ascii_whitespace();Self{iter}}#[inline]pub fn scan(&mut self)->::Output where T:IterScan{::scan(&mut self.iter).expect("scan error")}#[inline]pub fn mscan(&mut self,marker:T)->::Output where T:MarkedIterScan{marker.mscan(&mut self.iter).expect("scan error")}#[inline]pub fn scan_vec(&mut self,size:usize)->Vec<::Output>where T:IterScan{(0..size).map(|_|::scan(&mut self.iter).expect("scan error")).collect()}#[inline]pub fn iter<'b,T>(&'b mut self)->ScannerIter<'a,'b,T>where T:IterScan{ScannerIter{inner:self,_marker:std::marker::PhantomData}}}macro_rules!iter_scan_impls{($($t:ty)*)=>{$(impl IterScan for$t{type Output=Self;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{iter.next()?.parse::<$t>().ok()}})*};}iter_scan_impls!(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String);macro_rules!iter_scan_tuple_impl{(@impl$($T:ident)*)=>{impl<$($T:IterScan),*>IterScan for($($T,)*){type Output=($(<$T as IterScan>::Output,)*);#[inline]fn scan<'a,It:Iterator>(_iter:&mut It)->Option{Some(($(<$T as IterScan>::scan(_iter)?,)*))}}};(@inner$($T:ident)*,)=>{iter_scan_tuple_impl!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{iter_scan_tuple_impl!(@impl$($T)*);iter_scan_tuple_impl!(@inner$($T)*$U,$($Rest)*);};($($T:ident)*)=>{iter_scan_tuple_impl!(@inner,$($T)*);};}iter_scan_tuple_impl!(A B C D E F G H I J K);pub struct ScannerIter<'a,'b,T>{inner:&'b mut Scanner<'a>,_marker:std::marker::PhantomDataT>}impl<'a,'b,T>Iterator for ScannerIter<'a,'b,T>where T:IterScan{type Item=::Output;#[inline]fn next(&mut self)->Option{::scan(&mut self.inner.iter)}}#[doc=" - `scan_value!(scanner, ELEMENT)`"]#[doc=""]#[doc=" ELEMENT :="]#[doc=" - `$ty`: IterScan"]#[doc=" - `@$expr`: MarkedIterScan"]#[doc=" - `[ELEMENT; $expr]`: vector"]#[doc=" - `[ELEMENT]`: iterator"]#[doc=" - `($(ELEMENT)*,)`: tuple"]#[macro_export]macro_rules!scan_value{(@repeat$scanner:expr,[$($t:tt)*]$($len:expr)?)=>{::std::iter::repeat_with(||$crate::scan_value!(@inner$scanner,[]$($t)*))$(.take($len).collect::>())?};(@tuple$scanner:expr,[$([$($args:tt)*])*])=>{($($($args)*,)*)};(@$tag:ident$scanner:expr,[[$($args:tt)*]])=>{$($args)*};(@$tag:ident$scanner:expr,[$($args:tt)*]@$e:expr)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.mscan($e)]])};(@$tag:ident$scanner:expr,[$($args:tt)*]@$e:expr,$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.mscan($e)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*]($($tuple:tt)*)$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@tuple$scanner,[]$($tuple)*)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][@$e:expr;$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[@$e]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][[$($tt:tt)*];$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[[$($tt)*]]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][($($tt:tt)*);$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[($($tt)*)]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][$ty:ty;$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[$ty]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[$($tt)*])]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*]$ty:ty)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.scan::<$ty>()]])};(@$tag:ident$scanner:expr,[$($args:tt)*]$ty:ty,$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.scan::<$ty>()]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*],$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*])=>{::std::compile_error!(::std::stringify!($($args)*))};($scanner:expr,$($t:tt)*)=>{$crate::scan_value!(@inner$scanner,[]$($t)*)}}#[doc=" - `scan!(scanner, $($pat $(: ELEMENT)?),*)`"]#[macro_export]macro_rules!scan{(@assert$p:pat)=>{};(@assert$($p:tt)*)=>{::std::compile_error!(::std::concat!("expected pattern, found `",::std::stringify!($($p)*),"`"));};(@pat$scanner:expr,[][])=>{};(@pat$scanner:expr,[][],$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]$x:ident$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*$x][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]::$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*::][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]&$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*&][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]($($x:tt)*)$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*($($x)*)][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][][$($x:tt)*]$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*[$($x)*]][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]{$($x:tt)*}$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*{$($x)*}][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]:$($t:tt)*)=>{$crate::scan!(@ty$scanner,[$($p)*][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][usize]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]@$e:expr)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*@$e])};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]@$e:expr,$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*@$e],$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]($($x:tt)*)$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*($($x)*)]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*][$($x:tt)*]$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*[$($x)*]]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]$ty:ty)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*$ty])};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]$ty:ty,$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*$ty],$($t)*)};(@let$scanner:expr,[$($p:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::scan!{@assert$($p)*}let$($p)* =$crate::scan_value!($scanner,$($tt)*);$crate::scan!(@pat$scanner,[][]$($t)*)};($scanner:expr,$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)}}#[derive(Debug,Copy,Clone)]pub enum Usize1{}impl IterScan for Usize1{type Output=usize;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{::scan(iter)?.checked_sub(1)}}#[derive(Debug,Copy,Clone)]pub struct CharWithBase(pub char);impl MarkedIterScan for CharWithBase{type Output=usize;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{Some((::scan(iter)?as u8-self.0 as u8)as usize)}}#[derive(Debug,Copy,Clone)]pub enum Chars{}impl IterScan for Chars{type Output=Vec;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{Some(iter.next()?.chars().collect())}}#[derive(Debug,Copy,Clone)]pub struct CharsWithBase(pub char);impl MarkedIterScan for CharsWithBase{type Output=Vec;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{Some(iter.next()?.chars().map(|c|(c as u8-self.0 as u8)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub struct ByteWithBase(pub u8);impl MarkedIterScan for ByteWithBase{type Output=usize;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{Some((::scan(iter)?as u8-self.0)as usize)}}#[derive(Debug,Copy,Clone)]pub enum Bytes{}impl IterScan for Bytes{type Output=Vec;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{Some(iter.next()?.bytes().collect())}}#[derive(Debug,Copy,Clone)]pub struct BytesWithBase(pub u8);impl MarkedIterScan for BytesWithBase{type Output=Vec;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{Some(iter.next()?.bytes().map(|c|(c-self.0)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub struct Collect::Output>>where T:IterScan,B:FromIterator<::Output>{size:usize,_marker:PhantomData(T,B)>}implCollectwhere T:IterScan,B:FromIterator<::Output>{pub fn new(size:usize)->Self{Self{size,_marker:PhantomData}}}implMarkedIterScan for Collectwhere T:IterScan,B:FromIterator<::Output>{type Output=B;#[inline]fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{repeat_with(||::scan(iter)).take(self.size).collect()}}#[derive(Debug,Copy,Clone)]pub struct SizedCollect::Output>>where T:IterScan,B:FromIterator<::Output>{_marker:PhantomData(T,B)>}implIterScan for SizedCollectwhere T:IterScan,B:FromIterator<::Output>{type Output=B;#[inline]fn scan<'a,I:Iterator>(iter:&mut I)->Option{let size=usize::scan(iter)?;repeat_with(||::scan(iter)).take(size).collect()}}#[derive(Debug,Copy,Clone)]pub struct Splittedwhere T:IterScan{pat:P,_marker:PhantomDataT>}implSplittedwhere T:IterScan{pub fn new(pat:P)->Self{Self{pat,_marker:PhantomData}}}implMarkedIterScan for Splittedwhere T:IterScan{type Output=Vec<::Output>;fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{let mut iter=iter.next()?.split(self.pat);Some(from_fn(||::scan(&mut iter)).collect())}}implMarkedIterScan for Splittedwhere T:IterScan{type Output=Vec<::Output>;fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{let mut iter=iter.next()?.split(self.pat);Some(from_fn(||::scan(&mut iter)).collect())}}implMarkedIterScan for F where F:Fn(&str)->Option{type Output=T;fn mscan<'a,I:Iterator>(self,iter:&mut I)->Option{self(iter.next()?)}}} pub use self::complex::Complex; mod complex{use super::{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{pub re:T,pub im:T}implComplex{pub fn new(re:T,im:T)->Self{Complex{re,im}}pub fn transpose(self)->Self{Complex{re:self.im,im:self.re}}}implZero for Complexwhere T:Zero{fn zero()->Self{Self::new(T::zero(),T::zero())}}implOne for Complexwhere T:Zero+One{fn one()->Self{Self::new(T::one(),T::zero())}}implComplexwhere T:Zero+One{pub fn i()->Self{Self::new(T::zero(),T::one())}}implComplexwhere T:Neg{pub fn conjugate(self)->Self{Self::new(self.re,-self.im)}}implComplexwhere T:Mul,::Output:Add{pub fn dot(self,rhs:Self)-><::Output as Add>::Output{self.re*rhs.re+self.im*rhs.im}}implComplexwhere T:Mul,::Output:Sub{pub fn cross(self,rhs:Self)-><::Output as Sub>::Output{self.re*rhs.im-self.im*rhs.re}}implComplexwhere T:Mul+Clone,::Output:Add{pub fn norm(self)-><::Output as Add>::Output{self.re.clone()*self.re+self.im.clone()*self.im}}implComplexwhere T:Zero+Ord+Mul,::Output:Ord{pub fn cmp_by_arg(self,other:Self)->Ordering{fn pos(c:&Complex)->bool where T:Zero+Ord{let zero=T::zero();c.im{pub fn polar(r:f64,theta:f64)->Self{Self::new(r*theta.cos(),r*theta.sin())}pub fn primitive_nth_root_of_unity(n:f64)->Self{let theta=std::f64::consts::PI*2./n;Self::new(theta.cos(),theta.sin())}pub fn abs(self)->f64{self.re.hypot(self.im)}pub fn unit(self)->Self{self/self.abs()}pub fn angle(self)->f64{self.im.atan2(self.re)}}implAdd for Complexwhere T:Add{type Output=Complex<::Output>;fn add(self,rhs:Self)->Self::Output{Complex::new(self.re+rhs.re,self.im+rhs.im)}}implAddfor Complexwhere T:Add{type Output=Self;fn add(self,rhs:T)->Self::Output{Self::new(self.re+rhs,self.im)}}implSub for Complexwhere T:Sub{type Output=Complex<::Output>;fn sub(self,rhs:Self)->Self::Output{Complex::new(self.re-rhs.re,self.im-rhs.im)}}implSubfor Complexwhere T:Sub{type Output=Self;fn sub(self,rhs:T)->Self::Output{Self::new(self.re-rhs,self.im)}}implMul for Complexwhere T:Clone+Mul,::Output:Add+Sub{type Output=Complex;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)}}implMulfor Complexwhere T:Clone+Mul{type Output=Complex<::Output>;fn mul(self,rhs:T)->Self::Output{Complex::new(self.re*rhs.clone(),self.im*rhs)}}implDiv for Complexwhere T:Clone+Add+Sub+Mul+Div{type Output=Complex<::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)}}implDivfor Complexwhere T:Clone+Div{type Output=Complex<::Output>;fn div(self,rhs:T)->Self::Output{Complex::new(self.re/rhs.clone(),self.im/rhs)}}implNeg for Complexwhere T:Neg{type Output=Complex<::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$T:Clone$(+$w)*,{type Output=<$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)*,{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$T:Clone$(+$w)*,{type Output=<$l as$imp<$r>>::Output;fn$method(self,rhs:&$r)-><$l as$imp<$r>>::Output{$imp::$method(self.clone(),rhs.clone())}}};}impl_complex_ref_binop!(implAdd add(Complex,Complex)where Add);impl_complex_ref_binop!(implAdd add(Complex,T)where Add);impl_complex_ref_binop!(implSub sub(Complex,Complex)where Sub);impl_complex_ref_binop!(implSub sub(Complex,T)where Sub);impl_complex_ref_binop!(implMul mul(Complex,Complex)where Add Sub Mul);impl_complex_ref_binop!(implMul mul(Complex,T)where Mul);impl_complex_ref_binop!(implDiv div(Complex,Complex)where Add Sub Mul Div);impl_complex_ref_binop!(implDiv div(Complex,T)where Div);macro_rules!impl_complex_ref_unop{(impl<$T:ident>$imp:ident$method:ident($t:ty)where$($w:ident)*)=>{impl<$T>$imp for&$t where$T:Clone$(+$w)*,{type Output=<$t as$imp>::Output;fn$method(self)-><$t as$imp>::Output{$imp::$method(self.clone())}}};}impl_complex_ref_unop!(implNeg neg(Complex)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)*,{fn$method(&mut self,rhs:$r){*self=$fromimp::$frommethod(self.clone(),rhs);}}impl<$T>$imp<&$r>for$l where$T:Clone$(+$w)*,{fn$method(&mut self,rhs:&$r){$imp::$method(self,rhs.clone());}}};}impl_complex_op_assign!(implAddAssign add_assign(Complex,Complex)Add add where Add);impl_complex_op_assign!(implAddAssign add_assign(Complex,T)Add add where Add);impl_complex_op_assign!(implSubAssign sub_assign(Complex,Complex)Sub sub where Sub);impl_complex_op_assign!(implSubAssign sub_assign(Complex,T)Sub sub where Sub);impl_complex_op_assign!(implMulAssign mul_assign(Complex,Complex)Mul mul where Add Sub Mul);impl_complex_op_assign!(implMulAssign mul_assign(Complex,T)Mul mul where Mul);impl_complex_op_assign!(implDivAssign div_assign(Complex,Complex)Div div where Add Sub Mul Div);impl_complex_op_assign!(implDivAssign div_assign(Complex,T)Div div where Div);macro_rules!impl_complex_fold{(impl<$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)*$(+$x)*,{fn$method>(iter:I)->Self{iter.fold(::$identmethod(),$fromimp::$frommethod)}}impl<'a,$T:'a>$imp<&'a$t>for$t where$T:Clone+$identimp$(+$w)*$(+$x)*,{fn$method>(iter:I)->Self{iter.fold(::$identmethod(),$fromimp::$frommethod)}}};}impl_complex_fold!(implSum sum(Complex)Zero zero Add add where Add);impl_complex_fold!(implProduct product(Complex)One one Mul mul where Add Sub Mul+Zero+Clone);implIterScan for Complex{type Output=Complex<::Output>;fn scan<'a,I:Iterator>(iter:&mut I)->Option{Some(Complex::new(::scan(iter)?,::scan(iter)?))}}} 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 fn convex_hull(ps:Vec)->Vec{let mut ps=ps;ps.sort_by(|p1,p2|((p1.re,p1.im).partial_cmp(&(p2.re,p2.im)).unwrap()));let mut qs=Vec::new();for&p in ps.iter().chain(ps.iter().rev().skip(1)){while{let k=qs.len();k>1&&Ccw::ccw(qs[k-2],qs[k-1],p)==Ccw::Clockwise}{qs.pop();}qs.push(p);}qs.pop();qs} 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()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()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(pub T)where T:ApproxOrd;implPartialEq for Approxwhere T:ApproxOrd{fn eq(&self,other:&Self)->bool{self.0.approx_eq(&other.0)}}implEq for Approxwhere T:ApproxOrd{}implPartialOrd for Approxwhere T:ApproxOrd{fn partial_cmp(&self,other:&Self)->Option{Some(self.0.approx_cmp(&other.0))}}implOrd for Approxwhere T:ApproxOrd{fn cmp(&self,other:&Self)->Ordering{self.0.approx_cmp(&other.0)}}} pub use self::ccw::Ccw; mod ccw{use super::{Approx,ApproxOrd,Complex,Zero};use std::{cmp::Ordering,ops::{Add,Mul,Sub}};#[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(a:Complex,b:Complex,c:Complex)->Self where T:ApproxOrd+Copy+Zero+Add+Sub+Mul{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))(a:Complex,b:Complex,c:Complex)->Self where T:ApproxOrd+Copy+Zero+Add+Sub+Mul{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 type Point=Complex; #[doc=" binary gcd"]pub fn gcd(mut a:u64,mut b:u64)->u64{if a==0{return b;}if b==0{return a;}let u=a.trailing_zeros();let v=b.trailing_zeros();a>>=u;b>>=v;let k=std::cmp::min(u,v);while a!=b{if a>=a.trailing_zeros();}a<Self{Line{p1,p2}}pub fn dir(&self)->Point{self.p2-self.p1}pub fn ccw(&self,p:Point)->Ccw{Ccw::ccw(self.p1,self.p2,p)}pub fn projection(&self,p:Point)->Point{let e=self.dir().unit();self.p1+e*(p-self.p1).dot(e)}pub fn reflection(&self,p:Point)->Point{p+(self.projection(p)-p)*2.0}pub fn distance_point(&self,p:Point)->f64{(p/self.dir().unit()).re}pub fn is_parallel(&self,other:&Self)->bool{Approx(self.dir().cross(other.dir()))==Approx(0.)}pub fn is_orthogonal(&self,other:&Self)->bool{Approx(self.dir().dot(other.dir()))==Approx(0.)}}#[derive(Clone,Debug,PartialEq)]pub struct LineSegment{p1:Point,p2:Point}impl LineSegment{pub fn new(p1:Point,p2:Point)->Self{LineSegment{p1,p2}}pub fn dir(&self)->Point{self.p2-self.p1}pub fn ccw(&self,p:Point)->Ccw{Ccw::ccw(self.p1,self.p2,p)}pub fn projection(&self,p:Point)->Point{let e=self.dir().unit();self.p1+e*(p-self.p1).dot(e)}pub fn reflection(&self,p:Point)->Point{p+(self.projection(p)-p)*2.0}pub fn is_parallel(&self,other:&Self)->bool{Approx(self.dir().cross(other.dir()))==Approx(0.)}pub fn is_orthogonal(&self,other:&Self)->bool{Approx(self.dir().dot(other.dir()))==Approx(0.)}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:Point)->bool{self.ccw(p)==Ccw::OnSegment}pub fn cross_point(&self,other:&Self)->Option{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(0.)&&Approx(b.abs())==Approx(0.){Some(other.p1)}else{Some(other.p1+(other.dir()*b/a))}}else{None}}pub fn distance_point(&self,p:Point)->f64{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)->f64{if self.intersect(other){0.}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)}}}}