// codesnip-guard: polygon
#[cfg_attr(any(),rustfmt::skip)]pub use self::polygon::{polygon_area2,polygon_centroid,polygon_edge_moments,polygon_moments};#[cfg_attr(any(),rustfmt::skip)]mod polygon{use super::{Approx,ApproxOrd,Complex,Float,Zero};use std::ops::{Add,Mul,Sub};#[doc=" Signed area times two; positive for counterclockwise input."]pub fn polygon_area2<T>(ps:&[Complex<T>])->T where T:Copy+Zero+Add<Output=T>+Sub<Output=T>+Mul<Output=T>{ps.iter().zip(ps.iter().cycle().skip(1)).fold(T::zero(),|sum,(&a,&b)|sum+a.cross(b))}#[doc=" `(area2, moment6)` contribution."]pub fn polygon_edge_moments<T>(a:Complex<T>,b:Complex<T>)->(T,Complex<T>)where T:Copy+Add<Output=T>+Sub<Output=T>+Mul<Output=T>{let cross=a.cross(b);(cross,(a+b)*cross)}#[doc=" `None` if the signed area is approximately zero."]pub fn polygon_centroid<T>(ps:&[Complex<T>])->Option<Complex<T>>where T:Float+ApproxOrd{let(area,moment)=polygon_moments(ps);if Approx(area)==Approx(T::zero()){None}else{Some(moment/(area+area+area))}}#[doc=" Signed `(area2, moment6)`; centroid is `moment6 / (3 * area2)`."]pub fn polygon_moments<T>(ps:&[Complex<T>])->(T,Complex<T>)where T:Copy+Zero+Add<Output=T>+Sub<Output=T>+Mul<Output=T>{ps.iter().zip(ps.iter().cycle().skip(1)).fold((T::zero(),Complex::zero()),|(area,moment),(&a,&b)|{let(cross,contribution)=polygon_edge_moments(a,b);(area+cross,moment+contribution)})}}
// codesnip-guard: Approx
#[cfg_attr(any(),rustfmt::skip)]pub use self::approx::{Approx,ApproxOrd};#[cfg_attr(any(),rustfmt::skip)]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.cmp(other))}}impl<T>Ord for Approx<T>where T:ApproxOrd{fn cmp(&self,other:&Self)->Ordering{self.0 .approx_cmp(&other.0)}}}
// codesnip-guard: Complex
#[cfg_attr(any(),rustfmt::skip)]pub use self::complex::Complex;#[cfg_attr(any(),rustfmt::skip)]mod complex{use super::{Float,One,Scan,ScanSource,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{Self{re,im}}pub fn transpose(self)->Self{Self::new(self.im,self.re)}pub fn map<U>(self,mut f:impl FnMut(T)->U)->Complex<U>{Complex::new(f(self.re),f(self.im))}}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<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<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<Output:Add>+Clone{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<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:Scan>Scan for Complex<T>{type Output=Complex<<T as Scan>::Output>;fn scan<I:ScanSource>(iter:&mut I)->Option<Self::Output>{Some(Complex::new(<T as Scan>::scan(iter)?,<T as Scan>::scan(iter)?))}}}
// codesnip-guard: array
#[cfg_attr(any(),rustfmt::skip)]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]}};}}
// codesnip-guard: bounded
#[cfg_attr(any(),rustfmt::skip)]pub use self::bounded::Bounded;#[cfg_attr(any(),rustfmt::skip)]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())}}}
// codesnip-guard: float
#[cfg_attr(any(),rustfmt::skip)]pub use self::float::{Float,Float32,Float64};#[cfg_attr(any(),rustfmt::skip)]mod float{use super::{Bounded,One,Scan,ScanSource,Zero};use std::{cmp::Ordering,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>{type Bits;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 midpoint(self,other:Self)->Self;fn to_bits(self)->Self::Bits;fn from_bits(v:Self::Bits)->Self;fn total_cmp(&self,other:&Self)->Ordering;fn clamp(self,min:Self,max:Self)->Self;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!impl_primitive_float{($({$t:ident$i:ident$u:ident$e:expr})*)=>{$(impl Float for$t{type Bits=$u;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 midpoint(self,other:Self)->Self{$t::midpoint(self,other)}fn to_bits(self)->Self::Bits{$t::to_bits(self)}fn from_bits(v:Self::Bits)->Self{$t::from_bits(v)}fn total_cmp(&self,other:&Self)->Ordering{$t::total_cmp(self,other)}fn clamp(self,min:Self,max:Self)->Self{$t::clamp(self,min,max)}const RADIX:u32=$t::RADIX;const MANTISSA_DIGITS:u32=$t::MANTISSA_DIGITS;const DIGITS:u32=$t::DIGITS;const EPSILON:Self=$t::EPSILON;const MIN:Self=$t::MIN;const MIN_POSITIVE:Self=$t::MIN_POSITIVE;const MAX:Self=$t::MAX;const MIN_EXP:i32=$t::MIN_EXP;const MAX_EXP:i32=$t::MAX_EXP;const MIN_10_EXP:i32=$t::MIN_10_EXP;const MAX_10_EXP:i32=$t::MAX_10_EXP;const NAN:Self=$t::NAN;const INFINITY:Self=$t::INFINITY;const NEG_INFINITY:Self=$t::NEG_INFINITY;const PI:Self=std::$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;})*};}impl_primitive_float!({f32 i32 u32 31}{f64 i64 u64 63});macro_rules!impl_ord_float{($({$t:ident$n:ident})*)=>{$(#[derive(Debug,Copy,Clone,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(<$t as Zero>::zero())}fn is_zero(&self)->bool{self.0==0.0}}impl One for$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 PartialEq for$n{fn eq(&self,other:&Self)->bool{self.total_cmp(other).is_eq()}}impl Eq for$n{}impl PartialOrd for$n{fn partial_cmp(&self,other:&Self)->Option<Ordering>{Some(self.cmp(other))}}impl Ord for$n{fn cmp(&self,other:&Self)->Ordering{self.total_cmp(other)}}impl Scan for$n{type Output=Self;fn scan<I:ScanSource>(iter:&mut I)->Option<Self::Output>{<$t as Scan>::scan(iter).map(Self)}}impl Float for$n{type Bits=<$t as Float>::Bits;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 midpoint(self,other:Self)->Self{Self(<$t as Float>::midpoint(self.0,other.0))}fn to_bits(self)->Self::Bits{<$t as Float>::to_bits(self.0)}fn from_bits(v:Self::Bits)->Self{Self(<$t as Float>::from_bits(v))}fn total_cmp(&self,other:&Self)->Ordering{<$t as Float>::total_cmp(&self.0,&other.0)}fn clamp(self,min:Self,max:Self)->Self{Self(<$t as Float>::clamp(self.0,min.0,max.0))}const RADIX:u32=<$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);})*};}impl_ord_float!({f32 Float32}{f64 Float64});}
// codesnip-guard: scanner
#[cfg_attr(any(),rustfmt::skip)]pub use self::scanner::*;#[cfg_attr(any(),rustfmt::skip)]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 Scan:Sized{type Output;fn scan<S:ScanSource>(source:&mut S)->Option<Self::Output>;fn scan_vec<S:ScanSource>(source:&mut S,size:usize,capacity:usize)->Vec<Self::Output>{let mut values=Vec::with_capacity(capacity.max(size));values.extend((0..size).map(|_|source.scan::<Self>()));values}}pub trait MarkedScan:Sized{type Output;fn mscan<S:ScanSource>(self,source:&mut S)->Option<Self::Output>;}pub trait ScanSource:Sized{#[doc=" Reads a token under the source's input requirements."]#[doc=" Checked sources return `None` at EOF; unchecked sources require available input."]fn next_token(&mut self)->Option<&str>;#[doc=" Skips separators without consuming the next token."]#[inline]fn skip_whitespace(&mut self){}#[inline]fn read_u8(&mut self)->Option<u8>{self.next_token()?.parse().ok()}#[inline]fn read_u16(&mut self)->Option<u16>{self.next_token()?.parse().ok()}#[inline]fn read_u32(&mut self)->Option<u32>{self.next_token()?.parse().ok()}fn read_u32_vec(&mut self,size:usize,capacity:usize)->Vec<u32>{let mut values=Vec::with_capacity(capacity.max(size));values.extend((0..size).map(|_|self.scan::<u32>()));values}#[inline]fn read_u64(&mut self)->Option<u64>{self.next_token()?.parse().ok()}#[inline]fn read_u128(&mut self)->Option<u128>{self.next_token()?.parse().ok()}#[inline]fn read_usize(&mut self)->Option<usize>{self.next_token()?.parse().ok()}#[inline]fn read_i8(&mut self)->Option<i8>{self.next_token()?.parse().ok()}#[inline]fn read_i16(&mut self)->Option<i16>{self.next_token()?.parse().ok()}#[inline]fn read_i32(&mut self)->Option<i32>{self.next_token()?.parse().ok()}#[inline]fn read_i64(&mut self)->Option<i64>{self.next_token()?.parse().ok()}#[inline]fn read_i128(&mut self)->Option<i128>{self.next_token()?.parse().ok()}#[inline]fn read_isize(&mut self)->Option<isize>{self.next_token()?.parse().ok()}#[doc=" Panics if reading fails."]#[inline]fn scan<T:Scan>(&mut self)->T::Output{T::scan(self).expect("scan error")}#[doc=" Panics if reading fails."]#[inline]fn mscan<T:MarkedScan>(&mut self,marker:T)->T::Output{marker.mscan(self).expect("scan error")}fn scan_vec<T:Scan>(&mut self,size:usize,capacity:usize)->Vec<T::Output>{if size==0{self.skip_whitespace();}T::scan_vec(self,size,capacity)}#[inline]fn iter<T:Scan>(&mut self)->ScannerIter<'_,Self,T>{ScannerIter{inner:self,_marker:PhantomData}}}#[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{Self{iter:s.split_ascii_whitespace()}}}impl<'a,I:Iterator<Item=&'a str>>Scanner<'a,I>{pub fn new_from_iter(iter:I)->Self{Self{iter}}}impl<'a,I:Iterator<Item=&'a str>>ScanSource for Scanner<'a,I>{fn next_token(&mut self)->Option<&str>{self.iter.next()}}macro_rules!impl_scan{($($t:ty)*)=>{$(impl Scan for$t{type Output=Self;fn scan<I:ScanSource>(iter:&mut I)->Option<Self>{iter.next_token()?.parse::<$t>().ok()}})*};}impl_scan!(char f32 f64 String);macro_rules!impl_integer_scan{($($t:ty=>$read:ident),*$(,)?)=>{$(impl Scan for$t{type Output=Self;#[inline]fn scan<S:ScanSource>(source:&mut S)->Option<Self>{source.$read()}})*};}impl_integer_scan!(u8=>read_u8,u16=>read_u16,u64=>read_u64,u128=>read_u128,usize=>read_usize,i8=>read_i8,i16=>read_i16,i32=>read_i32,i64=>read_i64,i128=>read_i128,isize=>read_isize,);impl Scan for u32{type Output=Self;#[inline]fn scan<S:ScanSource>(source:&mut S)->Option<Self>{source.read_u32()}fn scan_vec<S:ScanSource>(source:&mut S,size:usize,capacity:usize)->Vec<Self>{source.read_u32_vec(size,capacity)}}macro_rules!impl_scan_tuple{(@impl$($T:ident)*)=>{impl<$($T:Scan),*>Scan for($($T,)*){type Output=($(<$T as Scan>::Output,)*);fn scan<It:ScanSource>(_iter:&mut It)->Option<Self::Output>{Some(($(<$T as Scan>::scan(_iter)?,)*))}}};(@inner$($T:ident)*,)=>{impl_scan_tuple!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{impl_scan_tuple!(@impl$($T)*);impl_scan_tuple!(@inner$($T)*$U,$($Rest)*);};($($T:ident)*)=>{impl_scan_tuple!(@inner,$($T)*);};}impl_scan_tuple!(A B C D E F G H I J K);pub struct ScannerIter<'a,S,T>{inner:&'a mut S,_marker:PhantomData<fn()->T>}impl<S:ScanSource,T:Scan>Iterator for ScannerIter<'_,S,T>{type Item=T::Output;#[inline]fn next(&mut self)->Option<Self::Item>{T::scan(self.inner)}}#[doc=" scan a value with Scanner"]#[doc=""]#[doc=" - `scan_value!(scanner, ELEMENT)`"]#[doc=""]#[doc=" ELEMENT :="]#[doc=" - `$ty`: Scan"]#[doc=" - `&str`: borrowed token; the source stays borrowed until its last use"]#[doc=" - `@$expr`: MarkedScan"]#[doc=" - `$ty = $expr`: MarkedScan"]#[doc=" - `[ELEMENT; $expr]`: vector"]#[doc=" - `[$ty; $len; capacity $capacity]`: vector with reserved capacity"]#[doc=" - `[ELEMENT; const $expr]`: array"]#[doc=" - `[ELEMENT]`: iterator"]#[doc=" - `[ELEMENT; iter $expr]`: iterator of the specified length"]#[doc=" - `($(ELEMENT)*,)`: tuple"]#[macro_export]macro_rules!scan_value{(@repeat$scanner:expr,[$($t:tt)*]$len:expr)=>{{$crate::scan_value!(@iter$scanner,[$($t)*]$len).collect::<Vec<_>>()}};(@repeat$scanner:expr,[$($t:tt)*])=>{{::std::iter::repeat_with(||$crate::scan_value!(@inner$scanner,[]$($t)*))}};(@iter$scanner:expr,[$($t:tt)*]$len:expr)=>{{let size=$len;if size==0{$scanner.skip_whitespace();}$crate::scan_value!(@repeat$scanner,[$($t)*]).take(size)}};(@array$scanner:expr,[$($t:tt)*]$len:expr)=>{{if$len==0{$scanner.skip_whitespace();}$crate::array![||$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$scanner:expr,[$($args:tt)+]iter$len:expr)=>{$crate::scan_value!(@iter$scanner,[$($args)+]$len)};(@sparen$scanner:expr,[$($args:tt)+]$len:expr;capacity$capacity:expr)=>{{let size=$len;let capacity=$capacity;$scanner.scan_vec::<$($args)+>(size,capacity)}};(@sparen$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)*]&str$(,$($t:tt)*)?)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.next_token().expect("scan error")]]$(,$($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)*]&str$(,$($t:tt)*)?)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*&str]$(,$($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$scanner,[][]$($t)*)}}#[doc=" define enum scan rules"]#[doc=""]#[doc=" # Example"]#[doc=" ```rust"]#[doc=" # use competitive::{define_enum_scan, tools::{CharsWithBase, Scan, ScanSource, Scanner, Usize1}};"]#[doc=" define_enum_scan! {"]#[doc="   enum Query: u8 {"]#[doc="     0 => Noop,"]#[doc="     1 => Args { i: Usize1, s: char },"]#[doc="     9 => Complex { n: usize, c: [(usize, Vec<usize> = CharsWithBase('a')); n] },"]#[doc="   }"]#[doc=" }"]#[doc=" ```"]#[macro_export]macro_rules!define_enum_scan{(@field_ty@repeat[$($t:tt)*]$($len:expr)?)=>{Vec<$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 Scan>::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)=>{ScanSource::next_token($iter)?};(@tag_expr$d:ty,$iter:ident)=>{<$d as Scan>::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:$crate::define_enum_scan!(@field_ty$($spec)*)),*})?),*}impl Scan for$T{type Output=Self;fn scan<I:ScanSource>(iter:&mut I)->Option<Self>{let tag=$crate::define_enum_scan!(@tag_expr$d,iter);match tag{$($p=>{$($(let$f=$crate::scan_value!((*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 Scan for Usize1{type Output=usize;fn scan<I:ScanSource>(iter:&mut I)->Option<Self::Output>{<usize as Scan>::scan(iter)?.checked_sub(1)}}#[derive(Debug,Copy,Clone)]pub struct CharWithBase(pub char);impl MarkedScan for CharWithBase{type Output=usize;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{Some((<char as Scan>::scan(iter)?as u8-self.0 as u8)as usize)}}#[derive(Debug,Copy,Clone)]pub enum Chars{}impl Scan for Chars{type Output=Vec<char>;fn scan<I:ScanSource>(iter:&mut I)->Option<Self::Output>{Some(iter.next_token()?.chars().collect())}}#[derive(Debug,Copy,Clone)]pub struct CharsWithBase(pub char);impl MarkedScan for CharsWithBase{type Output=Vec<usize>;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{Some(iter.next_token()?.chars().map(|c|(c as u8-self.0 as u8)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub enum Byte1{}impl Scan for Byte1{type Output=u8;fn scan<I:ScanSource>(iter:&mut I)->Option<Self::Output>{let bytes=iter.next_token()?.as_bytes();assert_eq!(bytes.len(),1);Some(bytes[0])}}#[derive(Debug,Copy,Clone)]pub struct ByteWithBase(pub u8);impl MarkedScan for ByteWithBase{type Output=usize;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{Some((<char as Scan>::scan(iter)?as u8-self.0)as usize)}}#[derive(Debug,Copy,Clone)]pub enum Bytes{}impl Scan for Bytes{type Output=Vec<u8>;fn scan<I:ScanSource>(iter:&mut I)->Option<Self::Output>{Some(iter.next_token()?.bytes().collect())}}#[derive(Debug,Copy,Clone)]pub struct BytesWithBase(pub u8);impl MarkedScan for BytesWithBase{type Output=Vec<usize>;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{Some(iter.next_token()?.bytes().map(|c|(c-self.0)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub struct Collect<T,B=Vec<<T as Scan>::Output>>where T:Scan,B:FromIterator<<T as Scan>::Output>{size:usize,_marker:PhantomData<fn()->(T,B)>}impl<T,B>Collect<T,B>where T:Scan,B:FromIterator<<T as Scan>::Output>{pub fn new(size:usize)->Self{Self{size,_marker:PhantomData}}}impl<T,B>MarkedScan for Collect<T,B>where T:Scan,B:FromIterator<<T as Scan>::Output>{type Output=B;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{if self.size==0{iter.skip_whitespace();}repeat_with(| |<T as Scan>::scan(iter)).take(self.size).collect()}}#[derive(Debug,Copy,Clone)]pub struct SizedCollect<T,B=Vec<<T as Scan>::Output>>where T:Scan,B:FromIterator<<T as Scan>::Output>{_marker:PhantomData<fn()->(T,B)>}impl<T,B>Scan for SizedCollect<T,B>where T:Scan,B:FromIterator<<T as Scan>::Output>{type Output=B;fn scan<I:ScanSource>(iter:&mut I)->Option<Self::Output>{let size=usize::scan(iter)?;if size==0{iter.skip_whitespace();}repeat_with(| |<T as Scan>::scan(iter)).take(size).collect()}}#[derive(Debug,Copy,Clone)]pub struct Splitted<T,P>where T:Scan{pat:P,_marker:PhantomData<fn()->T>}impl<T,P>Splitted<T,P>where T:Scan{pub fn new(pat:P)->Self{Self{pat,_marker:PhantomData}}}impl<T>MarkedScan for Splitted<T,char>where T:Scan{type Output=Vec<<T as Scan>::Output>;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{let mut iter=Scanner::new_from_iter(iter.next_token()?.split(self.pat));Some(from_fn(| |<T as Scan>::scan(&mut iter)).collect())}}impl<T>MarkedScan for Splitted<T,&str>where T:Scan{type Output=Vec<<T as Scan>::Output>;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{let mut iter=Scanner::new_from_iter(iter.next_token()?.split(self.pat));Some(from_fn(| |<T as Scan>::scan(&mut iter)).collect())}}impl<T,F>MarkedScan for F where F:Fn(&str)->Option<T>{type Output=T;fn mscan<I:ScanSource>(self,iter:&mut I)->Option<Self::Output>{self(iter.next_token()?)}}}
// codesnip-guard: zero_one
#[cfg_attr(any(),rustfmt::skip)]pub use self::zero_one::{One,Zero};#[cfg_attr(any(),rustfmt::skip)]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{($({$(<$T:ident:$Bound:ident>)?$Trait:ident$method:ident$($t:ty)*,$e:expr})*)=>{$(impl_zero_one!(@impl[$(<$T:$Bound>)?]$Trait$method[$($t)*],$e);)*};(@impl[<$T:ident:$Bound:ident>]$Trait:ident$method:ident[$($t:ty)*],$e:expr)=>{$(impl<$T:$Bound>$Trait for$t{fn$method()->Self{$e}})*};(@impl[]$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.}{<T:Zero>Zero zero std::num::Wrapping<T>,Self(T::zero())}{<T:One>One one std::num::Wrapping<T>,Self(T::one())});}