#912930 (Rust) No.3024 等式

提出ソース
結果

問題	No.3024 等式
ユーザー	to-omer
提出日時	2023-09-12 01:56:28
言語	Rust (1.77.0 + proconio)
結果	AC
実行時間	820 ms / 5,000 ms
コード長	47,522 bytes
コンパイル時間	19,510 ms
コンパイル使用メモリ	400,832 KB
実行使用メモリ	85,704 KB
最終ジャッジ日時	2024-06-30 04:15:41
合計ジャッジ時間	16,479 ms
ジャッジサーバーID （参考情報）	judge5 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 6,816 KB
testcase_01	AC	1 ms 6,944 KB
testcase_02	AC	1 ms 6,944 KB
testcase_03	AC	1 ms 6,940 KB
testcase_04	AC	1 ms 6,944 KB
testcase_05	AC	0 ms 6,940 KB
testcase_06	AC	1 ms 6,944 KB
testcase_07	AC	2 ms 6,944 KB
testcase_08	AC	2 ms 6,944 KB
testcase_09	AC	1 ms 6,944 KB
testcase_10	AC	1 ms 6,940 KB
testcase_11	AC	2 ms 6,944 KB
testcase_12	AC	23 ms 6,940 KB
testcase_13	AC	23 ms 6,944 KB
testcase_14	AC	31 ms 6,944 KB
testcase_15	AC	2 ms 6,940 KB
testcase_16	AC	5 ms 6,940 KB
testcase_17	AC	1 ms 6,940 KB
testcase_18	AC	3 ms 6,940 KB
testcase_19	AC	2 ms 6,940 KB
testcase_20	AC	2 ms 6,940 KB
testcase_21	AC	2 ms 6,940 KB
testcase_22	AC	820 ms 85,704 KB
権限があれば一括ダウンロードができます
ソースコード

raw source code
pub fn solve() {
    crate::prepare!();
    sc!(n, mut a: [i64; n]);
    a.sort_unstable();
    let mut dp: Vec<HashSet<Rational<i64>>> = (0..1 << n).map(|_| Default::default()).collect();
    for i in 0..n {
        dp[1 << i].insert(Rational::new(a[i], 1));
    }
    for bit in 1usize..(1 << n) - 1 {
        for sub in BitDp::subsets((1 << n) - 1 ^ bit) {
            if sub != 0 && sub ^ bit != (1 << n) - 1 {
                let mut ep = std::mem::take(&mut dp[bit ^ sub]);
                for &x in &dp[bit] {
                    for &y in &dp[sub] {
                        macro_rules! go {
                            ($z:expr) => {
                                let z = $z;
                                if z.is_zero() {
                                    pp!("YES");
                                    return;
                                }
                                if z.num <= 1_000_000 && z.den <= 1_000_000 {
                                    ep.insert(z);
                                }
                            };
                        }
                        go!(x + y);
                        go!((x - y).abs());
                        go!(x * y);
                        go!(x / y);
                        go!(y / x);
                    }
                }
                dp[bit ^ sub] = ep;
            }
        }
    }
    for bit in 1usize..(1 << n) - 1 {
        let sub = (1 << n) - 1 ^ bit;
        for &x in &dp[bit] {
            for &y in &dp[sub] {
                if x == y {
                    pp!("YES");
                    return;
                }
            }
        }
    }
    pp!("NO");
}
crate::main!();
#[allow(unused_imports)]use std::{cmp::{Ordering,Reverse},collections::{BTreeMap,BTreeSet,BinaryHeap,HashMap,HashSet,VecDeque}};
mod main_macros{#[doc=" Prepare useful macros."]#[doc=" - `prepare!();`: default (all input scanner (`sc!`, `sv!`) + buf print (`pp!`, `dg!`))"]#[doc=" - `prepare!(?);`: interactive (line scanner (`scln!`) + buf print (`pp!`, `dg!`))"]#[macro_export]macro_rules!prepare{(@output($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;$len:expr]]=>{{use::std::mem::{ManuallyDrop,MaybeUninit};let mut$data:[MaybeUninit<_>;$len]=unsafe{MaybeUninit::uninit().assume_init()};$init;#[repr(C)]union __Transmuter<const N:usize,T:Clone>{src:ManuallyDrop<[MaybeUninit<T>;N]>,dst:ManuallyDrop<[T;N]>,}ManuallyDrop::into_inner(unsafe{__Transmuter{src:ManuallyDrop::new($data)}.dst})}};[||$e:expr;$len:expr]=>{$crate::array![@inner data=[data.iter_mut().for_each(|item|*item=MaybeUninit::new($e));$len]]};[|$i:pat_param|$e:expr;$len:expr]=>{$crate::array![@inner data=[data.iter_mut().enumerate().for_each(|($i,item)|*item=MaybeUninit::new($e));$len]]};[$e:expr;$len:expr]=>{{let e=$e;$crate::array![||Clone::clone(&e);$len]}};}}
pub use self::scanner::*;
mod scanner{use std::{iter::{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::rational::Rational;
mod rational{use super::{Bounded,One,Signed,Unsigned,Zero};use std::{cmp::Ordering,fmt::{self,Debug},ops::{Add,AddAssign,Div,DivAssign,Mul,MulAssign,Neg,Sub,SubAssign}};#[derive(Clone,Copy,Hash)]pub struct Rational<T>where T:Signed{pub num:T,pub den:T}impl<T>PartialEq for Rational<T>where T:Signed{fn eq(&self,other:&Self)->bool{self.num==other.num&&self.den==other.den}}impl<T>Eq for Rational<T>where T:Signed{}impl<T>PartialOrd for Rational<T>where T:Signed{fn partial_cmp(&self,other:&Self)->Option<Ordering>{Some(self.cmp(other))}}impl<T>Ord for Rational<T>where T:Signed{fn cmp(&self,other:&Self)->Ordering{match(self.den.is_zero(),other.den.is_zero()){(true,true)=>self.num.cmp(&other.num),(true,false)=>self.num.cmp(&T::zero()),(false,true)=>T::zero().cmp(&other.num),(false,false)=>(self.num*other.den).cmp(&(self.den*other.num)),}}}impl<T>Debug for Rational<T>where T:Signed+Debug{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{write!(f,"{:?}/{:?}",self.num,self.den)}}impl<T>Rational<T>where T:Signed{pub fn new(num:T,den:T)->Self{let g=num.abs().unsigned().gcd(den.abs().unsigned()).signed();let g=if den.is_negative(){-g}else{g};Self::new_unchecked(num/g,den/g)}pub fn new_unchecked(num:T,den:T)->Self{Self{num,den}}pub fn abs(self)->Self{Self::new_unchecked(self.num.abs(),self.den)}pub fn inner(self)->T{self.num/self.den}}impl<T>Bounded for Rational<T>where T:Signed{fn maximum()->Self{Self::new_unchecked(T::one(),T::zero())}fn minimum()->Self{Self::new_unchecked(-T::one(),T::zero())}}impl<T>Zero for Rational<T>where T:Signed{fn zero()->Self{Self::new_unchecked(T::zero(),T::one())}}impl<T>One for Rational<T>where T:Signed{fn one()->Self{Self::new_unchecked(T::one(),T::one())}}impl<T>Add for Rational<T>where T:Signed{type Output=Self;fn add(self,rhs:Self)->Self::Output{Self::new(self.num*rhs.den+self.den*rhs.num,self.den*rhs.den)}}impl<T>Sub for Rational<T>where T:Signed{type Output=Self;fn sub(self,rhs:Self)->Self::Output{Self::new(self.num*rhs.den-self.den*rhs.num,self.den*rhs.den)}}impl<T>Mul for Rational<T>where T:Signed{type Output=Self;fn mul(self,rhs:Self)->Self::Output{Self::new(self.num*rhs.num,self.den*rhs.den)}}impl<T>Div for Rational<T>where T:Signed{type Output=Self;fn div(self,rhs:Self)->Self::Output{Self::new(self.num*rhs.den,self.den*rhs.num)}}impl<T>Neg for Rational<T>where T:Signed{type Output=Self;fn neg(self)->Self::Output{Self::new_unchecked(-self.num,self.den)}}impl<T>AddAssign for Rational<T>where T:Signed{fn add_assign(&mut self,rhs:Self){*self=*self+rhs;}}impl<T>SubAssign for Rational<T>where T:Signed{fn sub_assign(&mut self,rhs:Self){*self=*self-rhs;}}impl<T>MulAssign for Rational<T>where T:Signed{fn mul_assign(&mut self,rhs:Self){*self=*self*rhs;}}impl<T>DivAssign for Rational<T>where T:Signed{fn div_assign(&mut self,rhs:Self){*self=*self/rhs;}}}
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$T,$($Rest)*);};}bounded_tuple_impls!(A B C D E F G H I J);impl Bounded for(){fn maximum()->Self{}fn minimum()->Self{}}impl Bounded for bool{fn maximum()->Self{true}fn minimum()->Self{false}}impl<T>Bounded for Option<T>where T:Bounded{fn maximum()->Self{Some(<T as Bounded>::maximum())}fn minimum()->Self{None}}impl<T>Bounded for std::cmp::Reverse<T>where T:Bounded{fn maximum()->Self{std::cmp::Reverse(<T as Bounded>::minimum())}fn minimum()->Self{std::cmp::Reverse(<T as Bounded>::maximum())}}}
pub use self::integer::{BinaryRepr,ExtendedGcd,IntBase,Saturating,Signed,Unsigned,Wrapping};
mod integer{use super::{Bounded,IterScan,One,Zero};use std::{convert::TryFrom,fmt::{self,Display},ops::{Add,AddAssign,BitAnd,BitAndAssign,BitOr,BitOrAssign,BitXor,BitXorAssign,Div,DivAssign,Mul,MulAssign,Neg,Not,Rem,RemAssign,Shl,ShlAssign,Shr,ShrAssign,Sub,SubAssign},str::FromStr};#[doc=" Trait for basic primitive integer operations."]pub trait IntBase:Copy+Bounded+Zero+One+Eq+Ord+Default+FromStr+Display+Add<Output=Self>+Sub<Output=Self>+Mul<Output=Self>+Div<Output=Self>+Rem<Output=Self>+AddAssign+SubAssign+MulAssign+DivAssign+RemAssign{type Error;fn div_euclid(self,rhs:Self)->Self;fn rem_euclid(self,rhs:Self)->Self;fn pow(self,exp:u32)->Self;fn from_str_radix(src:&str,radix:u32)->Result<Self,Self::Error>;fn ilog(self,base:Self)->u32;fn ilog2(self)->u32;fn ilog10(self)->u32;}macro_rules!impl_int_base{($($t:ty)*)=>{$(impl IntBase for$t{type Error=std::num::ParseIntError;fn div_euclid(self,rhs:Self)->Self{self.div_euclid(rhs)}fn rem_euclid(self,rhs:Self)->Self{self.rem_euclid(rhs)}fn pow(self,exp:u32)->Self{self.pow(exp)}fn from_str_radix(src:&str,radix:u32)->Result<Self,Self::Error>{Self::from_str_radix(src,radix)}fn ilog(self,base:Self)->u32{self.ilog(base)}fn ilog2(self)->u32{self.ilog2()}fn ilog10(self)->u32{self.ilog10()}})*};}impl_int_base!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);#[doc=" extended_gcd(a,b): ax + by = g = gcd(a,b)"]pub struct ExtendedGcd<T:Unsigned>{#[doc=" gcd"]pub g:T,pub x:T::Signed,pub y:T::Signed}#[doc=" Trait for unsigned integer operations."]pub trait Unsigned:IntBase{type Signed:Signed<Unsigned=Self>;fn signed(self)->Self::Signed;fn abs_diff(self,other:Self)->Self;fn next_power_of_two(self)->Self;fn gcd(self,other:Self)->Self;fn lcm(self,other:Self)->Self{if self.is_zero()&&other.is_zero(){Self::zero()}else{self/self.gcd(other)*other}}fn extgcd(self,other:Self)->ExtendedGcd<Self>{let(mut a,mut b)=(self.signed(),other.signed());let(mut u,mut v,mut x,mut y)=(Self::Signed::one(),Self::Signed::zero(),Self::Signed::zero(),Self::Signed::one());while!a.is_zero(){let k=b/a;x-=k*u;y-=k*v;b-=k*a;std::mem::swap(&mut x,&mut u);std::mem::swap(&mut y,&mut v);std::mem::swap(&mut b,&mut a);}ExtendedGcd{g:b.unsigned(),x,y}}fn modinv(self,modulo:Self)->Self{assert!(!self.is_zero(),"attempt to inverse zero with modulo {}",modulo);let extgcd=self.extgcd(modulo);assert!(extgcd.g.is_one(),"there is no inverse {} modulo {}",self,modulo);extgcd.x.rem_euclid(modulo.signed()).unsigned()}}#[doc=" Trait for signed integer operations."]pub trait Signed:IntBase+Neg<Output=Self>{type Unsigned:Unsigned<Signed=Self>;fn unsigned(self)->Self::Unsigned;fn abs(self)->Self;fn abs_diff(self,other:Self)->Self::Unsigned;fn is_negative(self)->bool;fn is_positive(self)->bool;fn signum(self)->Self;}macro_rules!impl_unsigned_signed{($($unsigned:ident$signed:ident)*)=>{$(impl Unsigned for$unsigned{type Signed=$signed;fn signed(self)->Self::Signed{self as Self::Signed}fn abs_diff(self,other:Self)->Self{self.abs_diff(other)}fn next_power_of_two(self)->Self{self.next_power_of_two()}fn gcd(self,other:Self)->Self{let(mut a,mut b)=(self,other);if a.is_zero()||b.is_zero(){return a|b;}let u=a.trailing_zeros();let v=b.trailing_zeros();a>>=u;b>>=v;let k=u.min(v);while a!=b{if a<b{std::mem::swap(&mut a,&mut b);}a-=b;a>>=a.trailing_zeros();}a<<k}}impl Signed for$signed{type Unsigned=$unsigned;fn unsigned(self)->Self::Unsigned{self as Self::Unsigned}fn abs_diff(self,other:Self)->Self::Unsigned{self.abs_diff(other)}fn abs(self)->Self{self.abs()}fn is_negative(self)->bool{self.is_negative()}fn is_positive(self)->bool{self.is_positive()}fn signum(self)->Self{self.signum()}})*};}impl_unsigned_signed!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);#[doc=" Trait for operations of integer in binary representation."]pub trait BinaryRepr<Size=u32>:Sized+Not<Output=Self>+BitAnd<Output=Self>+BitOr<Output=Self>+BitXor<Output=Self>+Shl<Size,Output=Self>+Shr<Size,Output=Self>+BitAndAssign+BitOrAssign+BitXorAssign+ShlAssign<Size>+ShrAssign<Size>{fn count_ones(self)->Size;fn count_zeros(self)->Size;fn leading_ones(self)->Size;fn leading_zeros(self)->Size;fn reverse_bits(self)->Self;fn rotate_left(self,n:Size)->Self;fn rotate_right(self,n:Size)->Self;fn swap_bytes(self)->Self;fn trailing_ones(self)->Size;fn trailing_zeros(self)->Size;}macro_rules!impl_binary_repr{($($t:ty)*)=>{$(impl BinaryRepr for$t{fn count_ones(self)->u32{self.count_ones()}fn count_zeros(self)->u32{self.count_zeros()}fn leading_ones(self)->u32{self.leading_ones()}fn leading_zeros(self)->u32{self.leading_zeros()}fn reverse_bits(self)->Self{self.reverse_bits()}fn rotate_left(self,n:u32)->Self{self.rotate_left(n)}fn rotate_right(self,n:u32)->Self{self.rotate_right(n)}fn swap_bytes(self)->Self{self.swap_bytes()}fn trailing_ones(self)->u32{self.trailing_ones()}fn trailing_zeros(self)->u32{self.trailing_zeros()}})*};}impl_binary_repr!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);macro_rules!impl_binop{(impl<$T:ident>$Trait:ident$impl:ident for$t:ty)=>{impl<$T>$Trait for$t where$T:$Trait<Output=$T>,{type Output=Self;fn$impl(self,rhs:Self)->Self::Output{Self($Trait::$impl(self.0,rhs.0))}}};}macro_rules!impl_opassign{(impl<$T:ident>$Trait:ident$impl:ident for$t:ty)=>{impl<$T>$Trait for$t where$T:$Trait,{fn$impl(&mut self,rhs:Self){$Trait::$impl(&mut self.0,rhs.0)}}};}#[derive(Default,PartialEq,Eq,PartialOrd,Ord,Hash,Clone,Copy)]#[repr(transparent)]#[doc=" Wrapper type of arithmetic `saturating_*` operations."]pub struct Saturating<T>(pub T);impl<T>fmt::Debug for Saturating<T>where T:fmt::Debug{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{T::fmt(&self.0,f)}}impl<T>Bounded for Saturating<T>where T:Bounded{fn maximum()->Self{Self(T::maximum())}fn minimum()->Self{Self(T::minimum())}}impl<T>Zero for Saturating<T>where T:Zero{fn zero()->Self{Self(T::zero())}}impl<T>One for Saturating<T>where T:One{fn one()->Self{Self(T::one())}}impl<T>FromStr for Saturating<T>where T:FromStr{type Err=T::Err;fn from_str(s:&str)->Result<Self,Self::Err>{T::from_str(s).map(Self)}}impl<T>Display for Saturating<T>where T:Display{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{T::fmt(&self.0,f)}}impl<T>IterScan for Saturating<T>where T:IterScan<Output=T>{type Output=Self;fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{T::scan(iter).map(Self)}}impl_binop!(impl<T>Div div for Saturating<T>);impl_binop!(impl<T>Rem rem for Saturating<T>);impl_binop!(impl<T>BitAnd bitand for Saturating<T>);impl_binop!(impl<T>BitOr bitor for Saturating<T>);impl_binop!(impl<T>BitXor bitxor for Saturating<T>);impl_opassign!(impl<T>DivAssign div_assign for Saturating<T>);impl_opassign!(impl<T>RemAssign rem_assign for Saturating<T>);impl_opassign!(impl<T>BitAndAssign bitand_assign for Saturating<T>);impl_opassign!(impl<T>BitOrAssign bitor_assign for Saturating<T>);impl_opassign!(impl<T>BitXorAssign bitxor_assign for Saturating<T>);impl<T>Not for Saturating<T>where T:Not<Output=T>{type Output=Self;fn not(self)->Self::Output{Self(Not::not(self.0))}}macro_rules!impl_int_base_for_saturating{($($t:ty)*)=>{$(impl Add for Saturating<$t>{type Output=Self;fn add(self,rhs:Self)->Self::Output{Self(self.0 .saturating_add(rhs.0))}}impl Sub for Saturating<$t>{type Output=Self;fn sub(self,rhs:Self)->Self::Output{Self(self.0 .saturating_sub(rhs.0))}}impl Mul for Saturating<$t>{type Output=Self;fn mul(self,rhs:Self)->Self::Output{Self(self.0 .saturating_mul(rhs.0))}}impl AddAssign for Saturating<$t>{fn add_assign(&mut self,rhs:Self){*self=Add::add(*self,rhs);}}impl SubAssign for Saturating<$t>{fn sub_assign(&mut self,rhs:Self){*self=Sub::sub(*self,rhs);}}impl MulAssign for Saturating<$t>{fn mul_assign(&mut self,rhs:Self){*self=Mul::mul(*self,rhs);}}impl IntBase for Saturating<$t>{type Error=<$t as IntBase>::Error;fn div_euclid(self,rhs:Self)->Self{Self(self.0 .div_euclid(rhs.0))}fn rem_euclid(self,rhs:Self)->Self{Self(self.0 .rem_euclid(rhs.0))}fn pow(self,exp:u32)->Self{Self(self.0 .saturating_pow(exp))}fn from_str_radix(src:&str,radix:u32)->Result<Self,Self::Error>{<$t as IntBase>::from_str_radix(src,radix).map(Self)}fn ilog(self,base:Self)->u32{self.0 .ilog(base.0)}fn ilog2(self)->u32{self.0 .ilog2()}fn ilog10(self)->u32{self.0 .ilog10()}}impl From<$t>for Saturating<$t>{fn from(t:$t)->Self{Self(t)}})*};}impl_int_base_for_saturating!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);macro_rules!impl_unsigned_signed_for_saturating{($($unsigned:ident$signed:ident)*)=>{$(impl Unsigned for Saturating<$unsigned>{type Signed=Saturating<$signed>;fn signed(self)->Self::Signed{Saturating(TryFrom::try_from(self.0).ok().unwrap_or_else($signed::maximum))}fn abs_diff(self,other:Self)->Self{Self(self.0 .abs_diff(other.0))}fn next_power_of_two(self)->Self{Self(self.0 .next_power_of_two())}fn gcd(self,other:Self)->Self{Self(self.0 .gcd(other.0))}}impl Signed for Saturating<$signed>{type Unsigned=Saturating<$unsigned>;fn unsigned(self)->Self::Unsigned{Saturating(TryFrom::try_from(self.0).ok().unwrap_or_else($unsigned::minimum))}fn abs(self)->Self{Self(self.0 .saturating_abs())}fn abs_diff(self,other:Self)->Self::Unsigned{Saturating(self.0 .abs_diff(other.0))}fn is_negative(self)->bool{self.0 .is_negative()}fn is_positive(self)->bool{self.0 .is_positive()}fn signum(self)->Self{Self(self.0 .signum())}}impl Neg for Saturating<$signed>{type Output=Self;fn neg(self)->Self::Output{Self(self.0 .saturating_neg())}})*};}impl_unsigned_signed_for_saturating!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);macro_rules!impl_binary_repr_for_saturating{($($t:ty)*)=>{$(impl Shl<u32>for Saturating<$t>{type Output=Self;fn shl(self,rhs:u32)->Self::Output{Self(self.0 .checked_shl(rhs).unwrap_or(0))}}impl Shr<u32>for Saturating<$t>{type Output=Self;fn shr(self,rhs:u32)->Self::Output{Self(self.0 .checked_shr(rhs).unwrap_or(0))}}impl ShlAssign<u32>for Saturating<$t>{fn shl_assign(&mut self,rhs:u32){*self=Shl::shl(*self,rhs);}}impl ShrAssign<u32>for Saturating<$t>{fn shr_assign(&mut self,rhs:u32){*self=Shr::shr(*self,rhs);}}impl BinaryRepr for Saturating<$t>{fn count_ones(self)->u32{self.0 .count_ones()}fn count_zeros(self)->u32{self.0 .count_zeros()}fn leading_ones(self)->u32{self.0 .leading_ones()}fn leading_zeros(self)->u32{self.0 .leading_zeros()}fn reverse_bits(self)->Self{Self(self.0 .reverse_bits())}fn rotate_left(self,n:u32)->Self{Self(self.0 .rotate_left(n))}fn rotate_right(self,n:u32)->Self{Self(self.0 .rotate_right(n))}fn swap_bytes(self)->Self{Self(self.0 .swap_bytes())}fn trailing_ones(self)->u32{self.0 .trailing_ones()}fn trailing_zeros(self)->u32{self.0 .trailing_zeros()}})*};}impl_binary_repr_for_saturating!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);#[derive(Default,PartialEq,Eq,PartialOrd,Ord,Hash,Clone,Copy)]#[repr(transparent)]#[doc=" Wrapper type of arithmetic `wrapping_*` operations."]pub struct Wrapping<T>(pub T);impl<T>fmt::Debug for Wrapping<T>where T:fmt::Debug{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{T::fmt(&self.0,f)}}impl<T>Bounded for Wrapping<T>where T:Bounded{fn maximum()->Self{Self(T::maximum())}fn minimum()->Self{Self(T::minimum())}}impl<T>Zero for Wrapping<T>where T:Zero{fn zero()->Self{Self(T::zero())}}impl<T>One for Wrapping<T>where T:One{fn one()->Self{Self(T::one())}}impl<T>FromStr for Wrapping<T>where T:FromStr{type Err=T::Err;fn from_str(s:&str)->Result<Self,Self::Err>{T::from_str(s).map(Self)}}impl<T>Display for Wrapping<T>where T:Display{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{T::fmt(&self.0,f)}}impl<T>IterScan for Wrapping<T>where T:IterScan<Output=T>{type Output=Self;fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{T::scan(iter).map(Self)}}impl_binop!(impl<T>BitAnd bitand for Wrapping<T>);impl_binop!(impl<T>BitOr bitor for Wrapping<T>);impl_binop!(impl<T>BitXor bitxor for Wrapping<T>);impl_opassign!(impl<T>BitAndAssign bitand_assign for Wrapping<T>);impl_opassign!(impl<T>BitOrAssign bitor_assign for Wrapping<T>);impl_opassign!(impl<T>BitXorAssign bitxor_assign for Wrapping<T>);impl<T>Not for Wrapping<T>where T:Not<Output=T>{type Output=Self;fn not(self)->Self::Output{Self(Not::not(self.0))}}macro_rules!impl_int_base_for_wrapping{($($t:ty)*)=>{$(impl Add for Wrapping<$t>{type Output=Self;fn add(self,rhs:Self)->Self::Output{Self(self.0 .wrapping_add(rhs.0))}}impl Sub for Wrapping<$t>{type Output=Self;fn sub(self,rhs:Self)->Self::Output{Self(self.0 .wrapping_sub(rhs.0))}}impl Mul for Wrapping<$t>{type Output=Self;fn mul(self,rhs:Self)->Self::Output{Self(self.0 .wrapping_mul(rhs.0))}}impl Div for Wrapping<$t>{type Output=Self;fn div(self,rhs:Self)->Self::Output{Self(self.0 .wrapping_div(rhs.0))}}impl Rem for Wrapping<$t>{type Output=Self;fn rem(self,rhs:Self)->Self::Output{Self(self.0 .wrapping_rem(rhs.0))}}impl AddAssign for Wrapping<$t>{fn add_assign(&mut self,rhs:Self){*self=Add::add(*self,rhs);}}impl SubAssign for Wrapping<$t>{fn sub_assign(&mut self,rhs:Self){*self=Sub::sub(*self,rhs);}}impl MulAssign for Wrapping<$t>{fn mul_assign(&mut self,rhs:Self){*self=Mul::mul(*self,rhs);}}impl DivAssign for Wrapping<$t>{fn div_assign(&mut self,rhs:Self){*self=Div::div(*self,rhs);}}impl RemAssign for Wrapping<$t>{fn rem_assign(&mut self,rhs:Self){*self=Rem::rem(*self,rhs);}}impl IntBase for Wrapping<$t>{type Error=<$t as IntBase>::Error;fn div_euclid(self,rhs:Self)->Self{Self(self.0 .wrapping_div_euclid(rhs.0))}fn rem_euclid(self,rhs:Self)->Self{Self(self.0 .wrapping_rem_euclid(rhs.0))}fn pow(self,exp:u32)->Self{Self(self.0 .wrapping_pow(exp))}fn from_str_radix(src:&str,radix:u32)->Result<Self,Self::Error>{<$t as IntBase>::from_str_radix(src,radix).map(Self)}fn ilog(self,base:Self)->u32{self.0 .ilog(base.0)}fn ilog2(self)->u32{self.0 .ilog2()}fn ilog10(self)->u32{self.0 .ilog10()}}impl From<$t>for Wrapping<$t>{fn from(t:$t)->Self{Self(t)}})*};}impl_int_base_for_wrapping!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);macro_rules!impl_unsigned_signed_for_wrapping{($($unsigned:ident$signed:ident)*)=>{$(impl Unsigned for Wrapping<$unsigned>{type Signed=Wrapping<$signed>;fn signed(self)->Self::Signed{Wrapping(self.0 .signed())}fn abs_diff(self,other:Self)->Self{Self(self.0 .abs_diff(other.0))}fn next_power_of_two(self)->Self{Self(self.0 .next_power_of_two())}fn gcd(self,other:Self)->Self{Self(self.0 .gcd(other.0))}}impl Signed for Wrapping<$signed>{type Unsigned=Wrapping<$unsigned>;fn unsigned(self)->Self::Unsigned{Wrapping(self.0 .unsigned())}fn abs(self)->Self{Self(self.0 .wrapping_abs())}fn abs_diff(self,other:Self)->Self::Unsigned{Wrapping(self.0 .abs_diff(other.0))}fn is_negative(self)->bool{self.0 .is_negative()}fn is_positive(self)->bool{self.0 .is_positive()}fn signum(self)->Self{Self(self.0 .signum())}}impl Neg for Wrapping<$signed>{type Output=Self;fn neg(self)->Self::Output{Self(self.0 .wrapping_neg())}})*};}impl_unsigned_signed_for_wrapping!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);macro_rules!impl_binary_repr_for_wrapping{($($t:ty)*)=>{$(impl Shl<u32>for Wrapping<$t>{type Output=Self;fn shl(self,rhs:u32)->Self::Output{Self(self.0 .wrapping_shl(rhs))}}impl Shr<u32>for Wrapping<$t>{type Output=Self;fn shr(self,rhs:u32)->Self::Output{Self(self.0 .wrapping_shr(rhs))}}impl ShlAssign<u32>for Wrapping<$t>{fn shl_assign(&mut self,rhs:u32){*self=Shl::shl(*self,rhs);}}impl ShrAssign<u32>for Wrapping<$t>{fn shr_assign(&mut self,rhs:u32){*self=Shr::shr(*self,rhs);}}impl BinaryRepr for Wrapping<$t>{fn count_ones(self)->u32{self.0 .count_ones()}fn count_zeros(self)->u32{self.0 .count_zeros()}fn leading_ones(self)->u32{self.0 .leading_ones()}fn leading_zeros(self)->u32{self.0 .leading_zeros()}fn reverse_bits(self)->Self{Self(self.0 .reverse_bits())}fn rotate_left(self,n:u32)->Self{Self(self.0 .rotate_left(n))}fn rotate_right(self,n:u32)->Self{Self(self.0 .rotate_right(n))}fn swap_bytes(self)->Self{Self(self.0 .swap_bytes())}fn trailing_ones(self)->u32{self.0 .trailing_ones()}fn trailing_zeros(self)->u32{self.0 .trailing_zeros()}})*};}impl_binary_repr_for_wrapping!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);}
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::bitdp::{BitDp,Combinations,Subsets};
mod bitdp{#[derive(Clone,Copy,PartialEq,Eq,Default,Debug)]pub struct BitDp(pub usize);impl BitDp{pub fn is_element(mask:usize,x:usize)->bool{mask&1<<x!=0}pub fn elements(self,mask:usize)->impl Iterator<Item=usize>{(0..self.0).filter(move|&x|Self::is_element(mask,x))}pub fn not_elements(self,mask:usize)->impl Iterator<Item=usize>{(0..self.0).filter(move|&x|!Self::is_element(mask,x))}pub fn is_subset(mask:usize,elements:usize)->bool{mask&elements==elements}fn next_subset(mask:usize,cur:usize)->Option<usize>{if cur==0{None}else{Some((cur-1)&mask)}}pub fn subsets(mask:usize)->Subsets{Subsets{mask,cur:Some(mask)}}fn next_combination(cur:usize)->Option<usize>{if cur==0{None}else{let x=cur&(!cur+1);let y=cur+x;Some(((cur&!y)/x/2)|y)}}pub fn combinations(self,k:usize)->Combinations{Combinations{mask:1<<self.0,cur:Some((1<<k)-1)}}}#[derive(Debug,Clone)]pub struct Subsets{mask:usize,cur:Option<usize>}impl Iterator for Subsets{type Item=usize;fn next(&mut self)->Option<Self::Item>{if let Some(cur)=self.cur{self.cur=BitDp::next_subset(self.mask,cur);Some(cur)}else{None}}}#[derive(Debug,Clone)]pub struct Combinations{mask:usize,cur:Option<usize>}impl Iterator for Combinations{type Item=usize;fn next(&mut self)->Option<Self::Item>{if let Some(cur)=self.cur{if cur<self.mask{self.cur=BitDp::next_combination(cur);Some(cur)}else{None}}else{None}}}}
yukicoder

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