結果
| 問題 | No.5010 Better Mo's Algorithm is Needed!! (Unweighted) |
| ユーザー |
 to-omer
|
| 提出日時 | 2022-12-17 14:54:18 |
| 言語 | Rust (1.77.0 + proconio) |
| 結果 |
AC
|
| 実行時間 | 4,932 ms / 5,000 ms |
| コード長 | 28,823 bytes |
| コンパイル時間 | 3,439 ms |
| 実行使用メモリ | 18,072 KB |
| スコア | 18,623,355,773 |
| 最終ジャッジ日時 | 2022-12-17 15:05:00 |
| 合計ジャッジ時間 | 639,480 ms |
|
ジャッジサーバーID （参考情報） |
judge13 / judge10 |
| 純コード判定しない問題か言語 |
（要ログイン）
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 | 4,928 ms
17,856 KB |
| testcase_01 | AC | 4,929 ms
17,980 KB |
| testcase_02 | AC | 4,928 ms
17,884 KB |
| testcase_03 | AC | 4,928 ms
17,900 KB |
| testcase_04 | AC | 4,928 ms
17,868 KB |
| testcase_05 | AC | 4,928 ms
17,836 KB |
| testcase_06 | AC | 4,928 ms
17,956 KB |
| testcase_07 | AC | 4,928 ms
17,808 KB |
| testcase_08 | AC | 4,927 ms
17,828 KB |
| testcase_09 | AC | 4,929 ms
17,972 KB |
| testcase_10 | AC | 4,929 ms
17,784 KB |
| testcase_11 | AC | 4,929 ms
17,920 KB |
| testcase_12 | AC | 4,927 ms
17,916 KB |
| testcase_13 | AC | 4,928 ms
17,908 KB |
| testcase_14 | AC | 4,928 ms
17,940 KB |
| testcase_15 | AC | 4,929 ms
17,832 KB |
| testcase_16 | AC | 4,929 ms
17,952 KB |
| testcase_17 | AC | 4,929 ms
17,820 KB |
| testcase_18 | AC | 4,928 ms
17,824 KB |
| testcase_19 | AC | 4,929 ms
17,804 KB |
| testcase_20 | AC | 4,930 ms
17,824 KB |
| testcase_21 | AC | 4,928 ms
17,884 KB |
| testcase_22 | AC | 4,928 ms
17,872 KB |
| testcase_23 | AC | 4,929 ms
17,900 KB |
| testcase_24 | AC | 4,930 ms
17,780 KB |
| testcase_25 | AC | 4,928 ms
17,900 KB |
| testcase_26 | AC | 4,928 ms
17,984 KB |
| testcase_27 | AC | 4,927 ms
17,908 KB |
| testcase_28 | AC | 4,929 ms
17,848 KB |
| testcase_29 | AC | 4,927 ms
17,968 KB |
| testcase_30 | AC | 4,928 ms
17,996 KB |
| testcase_31 | AC | 4,927 ms
17,904 KB |
| testcase_32 | AC | 4,929 ms
17,884 KB |
| testcase_33 | AC | 4,931 ms
17,912 KB |
| testcase_34 | AC | 4,931 ms
17,768 KB |
| testcase_35 | AC | 4,927 ms
17,892 KB |
| testcase_36 | AC | 4,929 ms
17,912 KB |
| testcase_37 | AC | 4,927 ms
17,928 KB |
| testcase_38 | AC | 4,928 ms
17,944 KB |
| testcase_39 | AC | 4,928 ms
17,920 KB |
| testcase_40 | AC | 4,929 ms
17,836 KB |
| testcase_41 | AC | 4,928 ms
17,780 KB |
| testcase_42 | AC | 4,928 ms
17,888 KB |
| testcase_43 | AC | 4,928 ms
17,900 KB |
| testcase_44 | AC | 4,927 ms
17,928 KB |
| testcase_45 | AC | 4,928 ms
17,976 KB |
| testcase_46 | AC | 4,928 ms
17,916 KB |
| testcase_47 | AC | 4,928 ms
17,968 KB |
| testcase_48 | AC | 4,927 ms
17,920 KB |
| testcase_49 | AC | 4,928 ms
17,804 KB |
| testcase_50 | AC | 4,928 ms
17,800 KB |
| testcase_51 | AC | 4,928 ms
17,972 KB |
| testcase_52 | AC | 4,927 ms
17,868 KB |
| testcase_53 | AC | 4,927 ms
17,840 KB |
| testcase_54 | AC | 4,929 ms
17,820 KB |
| testcase_55 | AC | 4,929 ms
17,764 KB |
| testcase_56 | AC | 4,928 ms
17,952 KB |
| testcase_57 | AC | 4,929 ms
17,896 KB |
| testcase_58 | AC | 4,928 ms
17,824 KB |
| testcase_59 | AC | 4,929 ms
17,980 KB |
| testcase_60 | AC | 4,927 ms
17,808 KB |
| testcase_61 | AC | 4,929 ms
17,916 KB |
| testcase_62 | AC | 4,928 ms
17,860 KB |
| testcase_63 | AC | 4,929 ms
17,852 KB |
| testcase_64 | AC | 4,928 ms
17,908 KB |
| testcase_65 | AC | 4,928 ms
17,784 KB |
| testcase_66 | AC | 4,927 ms
17,840 KB |
| testcase_67 | AC | 4,928 ms
17,784 KB |
| testcase_68 | AC | 4,928 ms
18,072 KB |
| testcase_69 | AC | 4,932 ms
17,920 KB |
| testcase_70 | AC | 4,927 ms
17,868 KB |
| testcase_71 | AC | 4,929 ms
17,940 KB |
| testcase_72 | AC | 4,931 ms
17,876 KB |
| testcase_73 | AC | 4,928 ms
17,920 KB |
| testcase_74 | AC | 4,928 ms
17,908 KB |
| testcase_75 | AC | 4,929 ms
17,880 KB |
| testcase_76 | AC | 4,930 ms
17,920 KB |
| testcase_77 | AC | 4,927 ms
17,852 KB |
| testcase_78 | AC | 4,929 ms
17,764 KB |
| testcase_79 | AC | 4,927 ms
17,900 KB |
| testcase_80 | AC | 4,930 ms
17,984 KB |
| testcase_81 | AC | 4,927 ms
17,900 KB |
| testcase_82 | AC | 4,928 ms
17,892 KB |
| testcase_83 | AC | 4,928 ms
17,776 KB |
| testcase_84 | AC | 4,929 ms
17,924 KB |
| testcase_85 | AC | 4,928 ms
17,936 KB |
| testcase_86 | AC | 4,929 ms
17,880 KB |
| testcase_87 | AC | 4,929 ms
17,876 KB |
| testcase_88 | AC | 4,929 ms
17,936 KB |
| testcase_89 | AC | 4,927 ms
17,976 KB |
| testcase_90 | AC | 4,928 ms
17,940 KB |
| testcase_91 | AC | 4,927 ms
17,924 KB |
| testcase_92 | AC | 4,928 ms
17,784 KB |
| testcase_93 | AC | 4,928 ms
17,784 KB |
| testcase_94 | AC | 4,929 ms
17,920 KB |
| testcase_95 | AC | 4,929 ms
17,888 KB |
| testcase_96 | AC | 4,929 ms
17,856 KB |
| testcase_97 | AC | 4,927 ms
17,912 KB |
| testcase_98 | AC | 4,929 ms
17,964 KB |
| testcase_99 | AC | 4,928 ms
17,988 KB |
| testcase_100 | AC | 4,928 ms
17,816 KB |
| testcase_101 | AC | 4,929 ms
17,924 KB |
| testcase_102 | AC | 4,928 ms
17,828 KB |
| testcase_103 | AC | 4,928 ms
17,984 KB |
| testcase_104 | AC | 4,928 ms
17,760 KB |
| testcase_105 | AC | 4,928 ms
17,836 KB |
| testcase_106 | AC | 4,928 ms
17,928 KB |
| testcase_107 | AC | 4,928 ms
17,976 KB |
| testcase_108 | AC | 4,928 ms
17,932 KB |
| testcase_109 | AC | 4,928 ms
17,920 KB |
| testcase_110 | AC | 4,928 ms
17,932 KB |
| testcase_111 | AC | 4,928 ms
17,952 KB |
| testcase_112 | AC | 4,928 ms
17,808 KB |
| testcase_113 | AC | 4,929 ms
17,880 KB |
| testcase_114 | AC | 4,929 ms
17,916 KB |
| testcase_115 | AC | 4,927 ms
17,896 KB |
| testcase_116 | AC | 4,930 ms
17,820 KB |
| testcase_117 | AC | 4,929 ms
17,804 KB |
| testcase_118 | AC | 4,928 ms
17,840 KB |
| testcase_119 | AC | 4,929 ms
17,896 KB |
ソースコード
pub fn main() {
crate::prepare!();
sc!(n, q, _wt, _st, w: [usize; n], lr: [(Usize1, usize); q]);
let p = solve(n, q, &w, &lr);
pp!(@it p.iter().map(|i| i + 1));
// check();
}
pub fn check() {
const N: usize = 200000;
const Q: usize = 200000;
const CASE: usize = 3;
let mut sc = 0usize;
let w: Vec<_> = (0..N).map(|_i| 100).collect();
for i in 0..CASE * 3 {
let lr = gen_lr(N, Q, i % 3);
let p = solve(N, Q, &w, &lr);
let t = score(&w, &lr, &p);
eprintln!("t = {:?}", t);
sc += ((1e18 / t as f64).round() as usize).min(10_000_000_000_000_000);
// vis(i, &w, &lr, &p);
}
sc *= 120 / CASE / 3;
eprintln!("sc = {:?}", sc);
}
// pub fn vis(id: usize, w: &[usize], lr: &[(usize, usize)], p: &[usize]) {
// let mut s = vec![0usize; w.len() + 1];
// for (i, &w) in w.iter().enumerate() {
// s[i + 1] += s[i] + w;
// }
// use svg::node::element::path::Data;
// use svg::node::element::Path;
// use svg::Document;
// let mut data = Data::new().move_to((
// s[lr[p[0]].1] as f64 / s[w.len()] as f64,
// s[lr[p[0]].0] as f64 / s[w.len()] as f64,
// ));
// for i in 1..p.len() {
// data = data.line_to((
// s[lr[p[i]].1] as f64 / s[w.len()] as f64,
// s[lr[p[i]].0] as f64 / s[w.len()] as f64,
// ));
// }
// let path = Path::new()
// .set("fill", "none")
// .set("stroke", "black")
// .set("stroke-width", 0.001)
// .set("d", data);
// let document = Document::new().set("viewBox", (0, 0, 1., 1.)).add(path);
// svg::save(format!("path{}.svg", id), &document).unwrap();
// }
pub fn score(w: &[usize], lr: &[(usize, usize)], p: &[usize]) -> usize {
let mut t = 0usize;
let mut s = vec![0usize; w.len() + 1];
for (i, &w) in w.iter().enumerate() {
s[i + 1] += s[i] + w;
}
t += s[lr[p[0]].1] - s[lr[p[0]].0];
for win in p.windows(2) {
let (a, b) = lr[win[0]];
let (c, d) = lr[win[1]];
t += s[a.max(c)] - s[a.min(c)];
t += s[b.max(d)] - s[b.min(d)];
}
t
}
pub fn hilbert_curve_order(mut x: usize, mut y: usize) -> usize {
let m = 30;
let n = 1usize << m;
let mut ord = 0usize;
for k in (0..m).rev() {
let rx = x >> k & 1;
let ry = y >> k & 1;
ord += (1 << k * 2) * (3 * rx ^ ry);
if ry == 0 {
if rx == 1 {
x = n - x - 1;
y = n - y - 1;
}
swap(&mut x, &mut y);
}
}
ord
}
pub fn moore_curve_order(mut x: usize, mut y: usize) -> usize {
assert!(x <= y);
let m = 30;
let n = 1usize << m;
let mut ord = 0usize;
let mut rord = 0usize;
let mut tri = true;
let mut size = 0usize;
for k in (0..m).rev() {
let rx = x >> k & 1;
let ry = y >> k & 1;
if tri {
tri = rx == ry;
ord += (1 << k * 2) * (rx + ry);
} else if size == 0 {
size = 1 << k * 2 + 2;
rord += (1 << k * 2) * (3 * ry ^ rx ^ 1);
if ry == 0 {
x = n - x - 1;
y = n - y - 1;
}
} else {
rord += (1 << k * 2) * (3 * rx ^ ry);
if rord < 1 << k * 2 {
rord += size;
}
rord -= 1 << k * 2;
if ry == 0 {
if rx == 1 {
x = n - x - 1;
y = n - y - 1;
}
swap(&mut x, &mut y);
}
}
}
ord + rord
}
pub fn solve(_n: usize, q: usize, w: &[usize], lr: &[(usize, usize)]) -> Vec<usize> {
let mut sa = SimuratedAnnealing::new()
.minimize()
.set_time_limit(4.9)
.set_start_temp(1.2e4)
.set_end_temp(1e-12);
let mut s = vec![0usize; w.len() + 1];
for (i, &w) in w.iter().enumerate() {
s[i + 1] += s[i] + w;
}
let mut p: Vec<usize> = (0..q).collect();
let ord: Vec<_> = lr
.iter()
.map(|&(l, r)| hilbert_curve_order(s[l], s[r]))
.collect();
p.sort_by_key(|&i| ord[i]);
let mut score = score(&w, &lr, &p);
let mut rng = Xorshift::default();
let mut cnt = 0usize;
while !sa.is_end() {
{
let i = cnt % (q - 2);
let j = (q - 1).min(i + 2 + rng.rand(50) as usize);
let mut nscore = score;
if i == 0 {
nscore -= s[lr[p[i]].1] - s[lr[p[i]].0];
nscore += s[lr[p[j - 1]].1] - s[lr[p[j - 1]].0];
} else {
let (a, b) = lr[p[i - 1]];
let (c, d) = lr[p[i + 0]];
nscore -= s[a.max(c)] - s[a.min(c)];
nscore -= s[b.max(d)] - s[b.min(d)];
let (a, b) = lr[p[i - 1]];
let (c, d) = lr[p[j - 1]];
nscore += s[a.max(c)] - s[a.min(c)];
nscore += s[b.max(d)] - s[b.min(d)];
}
if j < q {
let (a, b) = lr[p[j - 1]];
let (c, d) = lr[p[j + 0]];
nscore -= s[a.max(c)] - s[a.min(c)];
nscore -= s[b.max(d)] - s[b.min(d)];
let (a, b) = lr[p[i]];
let (c, d) = lr[p[j]];
nscore += s[a.max(c)] - s[a.min(c)];
nscore += s[b.max(d)] - s[b.min(d)];
}
if sa.is_accepted(score as _, nscore as _) {
score = nscore;
p[i..j].reverse();
}
}
cnt += 1;
}
eprintln!("cnt = {:?}", cnt);
p
}
pub fn gen_lr(n: usize, q: usize, st: usize) -> Vec<(usize, usize)> {
let mut rng = Xorshift::time();
(0..q)
.map(|_| match (st, rng.rand(2)) {
(0, _) | (2, 0) => {
let x = rng.rand(n as _) as usize;
let y = rng.rand(n as _) as usize;
if x > y {
(y, x + 1)
} else {
(x, y + 1)
}
}
_ => {
let l = rng.rand(n as _) as usize;
let x = rng.rand(n as u64 - l as u64) as usize;
let y = x + l;
(x, y)
}
})
.collect()
}
use std::mem::swap;
#[allow(unused_imports)]use std::{cmp::{Ordering,Reverse},collections::{BTreeMap,BTreeSet,BinaryHeap,HashMap,HashSet,VecDeque}};
mod main_macros{#[doc=" Prepare useful macros."]#[doc=" - `prepare!();`: default (all input scanner (`sc!`, `sv!`) + buf print (`pp!`, `dg!`))"]#[doc=" - `prepare!(?);`: interactive (line scanner (`scln!`) + buf print (`pp!`, `dg!`))"]#[macro_export]macro_rules!prepare{(@output($dol:tt))=>{#[allow(unused_imports)]use std::io::Write as _;let __out=std::io::stdout();#[allow(unused_mut,unused_variables)]let mut __out=std::io::BufWriter::new(__out.lock());#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stdout."]macro_rules!pp{($dol($dol t:tt)*)=>{$dol crate::iter_print!(__out,$dol($dol t)*)}}#[cfg(debug_assertions)]#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stderr. Do nothing in release mode."]macro_rules!dg{($dol($dol t:tt)*)=>{{#[allow(unused_imports)]use std::io::Write as _;let __err=std::io::stderr();#[allow(unused_mut,unused_variables)]let mut __err=std::io::BufWriter::new(__err.lock());$dol crate::iter_print!(__err,$dol($dol t)*);let _=__err.flush();}}}#[cfg(not(debug_assertions))]#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stderr. Do nothing in release mode."]macro_rules!dg{($dol($dol t:tt)*)=>{}}};(@normal($dol:tt))=>{let __in_buf=read_stdin_all_unchecked();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);#[allow(unused_macros)]macro_rules!sc{($dol($dol t:tt)*)=>{$dol crate::scan!(__scanner,$dol($dol t)*)}}#[allow(unused_macros)]macro_rules!sv{($dol($dol t:tt)*)=>{$dol crate::scan_value!(__scanner,$dol($dol t)*)}}};(@interactive($dol:tt))=>{#[allow(unused_macros)]#[doc=" Scan a line, and previous line will be truncated in the next call."]macro_rules!scln{($dol($dol t:tt)*)=>{let __in_buf=read_stdin_line();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);$dol crate::scan!(__scanner,$dol($dol t)*)}}};()=>{$crate::prepare!(@output($));$crate::prepare!(@normal($))};(?)=>{$crate::prepare!(@output($));$crate::prepare!(@interactive($))};}}
pub use self::iter_print::IterPrint;
mod iter_print{use std::{fmt::Display,io::{Error,Write}};pub trait IterPrint{fn iter_print<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=" - `@it2d $expr`: print 2d-iterator"]#[doc=" - `@tup $expr`: print tuple (need to import [`IterPrint`])"]#[doc=" - `@ittup $expr`: print iterative tuple (need to import [`IterPrint`])"]#[doc=" - `$expr`: print expr"]#[doc=" - `{ args... }`: scoped"]#[doc=" - `;`: print `'\\n'`"]#[doc=" - `!`: not print `'\\n'` at the end"]#[macro_export]macro_rules!iter_print{(@@fmt$writer:expr,$sep:expr,$is_head:expr,$lit:literal,$($e:expr),*)=>{if!$is_head{::std::write!($writer,"{}",$sep).expect("io error");}::std::write!($writer,$lit,$($e),*).expect("io error");};(@@item$writer:expr,$sep:expr,$is_head:expr,$e:expr)=>{$crate::iter_print!(@@fmt$writer,$sep,$is_head,"{}",$e);};(@@line_feed$writer:expr$(,)?)=>{::std::writeln!($writer).expect("io error");};(@@it$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,item);}}};(@@it2d$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@it$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@it$writer,$sep,true,item);}};(@@tup$writer:expr,$sep:expr,$is_head:expr,$tuple:expr)=>{IterPrint::iter_print($tuple,&mut$writer,$sep,$is_head).expect("io error");};(@@ittup$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@tup$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@tup$writer,$sep,true,item);}};(@@assert_tag item)=>{};(@@assert_tag it)=>{};(@@assert_tag it2d)=>{};(@@assert_tag tup)=>{};(@@assert_tag ittup)=>{};(@@assert_tag$tag:ident)=>{::std::compile_error!(::std::concat!("invalid tag in `iter_print!`: `",std::stringify!($tag),"`"));};(@@inner$writer:expr,$sep:expr,$is_head:expr,@sep$e:expr,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$e,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@ns$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,"",$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@lf$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,'\n',$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@sp$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,' ',$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@flush$($t:tt)*)=>{$writer.flush().expect("io error");$crate::iter_print!(@@inner$writer,$sep,$is_head,!$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@fmt$lit:literal=>{$($e:expr),*$(,)?}$($t:tt)*)=>{$crate::iter_print!(@@fmt$writer,$sep,$is_head,$lit,$($e),*);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr,$($t:tt)*)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@inner$writer,$sep,false,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr;$($t:tt)*)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@inner$writer,$sep,true,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@inner$writer,$sep,false,);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$($t:tt)*)=>{::std::compile_error!(::std::concat!("invalid expr in `iter_print!`: `",std::stringify!($($t)*),"`"));};(@@inner$writer:expr,$sep:expr,$is_head:expr,,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,;$($t:tt)*)=>{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,!$(,)?)=>{};(@@inner$writer:expr,$sep:expr,$is_head:expr,!$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,)=>{$crate::iter_print!(@@line_feed$writer);};(@@inner$writer:expr,$sep:expr,$is_head:expr,{$($t:tt)*}$($rest:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*,!);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($rest)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,@item$($t)*);};($writer:expr,$($t:tt)*)=>{{$crate::iter_print!(@@inner$writer,' ',true,$($t)*);}};}}
pub use self::scanner::*;
mod scanner{use std::{iter::{from_fn,repeat_with,FromIterator},marker::PhantomData};pub fn read_stdin_all()->String{use std::io::Read as _;let mut s=String::new();std::io::stdin().read_to_string(&mut s).expect("io error");s}pub fn read_stdin_all_unchecked()->String{use std::io::Read as _;let mut buf=Vec::new();std::io::stdin().read_to_end(&mut buf).expect("io error");unsafe{String::from_utf8_unchecked(buf)}}pub fn read_all(mut reader:impl std::io::Read)->String{let mut s=String::new();reader.read_to_string(&mut s).expect("io error");s}pub fn read_all_unchecked(mut reader:impl std::io::Read)->String{let mut buf=Vec::new();reader.read_to_end(&mut buf).expect("io error");unsafe{String::from_utf8_unchecked(buf)}}pub fn read_stdin_line()->String{let mut s=String::new();std::io::stdin().read_line(&mut s).expect("io error");s}pub trait IterScan:Sized{type Output;fn scan<'a,I:Iterator<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)*$U,$($Rest)*);};($($T:ident)*)=>{iter_scan_tuple_impl!(@inner,$($T)*);};}iter_scan_tuple_impl!(A B C D E F G H I J K);pub struct ScannerIter<'a,'b,T>{inner:&'b mut Scanner<'a>,_marker:std::marker::PhantomData<fn()->T>}impl<'a,'b,T>Iterator for ScannerIter<'a,'b,T>where T:IterScan{type Item=<T as IterScan>::Output;#[inline]fn next(&mut self)->Option<Self::Item>{<T as IterScan>::scan(&mut self.inner.iter)}}#[doc=" - `scan_value!(scanner, ELEMENT)`"]#[doc=""]#[doc=" ELEMENT :="]#[doc=" - `$ty`: IterScan"]#[doc=" - `@$expr`: MarkedIterScan"]#[doc=" - `[ELEMENT; $expr]`: vector"]#[doc=" - `[ELEMENT]`: iterator"]#[doc=" - `($(ELEMENT)*,)`: tuple"]#[macro_export]macro_rules!scan_value{(@repeat$scanner:expr,[$($t:tt)*]$($len:expr)?)=>{::std::iter::repeat_with(||$crate::scan_value!(@inner$scanner,[]$($t)*))$(.take($len).collect::<Vec<_>>())?};(@tuple$scanner:expr,[$([$($args:tt)*])*])=>{($($($args)*,)*)};(@$tag:ident$scanner:expr,[[$($args:tt)*]])=>{$($args)*};(@$tag:ident$scanner:expr,[$($args:tt)*]@$e:expr)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.mscan($e)]])};(@$tag:ident$scanner:expr,[$($args:tt)*]@$e:expr,$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.mscan($e)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*]($($tuple:tt)*)$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@tuple$scanner,[]$($tuple)*)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][@$e:expr;$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[@$e]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][[$($tt:tt)*];$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[[$($tt)*]]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][($($tt:tt)*);$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[($($tt)*)]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][$ty:ty;$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[$ty]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[$($tt)*])]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*]$ty:ty)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.scan::<$ty>()]])};(@$tag:ident$scanner:expr,[$($args:tt)*]$ty:ty,$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.scan::<$ty>()]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*],$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*])=>{::std::compile_error!(::std::stringify!($($args)*))};($scanner:expr,$($t:tt)*)=>{$crate::scan_value!(@inner$scanner,[]$($t)*)}}#[doc=" - `scan!(scanner, $($pat $(: ELEMENT)?),*)`"]#[macro_export]macro_rules!scan{(@assert$p:pat)=>{};(@assert$($p:tt)*)=>{::std::compile_error!(::std::concat!("expected pattern, found `",::std::stringify!($($p)*),"`"));};(@pat$scanner:expr,[][])=>{};(@pat$scanner:expr,[][],$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]$x:ident$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*$x][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]::$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*::][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]&$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*&][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]($($x:tt)*)$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*($($x)*)][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][][$($x:tt)*]$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*[$($x)*]][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]{$($x:tt)*}$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*{$($x)*}][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]:$($t:tt)*)=>{$crate::scan!(@ty$scanner,[$($p)*][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][usize]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]@$e:expr)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*@$e])};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]@$e:expr,$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*@$e],$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]($($x:tt)*)$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*($($x)*)]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*][$($x:tt)*]$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*[$($x)*]]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]$ty:ty)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*$ty])};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]$ty:ty,$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*$ty],$($t)*)};(@let$scanner:expr,[$($p:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::scan!{@assert$($p)*}let$($p)* =$crate::scan_value!($scanner,$($tt)*);$crate::scan!(@pat$scanner,[][]$($t)*)};($scanner:expr,$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)}}#[derive(Debug,Copy,Clone)]pub enum Usize1{}impl IterScan for Usize1{type Output=usize;#[inline]fn scan<'a,I:Iterator<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 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()?)}}}
#[derive(Clone,Debug)]pub struct Xorshift{y:u64}
impl Xorshift{pub fn new(seed:u64)->Self{Xorshift{y:seed}}pub fn time()->Self{let seed=std::time::SystemTime::now().duration_since(std::time::UNIX_EPOCH).ok().unwrap_or_default().as_secs()as u64;Xorshift::new(seed)}#[inline]pub fn rand64(&mut self)->u64{self.y^=self.y<<5;self.y^=self.y>>17;self.y^=self.y<<11;self.y}#[inline]pub fn rand(&mut self,k:u64)->u64{self.rand64()%k}#[inline]pub fn rands(&mut self,k:u64,n:usize)->Vec<u64>{(0..n).map(|_|self.rand(k)).collect::<Vec<_>>()}#[inline]pub fn randf(&mut self)->f64{const UPPER_MASK:u64=0x3FF0_0000_0000_0000;const LOWER_MASK:u64=0x000F_FFFF_FFFF_FFFF;let tmp=UPPER_MASK|(self.rand64()&LOWER_MASK);let result:f64=f64::from_bits(tmp);result-1.0}#[inline]pub fn gen_bool(&mut self,p:f64)->bool{self.randf()<p}pub fn shuffle<T>(&mut self,slice:&mut[T]){let mut n=slice.len();while n>1{let i=self.rand(n as _)as usize;n-=1;slice.swap(i,n);}}}
impl Default for Xorshift{fn default()->Self{Xorshift::new(0x2b99_2ddf_a232_49d6)}}
pub use self::heuristics::SimuratedAnnealing;
mod heuristics{use super::Xorshift;#[derive(Debug)]pub struct SimuratedAnnealing{pub iter_count:usize,pub now:std::time::Instant,pub time:f64,pub temperture:f64,pub log_table:Vec<f64>,pub rand:Xorshift,pub is_maximize:bool,pub start_temp:f64,pub end_temp:f64,pub time_limit:f64,pub update_interval:usize}impl Default for SimuratedAnnealing{fn default()->Self{let now=std::time::Instant::now();let log_table=(0..Self::LOG_TABLE_SIZE).map(|i|((i*2+1)as f64/(Self::LOG_TABLE_SIZE*2)as f64).ln()).collect();Self{iter_count:0,now,time:0.,temperture:3e3,log_table,rand:Xorshift::new(Self::SEED),is_maximize:true,start_temp:3e3,end_temp:1e-8,time_limit:1.99,update_interval:0xff}}}impl SimuratedAnnealing{pub const LOG_TABLE_SIZE:usize=0x10000;pub const SEED:u64=0xbeef_cafe;pub fn new()->Self{Default::default()}pub fn minimize(mut self)->Self{self.is_maximize=false;self}pub fn set_start_temp(mut self,start_temp:f64)->Self{assert_eq!(self.iter_count,0);self.start_temp=start_temp;self.temperture=start_temp;self}pub fn set_end_temp(mut self,end_temp:f64)->Self{self.end_temp=end_temp;self}pub fn set_time_limit(mut self,time_limit:f64)->Self{self.time_limit=time_limit;self}pub fn set_update_interval(mut self,update_interval:usize)->Self{assert!(update_interval>0);self.update_interval=update_interval;self}pub fn is_accepted(&mut self,current_score:f64,next_score:f64)->bool{let diff=if self.is_maximize{next_score-current_score}else{current_score-next_score};diff>=0.||diff>self.log_table[self.rand.rand(Self::LOG_TABLE_SIZE as u64)as usize]*self.temperture}pub fn is_end(&mut self)->bool{self.iter_count+=1;if self.iter_count%self.update_interval==0{self.time=self.now.elapsed().as_secs_f64();let temp_ratio=(self.end_temp-self.start_temp)/self.time_limit;self.temperture=self.start_temp+temp_ratio*self.time;self.time>=self.time_limit}else{false}}}}