#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr,) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => (read_value!($next, usize) - 1); ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); read_value!($next, [$t; len]) }}; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } // https://github.com/kth-competitive-programming/kactl/blob/main/content/data-structures/LineContainer.h // Verified by: https://judge.yosupo.jp/submission/63195 type Coord = i64; #[derive(Clone, Debug, Default)] struct MinCHT { lines: std::collections::BTreeSet, } #[derive(Copy, Clone, Ord, PartialOrd, Eq, PartialEq, Debug)] struct Point(Coord); #[derive(Eq, Debug, Clone)] struct Entry(Coord, Coord, std::cell::Cell); impl PartialEq for Entry { fn eq(&self, o: &Self) -> bool { (self.0, self.1) == (o.0, o.1) } } impl PartialOrd for Entry { fn partial_cmp(&self, o: &Self) -> Option { (o.0, o.1).partial_cmp(&(self.0, self.1)) } } impl Ord for Entry { fn cmp(&self, o: &Self) -> std::cmp::Ordering { (o.0, o.1).cmp(&(self.0, self.1)) } } impl std::borrow::Borrow for Entry { fn borrow(&self) -> &Point { unsafe { &*self.2.as_ptr() } } } impl MinCHT { const INF: i64 = 1 << 62; fn div(a: Coord, b: Coord) -> Coord { a / b - if (a ^ b) < 0 && a % b != 0 { 1 } else { 0 } } // Should we erase y from lines? // As well as modifying x.2 to the appropriate value fn isect(x: &Entry, y: Option<&Entry>) -> bool { let y = if let Some(y) = y { y } else { x.2.set(Point(Self::INF)); return false; }; assert!(!std::ptr::eq(&x.2, &y.2)); if x.0 == y.0 { let p = if x.1 < y.1 { Self::INF } else { -Self::INF }; x.2.set(Point(p)); } else { x.2.set(Point(Self::div(y.1 - x.1, x.0 - y.0))); } x.2 >= y.2 } fn new() -> Self { Default::default() } // Adds y = ax + b fn add(&mut self, a: Coord, b: Coord) { let e = Entry(a, b, std::cell::Cell::new(Point(0))); if self.lines.contains(&e) { return; } self.lines.insert(e.clone()); loop { let y = self.lines.get(&e).unwrap(); let z = self.lines.range(Entry(a, b - 1, std::cell::Cell::new(Point(0)))..).next(); if Self::isect(y, z) { let z = z.unwrap().clone(); self.lines.remove(&z); } else { break; } } let mut now; { let y = self.lines.range(e.clone()..).next(); let x = self.lines.range(..e.clone()).rev().next(); if let Some(x) = x { now = x.clone(); if Self::isect(x, y) { let y = y.unwrap().clone(); self.lines.remove(&y); let xx = self.lines.range(..e.clone()).rev().next().unwrap(); let yy = self.lines.range(e.clone()..).next(); Self::isect(xx, yy); } } else { return; } } loop { let y = self.lines.range(now.clone()..).next(); let x = self.lines.range(..now.clone()).rev().next(); if let Some(x) = x { if Self::isect(x, y) { let x = x.clone(); let y = y.unwrap().clone(); self.lines.remove(&y); let xx = self.lines.range(..now.clone()).rev().next().unwrap(); let yy = self.lines.range(now.clone()..).next(); Self::isect(xx, yy); now = x; continue; } } break; } } fn query(&self, x: Coord) -> Coord { assert!(!self.lines.is_empty()); let &Entry(a, b, _) = self.lines.range(Point(x)..).next().unwrap(); a * x + b } } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); } fn solve() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););} #[allow(unused)] macro_rules! putvec { ($v:expr) => { for i in 0..$v.len() { puts!("{}{}", $v[i], if i + 1 == $v.len() {"\n"} else {" "}); } } } input! { n: usize, a: [i64; n], } let mut dp = vec![0; n]; let mut cht = MinCHT::new(); for i in 0..n { dp[i] = if i > 0 { max(0, -cht.query(a[i])) } else { 0 }; cht.add(-a[i], -dp[i]); } let &ans = dp.iter().max().unwrap(); println!("{}", ans); }