use std::cmp::*; 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 ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } // Strong connected components. // Verified by: yukicoder No.470 (http://yukicoder.me/submissions/145785) // ABC214-H (https://atcoder.jp/contests/abc214/submissions/25082618) struct SCC { n: usize, ncc: usize, g: Vec>, // graph in adjacent list rg: Vec>, // reverse graph cmp: Vec, // topological order } impl SCC { fn new(n: usize) -> Self { SCC { n: n, ncc: n + 1, g: vec![Vec::new(); n], rg: vec![Vec::new(); n], cmp: vec![0; n], } } fn add_edge(&mut self, from: usize, to: usize) { self.g[from].push(to); self.rg[to].push(from); } fn dfs(&self, v: usize, used: &mut [bool], vs: &mut Vec) { used[v] = true; for &w in self.g[v].iter() { if !used[w] { self.dfs(w, used, vs); } } vs.push(v); } fn rdfs(&self, v: usize, k: usize, used: &mut [bool], cmp: &mut [usize]) { used[v] = true; cmp[v] = k; for &w in self.rg[v].iter() { if !used[w] { self.rdfs(w, k, used, cmp); } } } fn scc(&mut self) -> usize { let n = self.n; let mut used = vec![false; n]; let mut vs = Vec::new(); let mut cmp = vec![0; n]; for v in 0 .. n { if !used[v] { self.dfs(v, &mut used, &mut vs); } } for u in used.iter_mut() { *u = false; } let mut k = 0; for &t in vs.iter().rev() { if !used[t] { self.rdfs(t, k, &mut used, &mut cmp); k += 1; } } self.ncc = k; self.cmp = cmp; k } #[allow(dead_code)] fn top_order(&self) -> Vec { assert!(self.ncc <= self.n); self.cmp.clone() } /* * Returns a dag whose vertices are scc's, and whose edges are those of the original graph. */ #[allow(dead_code)] fn dag(&self) -> Vec> { assert!(self.ncc <= self.n); let ncc = self.ncc; let mut ret = vec![vec![]; ncc]; let n = self.n; for i in 0 .. n { for &to in self.g[i].iter() { if self.cmp[i] != self.cmp[to] { assert!(self.cmp[i] < self.cmp[to]); ret[self.cmp[i]].push(self.cmp[to]); } } } ret.into_iter().map(|mut v| { v.sort_unstable(); v.dedup(); v }).collect() } #[allow(dead_code)] fn rdag(&self) -> Vec> { assert!(self.ncc <= self.n); let ncc = self.ncc; let mut ret = vec![vec![]; ncc]; let n = self.n; for i in 0 .. n { for &to in self.g[i].iter() { if self.cmp[i] != self.cmp[to] { assert!(self.cmp[i] < self.cmp[to]); ret[self.cmp[to]].push(self.cmp[i]); } } } ret.into_iter().map(|mut v| { v.sort_unstable(); v.dedup(); v }).collect() } } fn main() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););} input! { n: usize, x: [i64; n], a: [i64; n], } let mut coo = vec![]; for i in 0..n { coo.extend_from_slice(&[x[i], x[i] + a[i], x[i] - a[i]]); } coo.sort(); coo.dedup(); let m = coo.len(); let mut scc = SCC::new(m); for i in 0..n { let from = coo.binary_search(&x[i]).unwrap(); for &to in &[x[i] - a[i], x[i] + a[i]] { let to = coo.binary_search(&to).unwrap(); scc.add_edge(from, to); } } let ncc = scc.scc(); let mut ma = vec![0; ncc]; let top_ord = scc.top_order(); for i in 0..n { ma[top_ord[i]] = max(ma[top_ord[i]], x[i]); } let dag = scc.dag(); for i in (0..ncc).rev() { for &j in &dag[i] { ma[i] = max(ma[i], ma[j]); } } for i in 0..n { puts!("{}\n", ma[top_ord[i]]); } }