// -*- coding:utf-8-unix -*- // #![feature(map_first_last)] #![allow(dead_code)] #![allow(unused_imports)] #![allow(unused_macros)] use core::num; use std::cmp::*; use std::*; const INF: i64 = 1223372036854775807; const UINF: usize = INF as usize; const LINF: i64 = 2147483647; const INF128: i128 = 1223372036854775807000000000000; // const MOD: i64 = 1000000007; const MOD: i64 = 998244353; const UMOD: usize = MOD as usize; const M_PI: f64 = 3.14159265358979323846; // const MOD: i64 = INF; use cmp::Ordering::*; use std::collections::*; use std::io::stdin; use std::io::stdout; use std::io::Write; macro_rules! p { ($x:expr) => { println!("{}", $x); }; } macro_rules! d { ($x:expr) => { println!("{:?}", $x); }; } #[allow(unused_macros)] pub mod macros { macro_rules! min { ($x: expr) => { $x }; ($x: expr, $($xs: expr),+) => {{ let y = macros::min!($($xs),+); std::cmp::min($x, y) } }} macro_rules! max { ($x: expr) => { $x }; ($x: expr, $($xs: expr),+) => {{ let y = macros::max!($($xs),+); std::cmp::max($x, y) } }} macro_rules! chmin { ($x: expr, $($xs: expr),+) => {{ let y = macros::min!($($xs),+); if $x > y { $x = y; true } else { false } }}} macro_rules! chmax { ($x: expr, $($xs: expr),+) => {{ let y = macros::max!($($xs),+); if $x < y { $x = y; true } else { false } }}} macro_rules! multi_vec { ($element: expr; ($len: expr, $($lens: expr),*)) => ( vec![macros::multi_vec![$element; ($($lens),*)]; $len] ); ($element: expr; ($len: expr)) => ( vec![$element; $len] ); } macro_rules! multi_box_array { ($element: expr; ($len: expr, $($lens: expr),*)) => ( vec![macros::multi_box_array![$element; ($($lens),*)]; $len].into_boxed_slice() ); ($element: expr; ($len: expr)) => ( vec![$element; $len].into_boxed_slice() ); } #[allow(unused_imports)] pub(super) use {chmax, chmin, max, min, multi_box_array, multi_vec}; } use macros::*; fn main() { solve(); } // use str::Chars; #[allow(dead_code)] fn read() -> T { let mut s = String::new(); std::io::stdin().read_line(&mut s).ok(); s.trim().parse().ok().unwrap() } #[allow(dead_code)] fn readi() -> (i64) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); iter.next().unwrap().parse::().unwrap() } #[allow(dead_code)] fn read_vec() -> Vec { read::() .split_whitespace() .map(|e| e.parse().ok().unwrap()) .collect() } #[allow(dead_code)] fn read_mat(n: u32) -> Vec> { (0..n).map(|_| read_vec()).collect() } #[allow(dead_code)] fn readii() -> (i64, i64) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } #[allow(dead_code)] fn readiii() -> (i64, i64, i64) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } #[allow(dead_code)] fn readuu() -> (usize, usize) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } #[allow(dead_code)] fn readff() -> (f64, f64) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } fn readcc() -> (char, char) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } fn readuuu() -> (usize, usize, usize) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } #[allow(dead_code)] fn readiiii() -> (i64, i64, i64, i64) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } #[allow(dead_code)] fn readuuuu() -> (usize, usize, usize, usize) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } fn djikstra(graph: &Vec>, start: usize) -> Vec { let mut dist = vec![INF as usize; graph.len()]; let mut heap = BinaryHeap::new(); heap.push(Reverse((0 as usize, start))); dist[start] = 0; while let Some(Reverse(x)) = heap.pop() { let cost = x.0; let v = x.1; if cost > dist[v] { continue; } for edge in &graph[v] { let nc = max(cost, edge.1); let nv = edge.0; if nc < dist[nv] { heap.push(Reverse((nc, nv))); dist[nv] = nc; } } } return dist; } fn solve() { let n: usize = read(); let mut data = vec![]; for i in 0..n { let (x, y, t) = readiii(); data.push((x, y, t)); } let mut graph = vec![vec![(0 as usize, 0 as usize); (0) as usize]; (n) as usize]; for i in 0..n { for j in 0..n { if i == j { continue; } let (x1, y1, t1) = data[i]; let (x2, y2, t2) = data[j]; let r1 = ((x1 * x1 + y1 * y1) as f64).sqrt(); let r2 = ((x2 * x2 + y2 * y2) as f64).sqrt(); let euc_dist = ((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)) as f64; if t1 != t2 { let d = ((r1 - r2).abs() * (r1 - r2).abs()).ceil() as usize; graph[i].push((j, d)); } else { graph[i].push((j, euc_dist as usize)); } } } let d = djikstra(&graph, 0); println!("{}", d[n - 1]); return; }