#![allow(unused_imports)] use std::cmp::*; use std::collections::*; use std::io::Write; use std::ops::Bound::*; #[allow(unused_macros)] macro_rules! debug { ($($e:expr),*) => { #[cfg(debug_assertions)] $({ let (e, mut err) = (stringify!($e), std::io::stderr()); writeln!(err, "{} = {:?}", e, $e).unwrap() })* }; } fn main() { let n = read::(); if n > 100 { println!("Impossible"); return; } let mut words = vec![]; for i in 0..n { let word = read::().chars().collect::>(); words.push(word); } let mut cons = vec![]; for i in 0..n { let w1 = &words[i]; for j in i + 1..n { let w2 = &words[j]; if w1[0] == w2[0] || w1[1..3] == w2[1..3] { cons.push((i as i32 + 1, j as i32 + 1)); } if w1[0] == w2[2] || w1[1..3] == w2[0..2] { cons.push((i as i32 + 1, -(j as i32 + 1))); } if w1[2] == w2[0] || w1[0..2] == w2[1..3] { cons.push((-(i as i32 + 1), j as i32 + 1)); } if w1[2] == w2[2] || w1[0..2] == w2[0..2] { cons.push((-(i as i32 + 1), -(j as i32 + 1))); } } } if let Some(result) = two_sat(n, &cons) { for i in 0..n { if result[i] { println!("{}{} {}", words[i][0], words[i][1], words[i][2]); } else { println!("{} {}{}", words[i][0], words[i][1], words[i][2]); } } } else { println!("Impossible"); } } fn read() -> T { let mut s = String::new(); std::io::stdin().read_line(&mut s).ok(); s.trim().parse().ok().unwrap() } fn read_vec() -> Vec { read::() .split_whitespace() .map(|e| e.parse().ok().unwrap()) .collect() } 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![HashSet::new(); 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]].insert(self.cmp[to]); } } } ret.into_iter() .map(|set| set.into_iter().collect()) .collect() } #[allow(dead_code)] fn rdag(&self) -> Vec> { assert!(self.ncc <= self.n); let ncc = self.ncc; let mut ret = vec![HashSet::new(); 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]].insert(self.cmp[i]); } } } ret.into_iter() .map(|set| set.into_iter().collect()) .collect() } } /** * 2-SAT solver. * n: the number of variables (v_1, ..., v_n) * cons: constraints, given in 2-cnf * i (1 <= i <= n) means v_i, -i (1 <= i <= n) means not v_i. * Returns: None if there's no assignment that satisfies cons. * Otherwise, it returns an assignment that safisfies cons. (true: true, false: false) * Dependencies: SCC.rs * Verified by: Codeforces #400 D * (http://codeforces.com/contest/776/submission/24957215) */ fn two_sat(n: usize, cons: &[(i32, i32)]) -> Option> { let mut scc = SCC::new(2 * n); let ni = n as i32; for &(c1, c2) in cons.iter() { let x = if c1 > 0 { c1 - 1 + ni } else { -c1 - 1 } as usize; let y = if c2 > 0 { c2 - 1 } else { -c2 - 1 + ni } as usize; scc.add_edge(x, y); scc.add_edge((y + n) % (2 * n), (x + n) % (2 * n)); } scc.scc(); let mut result = vec![false; n]; let top_ord = scc.top_order(); for i in 0..n { if top_ord[i] == top_ord[i + n] { return None; } result[i] = top_ord[i] > top_ord[i + n]; } Some(result) }