#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::*; #[allow(dead_code)] fn getline() -> String { let mut ret = String::new(); std::io::stdin().read_line(&mut ret).ok(); return ret; } fn get_word() -> String { let mut stdin = std::io::stdin(); let mut u8b: [u8; 1] = [0]; loop { let mut buf: Vec = Vec::with_capacity(16); loop { let res = stdin.read(&mut u8b); if res.is_err() || res.ok().unwrap() == 0 || u8b[0] <= ' ' as u8 { break; } else { buf.push(u8b[0]); } } if buf.len() >= 1 { let ret = std::string::String::from_utf8(buf).unwrap(); return ret; } } } fn parse(s: &str) -> T { s.parse::().ok().unwrap() } #[allow(dead_code)] fn get() -> T { parse(&get_word()) } /** * Strong connected components. * Verified by: yukicoder No.470 (http://yukicoder.me/submissions/145785) */ 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) */ 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) } fn main() { let n = get(); let u: Vec> = (0 .. n).map(|_| get_word().chars().collect()).collect(); { let mut res = HashSet::new(); for i in 0 .. n { res.insert(u[i][0]); res.insert(u[i][2]); if res.len() < i + 1 { println!("Impossible"); return; } } } assert!(n <= 52); let mut pool = Vec::new(); for i in 0 .. n { pool.push((u[i][0], u[i][1 .. 3].to_vec(), i as i32 + 1)); pool.push((u[i][2], u[i][0 .. 2].to_vec(), - (i as i32 + 1))); } let mut interfere = Vec::new(); for i in 0 .. 2 * n { for j in 0 .. 2 * n { if i == j { continue; } let t1 = &pool[i]; let t2 = &pool[j]; if t1.0 == t2.0 || t1.1 == t2.1 { interfere.push((-t1.2, -t2.2)); } } } let res = match two_sat(n, &interfere) { None => { println!("Impossible"); return; }, Some(x) => x, }; for i in 0 .. n { if res[i] { println!("{} {}{}", u[i][0], u[i][1], u[i][2]); } else { println!("{}{} {}", u[i][0], u[i][1], u[i][2]); } } }