fn main() { let mut io = IO::new(); input!{ from io, n: usize, s: [Usize1; n], t: [Usize1; n], u: [usize; n], } let mut sat = TwoSat::new(n*n); for i in 0..n { let f = (u[i] & 1) == 1; let g = (u[i] & 2) == 2; for j in 0..n { sat.add_clause(s[i] * n + j, !f, j * n + t[i], !g); } } if let Some(l) = sat.solve() { for h in l.chunks(n) { io.iterln(h.iter().map(|&x| x as i32), " "); } } else { io.println(-1); } } // ------------ 2-SAT start ------------ // * verified: https://judge.yosupo.jp/submission/26463 // ------------ Strongly Connected Components start ------------ // ! DirectedGraph::reverse() is too heavy pub trait SCC { fn strongly_connected(&self) -> (usize, Vec); fn groups(&self) -> Vec>; } impl SCC for DirectedGraph { fn strongly_connected(&self) -> (usize, Vec) { fn _scc_dfs(graph: &DirectedGraph, x: usize, res: &mut [Option]) { for y in graph.edges_from(x) { if res[y.to].is_none() { res[y.to] = res[x]; _scc_dfs(graph, y.to, res); } } } let n = self.size(); let post_backward = Traversal::post_order(&self.backward); let mut res: Vec> = vec![None; n]; let mut cnt = 0; for &x in post_backward.index.iter().rev() { if res[x].is_none() { res[x] = Some(cnt); _scc_dfs(self, x, &mut res); cnt += 1; } } ( cnt, res.iter().map(|x| cnt - 1 - x.unwrap()).collect(), ) } fn groups(&self) -> Vec> { let (c, g) = self.strongly_connected(); let mut res = vec![Vec::new(); c]; for (i, &x) in g.iter().enumerate() { res[x].push(i); } res } } // ------------ Strongly Connected Components end ------------ pub struct TwoSat(DirectedGraph); impl TwoSat { pub fn new(n: usize) -> Self { Self(DirectedGraph::new(2 * n)) } pub fn add_clause(&mut self, i: usize, f: bool, j: usize, g: bool) { self.0.add_edge(2 * i + !f as usize, 2 * j + g as usize, Void()); self.0.add_edge(2 * j + !g as usize, 2 * i + f as usize, Void()); } pub fn solve(&self) -> Option> { self.0 .strongly_connected().1 .chunks_exact(2) .map(|v| { use std::cmp::Ordering::*; match v[0].cmp(&v[1]) { Equal => None, Less => Some(true), Greater => Some(false), } }) .collect() } } // ------------ 2-SAT end ------------ #[derive(Debug, Clone)] pub struct Traversal { pub index: Vec, pub time: Vec, } impl Traversal { pub fn pre_order(graph: &[Vec>]) -> Self { fn _dfs(graph: &[Vec>], x: usize, res: &mut PermutationBuilder) { res.visit(x); for &y in graph[x].iter() { if !res.on_stack(y.to) { _dfs(graph, y.to, res); } } } let n = graph.len(); let mut res = PermutationBuilder::new(n); for i in 0..n { if !res.on_stack(i) { _dfs(graph, i, &mut res); } } res.build() } pub fn post_order(graph: &[Vec>]) -> Self { fn _dfs(graph: &[Vec>], x: usize, ckd: &mut [bool], res: &mut PermutationBuilder) { for &y in graph[x].iter() { if !std::mem::replace(&mut ckd[y.to], true) { _dfs(graph, y.to, ckd, res); } } res.visit(x); } let n = graph.len(); let mut ckd = vec![false; n]; let mut res = PermutationBuilder::new(n); for i in 0..n { if !std::mem::replace(&mut ckd[i], true) { _dfs(graph, i, &mut ckd, &mut res); } } res.build() } } #[derive(Debug, Clone)] struct PermutationBuilder { index: Vec, time: Vec, } impl PermutationBuilder { fn new(n: usize) -> Self { Self { index: Vec::with_capacity(n), time: vec![n; n], } } fn build(self) -> Traversal { Traversal { index: self.index, time: self.time, } } #[allow(dead_code)] fn is_empty(&self) -> bool { self.time.is_empty() } fn len(&self) -> usize { self.time.len() } fn time(&self) -> usize { self.index.len() } fn visit(&mut self, x: usize) { assert!(!self.on_stack(x)); self.time[x] = self.time(); self.index.push(x); } fn on_stack(&self, x: usize) -> bool { self.time[x] != self.len() } } // ------------ Graph impl start ------------ pub trait Cost: Element + Clone + Copy + std::fmt::Display + Eq + Ord + Zero + One + Add + AddAssign + Sub + Neg { const MAX: Self; } #[derive(Copy, Clone)] pub struct Edge { // pub from: usize, pub to: usize, pub cost: C, pub id: usize } pub struct UndirectedGraph(pub Vec>>, pub usize); pub struct DirectedGraph{ pub forward: Vec>>, pub backward: Vec>>, pub count: usize, } pub trait Graph { fn new(size: usize) -> Self; fn size(&self) -> usize; fn add_edge(&mut self, u: usize, v: usize, cost: C); fn edges_from(&self, v: usize) -> std::slice::Iter>; } impl Graph for UndirectedGraph { fn new(size: usize) -> Self { Self(vec![Vec::>::new(); size], 0) } fn size(&self) -> usize { self.0.len() } fn add_edge(&mut self, u: usize, v: usize, cost: C) { self.0[u].push(Edge{ to: v, cost: cost.clone(), id: self.1 }); self.0[v].push(Edge{ to: u, cost: cost.clone(), id: self.1 }); self.1 += 1; } fn edges_from(&self, v: usize) -> std::slice::Iter> { self.0[v].iter() } } impl Graph for DirectedGraph { fn new(size: usize) -> Self { Self { forward: vec![Vec::>::new(); size], backward: vec![Vec::>::new(); size], count: 0 } } fn size(&self) -> usize { self.forward.len() } fn add_edge(&mut self, u: usize, v: usize, cost: C) { self.forward[u].push(Edge{ to: v, cost: cost.clone(), id: self.count }); self.backward[v].push(Edge{ to: u, cost: cost.clone(), id: self.count }); self.count += 1; } fn edges_from(&self, v: usize) -> std::slice::Iter> { self.forward[v].iter() } } impl DirectedGraph { pub fn edges_to(&self, u: usize) -> std::slice::Iter> { self.backward[u].iter() } pub fn reverse(&self) -> Self { Self { forward: self.backward.clone(), backward: self.forward.clone(), count: self.count, } } } macro_rules! impl_cost { ($($T:ident,)*) => { $( impl Cost for $T { const MAX: Self = std::$T::MAX; } )* }; } impl_cost! { i8, i16, i32, i64, i128, isize, } #[derive(Clone, Copy, PartialEq, Eq, PartialOrd, Ord)] pub struct Void(); impl std::fmt::Display for Void { fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result { write!(f, "") } } impl Zero for Void { fn zero() -> Self { Void() } fn is_zero(&self) -> bool { true } } impl One for Void { fn one() -> Self { Void() } fn is_one(&self) -> bool { true } } impl Add for Void { type Output = Self; fn add(self, _: Self) -> Self { Void() } } impl AddAssign for Void { fn add_assign(&mut self, _: Self) {} } impl Sub for Void { type Output = Self; fn sub(self, _: Self) -> Self { Void() } } impl Neg for Void { type Output = Self; fn neg(self) -> Self { Void() } } impl Cost for Void { const MAX: Self = Void(); } // ------------ Graph impl end ------------ // ------------ algebraic traits start ------------ use std::marker::Sized; use std::ops::*; /// 元 pub trait Element: Sized + Clone + PartialEq {} impl Element for T {} /// 結合性 pub trait Associative: Magma {} /// マグマ pub trait Magma: Element + Add {} impl> Magma for T {} /// 半群 pub trait SemiGroup: Magma + Associative {} impl SemiGroup for T {} /// モノイド pub trait Monoid: SemiGroup + Zero {} impl Monoid for T {} pub trait ComMonoid: Monoid + AddAssign {} impl ComMonoid for T {} /// 群 pub trait Group: Monoid + Neg {} impl> Group for T {} pub trait ComGroup: Group + ComMonoid {} impl ComGroup for T {} /// 半環 pub trait SemiRing: ComMonoid + Mul + One {} impl + One> SemiRing for T {} /// 環 pub trait Ring: ComGroup + SemiRing {} impl Ring for T {} pub trait ComRing: Ring + MulAssign {} impl ComRing for T {} /// 体 pub trait Field: ComRing + Div + DivAssign {} impl + DivAssign> Field for T {} /// 加法単元 pub trait Zero: Element { fn zero() -> Self; fn is_zero(&self) -> bool { *self == Self::zero() } } /// 乗法単元 pub trait One: Element { fn one() -> Self; fn is_one(&self) -> bool { *self == Self::one() } } macro_rules! impl_integer { ($($T:ty,)*) => { $( impl Associative for $T {} impl Zero for $T { fn zero() -> Self { 0 } fn is_zero(&self) -> bool { *self == 0 } } impl<'a> Zero for &'a $T { fn zero() -> Self { &0 } fn is_zero(&self) -> bool { *self == &0 } } impl One for $T { fn one() -> Self { 1 } fn is_one(&self) -> bool { *self == 1 } } impl<'a> One for &'a $T { fn one() -> Self { &1 } fn is_one(&self) -> bool { *self == &1 } } )* }; } impl_integer! { i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, usize, } // ------------ algebraic traits end ------------ // ------------ io module start ------------ use std::io::{stdout, BufWriter, Read, StdoutLock, Write}; pub struct IO { iter: std::str::SplitAsciiWhitespace<'static>, buf: BufWriter>, } impl IO { pub fn new() -> Self { let mut input = String::new(); std::io::stdin().read_to_string(&mut input).unwrap(); let input = Box::leak(input.into_boxed_str()); let out = Box::new(stdout()); IO { iter: input.split_ascii_whitespace(), buf: BufWriter::new(Box::leak(out).lock()), } } fn scan_str(&mut self) -> &'static str { self.iter.next().unwrap() } pub fn scan(&mut self) -> ::Output { ::scan(self) } pub fn scan_vec(&mut self, n: usize) -> Vec<::Output> { (0..n).map(|_| self.scan::()).collect() } pub fn print(&mut self, x: T) { ::print(self, x); } pub fn println(&mut self, x: T) { self.print(x); self.print("\n"); } pub fn iterln>(&mut self, mut iter: I, delim: &str) { if let Some(v) = iter.next() { self.print(v); for v in iter { self.print(delim); self.print(v); } } self.print("\n"); } pub fn flush(&mut self) { self.buf.flush().unwrap(); } } impl Default for IO { fn default() -> Self { Self::new() } } pub trait Scan { type Output; fn scan(io: &mut IO) -> Self::Output; } macro_rules! impl_scan { ($($t:tt),*) => { $( impl Scan for $t { type Output = Self; fn scan(s: &mut IO) -> Self::Output { s.scan_str().parse().unwrap() } } )* }; } impl_scan!(i16, i32, i64, isize, u16, u32, u64, usize, String); pub enum Bytes {} impl Scan for Bytes { type Output = &'static [u8]; fn scan(s: &mut IO) -> Self::Output { s.scan_str().as_bytes() } } pub enum Chars {} impl Scan for Chars { type Output = Vec; fn scan(s: &mut IO) -> Self::Output { s.scan_str().chars().collect() } } pub enum Usize1 {} impl Scan for Usize1 { type Output = usize; fn scan(s: &mut IO) -> Self::Output { s.scan::().wrapping_sub(1) } } impl Scan for (T, U) { type Output = (T::Output, U::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s)) } } impl Scan for (T, U, V) { type Output = (T::Output, U::Output, V::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s), V::scan(s)) } } impl Scan for (T, U, V, W) { type Output = (T::Output, U::Output, V::Output, W::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s), V::scan(s), W::scan(s)) } } pub trait Print { fn print(w: &mut IO, x: Self); } macro_rules! impl_print_int { ($($t:ty),*) => { $( impl Print for $t { fn print(w: &mut IO, x: Self) { w.buf.write_all(x.to_string().as_bytes()).unwrap(); } } )* }; } impl_print_int!(i16, i32, i64, isize, u16, u32, u64, usize); impl Print for u8 { fn print(w: &mut IO, x: Self) { w.buf.write_all(&[x]).unwrap(); } } impl Print for &[u8] { fn print(w: &mut IO, x: Self) { w.buf.write_all(x).unwrap(); } } impl Print for &str { fn print(w: &mut IO, x: Self) { w.print(x.as_bytes()); } } impl Print for String { fn print(w: &mut IO, x: Self) { w.print(x.as_bytes()); } } impl Print for (T, U) { fn print(w: &mut IO, (x, y): Self) { w.print(x); w.print(" "); w.print(y); } } impl Print for (T, U, V) { fn print(w: &mut IO, (x, y, z): Self) { w.print(x); w.print(" "); w.print(y); w.print(" "); w.print(z); } } mod neboccoio_macro { #[macro_export] macro_rules! input { (@start $io:tt @read @rest) => {}; (@start $io:tt @read @rest, $($rest: tt)*) => { input!(@start $io @read @rest $($rest)*) }; (@start $io:tt @read @rest mut $($rest:tt)*) => { input!(@start $io @read @mut [mut] @rest $($rest)*) }; (@start $io:tt @read @rest $($rest:tt)*) => { input!(@start $io @read @mut [] @rest $($rest)*) }; (@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [$kind:tt; $len:expr] $($rest:tt)*) => { let $($mut)* $var = $io.scan_vec::<$kind>($len); input!(@start $io @read @rest $($rest)*) }; (@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: $kind:tt $($rest:tt)*) => { let $($mut)* $var = $io.scan::<$kind>(); input!(@start $io @read @rest $($rest)*) }; (from $io:tt $($rest:tt)*) => { input!(@start $io @read @rest $($rest)*) }; } } // ------------ io module end ------------