using System; using System.Collections; using System.Collections.Generic; using System.Diagnostics; using System.Globalization; using System.IO; using System.Text; using System.Linq; using E = System.Linq.Enumerable; internal partial class Solver { public void Run() { var n = ni(); var s = ni(n); var t = ni(n); var u = ni(n); var twoSat = new TwoSat(n * n); for (int i = 0; i < n; i++) { int sv = s[i] - 1; int tv = t[i] - 1; for (int j = 0; j < n; j++) { var asj = sv * n + j; var ajt = j * n + tv; for (int p = 0; p < 2; p++) { for (int q = 0; q < 2; q++) { if (p + q * 2 == u[i]) { twoSat.AddImplication(asj, p == 1, ajt, !(q == 1)); twoSat.AddImplication(ajt, q == 1, asj, !(p == 1)); } } } } } if (twoSat.Solve(out var result)) { for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { if (j > 0) cout.Write(" "); if (result[i * n + j]) { cout.Write(1); } else { cout.Write(0); } } cout.WriteLine(); } } else { cout.WriteLine(-1); } } } public class TwoSat { private struct TwoSatVariable { public int Index; public bool TrueOfFalse; } private class TwoSatImplication { public TwoSatVariable Variable1; public TwoSatVariable Variable2; } private readonly int _n; private readonly List _implications = new List(); public TwoSat(int n) { _n = n; } /// /// P OR Q /// public void AddOrClause(int variable1, bool trueOrFalse1, int variable2, bool trueOrFalse2) { // P or Q === (~P => Q) and (~Q =>P) AddImplication(variable1, !trueOrFalse1, variable2, trueOrFalse2); AddImplication(variable2, !trueOrFalse2, variable1, trueOrFalse1); } /// /// ~(P AND Q) (=== ~P OR ~Q) /// public void AddNandClause(int variable1, bool trueOrFalse1, int variable2, bool trueOrFalse2) { AddOrClause(variable1, !trueOrFalse1, variable2, !trueOrFalse2); } /// /// P (=== P OR P) /// public void AddIsTrueClause(int variable, bool trueOrFalse) { AddImplication(variable, !trueOrFalse, variable, trueOrFalse); } /// /// (P XOR Q) (=== (P OR Q) AND (~P OR ~Q)) /// public void AddXorClause(int variable1, bool trueOrFalse1, int variable2, bool trueOrFalse2) { AddOrClause(variable1, trueOrFalse1, variable2, trueOrFalse2); AddOrClause(variable1, !trueOrFalse1, variable2, !trueOrFalse2); } /// /// P -> Q /// public void AddImplication(int variable1, bool trueOrFalse1, int variable2, bool trueOrFalse2) { _implications.Add(new TwoSatImplication { Variable1 = new TwoSatVariable { Index = variable1, TrueOfFalse = trueOrFalse1 }, Variable2 = new TwoSatVariable { Index = variable2, TrueOfFalse = trueOrFalse2 }, }); } private int ToIndex(TwoSatVariable v) { return v.TrueOfFalse ? v.Index : v.Index + _n; } public bool Solve(out bool[] value) { value = null; var adj = Enumerable.Range(0, _n * 2).Select(_ => new List()).ToArray(); foreach (var c in _implications) { adj[ToIndex(c.Variable1)].Add(ToIndex(c.Variable2)); } var scc = new StronglyConnectedComponent(adj); int[] groupIndex = scc.GetGroupArray(); for (int i = 0; i < _n; i++) { if (groupIndex[i] == groupIndex[i + _n]) { return false; } } value = new bool[_n]; for (int i = 0; i < _n; i++) { if (groupIndex[i] > groupIndex[i + _n]) { value[i] = true; } } return true; } } public class StronglyConnectedComponent { private readonly int _n; private readonly bool[] _isVisited; private readonly List[] _adjacent; private readonly List[] _inverseAdjacent; private readonly Stack _stack = new Stack(); public StronglyConnectedComponent(List[] adj) { _adjacent = adj; _n = adj.Length; _isVisited = new bool[_n]; _inverseAdjacent = new List[_n]; for (var i = 0; i < _n; i++) { _inverseAdjacent[i] = new List(); } for (var i = 0; i < _n; i++) { foreach (var x in adj[i]) { _inverseAdjacent[x].Add(i); } } } private void Traverse(int k, List[] adjacent, List label) { if (_isVisited[k]) { return; } _stack.Push(k); while (_stack.Count > 0) { int top = _stack.Pop(); if (top < 0) { label.Add(-top - 1); continue; } if (_isVisited[top]) { continue; } _isVisited[top] = true; _stack.Push(-(top + 1)); foreach (int x in adjacent[top]) { if (!_isVisited[x]) { _stack.Push(x); } } } } public List> Run() { var label = new List(); for (var i = 0; i < _n; i++) { Traverse(i, _adjacent, label); } label.Reverse(); Array.Clear(_isVisited, 0, _isVisited.Length); var components = new List>(); foreach (var x in label) { if (!_isVisited[x]) { var group = new List(); Traverse(x, _inverseAdjacent, group); components.Add(group); } } return components; } public int[] GetGroupArray() { var component = Run(); var group = new int[_n]; for (var i = 0; i < component.Count; i++) { foreach (var x in component[i]) { group[x] = i; } } return group; // group index is topological order } } // PREWRITEN CODE BEGINS FROM HERE static public class StringExtensions { static public string JoinToString(this IEnumerable source, string separator = " ") { return string.Join(separator, source); } } internal partial class Solver : Scanner { public static void Main() { #if LOCAL byte[] inputBuffer = new byte[1000000]; var inputStream = Console.OpenStandardInput(inputBuffer.Length); using (var reader = new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length)) { Console.SetIn(reader); new Solver(Console.In, Console.Out).Run(); } #else Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }); new Solver(Console.In, Console.Out).Run(); Console.Out.Flush(); #endif } #pragma warning disable IDE0052 private readonly TextReader cin; private readonly TextWriter cout; private readonly TextWriter cerr; #pragma warning restore IDE0052 public Solver(TextReader reader, TextWriter writer) : base(reader) { cin = reader; cout = writer; cerr = Console.Error; } public Solver(string input, TextWriter writer) : this(new StringReader(input), writer) { } #pragma warning disable IDE1006 #pragma warning disable IDE0051 private int ni() { return NextInt(); } private int[] ni(int n) { return NextIntArray(n); } private long nl() { return NextLong(); } private long[] nl(int n) { return NextLongArray(n); } private double nd() { return NextDouble(); } private double[] nd(int n) { return NextDoubleArray(n); } private string ns() { return Next(); } private string[] ns(int n) { return NextArray(n); } #pragma warning restore IDE1006 #pragma warning restore IDE0051 } #if DEBUG internal static class LinqPadExtension { public static string TextDump(this T obj) { if (obj is IEnumerable) return (obj as IEnumerable).Cast().JoinToString().Dump(); else return obj.ToString().Dump(); } public static T Dump(this T obj) { return LINQPad.Extensions.Dump(obj); } } #endif public class Scanner { private readonly TextReader Reader; private readonly CultureInfo ci = CultureInfo.InvariantCulture; private readonly char[] buffer = new char[2 * 1024]; private int cursor = 0, length = 0; private string Token; private readonly StringBuilder sb = new StringBuilder(1024); public Scanner() : this(Console.In) { } public Scanner(TextReader reader) { Reader = reader; } public int NextInt() { return checked((int)NextLong()); } public long NextLong() { var s = Next(); long r = 0; int i = 0; bool negative = false; if (s[i] == '-') { negative = true; i++; } for (; i < s.Length; i++) { r = r * 10 + (s[i] - '0'); #if DEBUG if (!char.IsDigit(s[i])) throw new FormatException(); #endif } return negative ? -r : r; } public double NextDouble() { return double.Parse(Next(), ci); } public string[] NextArray(int size) { string[] array = new string[size]; for (int i = 0; i < size; i++) { array[i] = Next(); } return array; } public int[] NextIntArray(int size) { int[] array = new int[size]; for (int i = 0; i < size; i++) { array[i] = NextInt(); } return array; } public long[] NextLongArray(int size) { long[] array = new long[size]; for (int i = 0; i < size; i++) { array[i] = NextLong(); } return array; } public double[] NextDoubleArray(int size) { double[] array = new double[size]; for (int i = 0; i < size; i++) { array[i] = NextDouble(); } return array; } public string Next() { if (Token == null) { if (!StockToken()) { throw new Exception(); } } var token = Token; Token = null; return token; } public bool HasNext() { if (Token != null) { return true; } return StockToken(); } private bool StockToken() { while (true) { sb.Clear(); while (true) { if (cursor >= length) { cursor = 0; if ((length = Reader.Read(buffer, 0, buffer.Length)) <= 0) { break; } } var c = buffer[cursor++]; if (33 <= c && c <= 126) { sb.Append(c); } else { if (sb.Length > 0) break; } } if (sb.Length > 0) { Token = sb.ToString(); return true; } return false; } } }