using System; using static System.Console; using System.Linq; using System.Collections.Generic; class Program { static int NN => int.Parse(ReadLine()); static int[] NList => ReadLine().Split().Select(int.Parse).ToArray(); static int[][] NArr(long n) => Enumerable.Repeat(0, (int)n).Select(_ => NList).ToArray(); static int[] NMi => ReadLine().Split().Select(c => int.Parse(c) - 1).ToArray(); static int[][] NMap(int n) => Enumerable.Repeat(0, n).Select(_ => NMi).ToArray(); static string[] SList(long n) => Enumerable.Repeat(0, (int)n).Select(_ => ReadLine()).ToArray(); static long[] LList(long n) => Enumerable.Repeat(0, (int)n).Select(_ => long.Parse(ReadLine())).ToArray(); public static void Main() { Solve(); } static void Solve() { var n = NN; var s = NMi; var t = NMi; var u = NList; var ts = new TwoSat(n * n); for (var i = 0; i < n; ++i) { for (var j = 0; j < n; ++j) { // a_Si,j + 2 * a_j,Ti != Ui ts.AddOrClause(s[i] * n + j, u[i] % 2 == 1, j * n + t[i], u[i] / 2 == 1); } } var solve = ts.Solve(); if (solve.res) { var ans = new int[n][]; for (var i = 0; i < n; ++i) { ans[i] = new int[n]; for (var j = 0; j < n; ++j) ans[i][j] = solve.ans[i * n + j] ? 1 : 0; } WriteLine(string.Join("\n", ans.Select(ai => string.Join(" ", ai)))); } else { WriteLine("-1"); } } /// /// 有向グラフを作成し、強連結成分分解を行う /// /// 0 <= n <= 10^8 /// 0 <= from,to < n /// SCCの計算量は O(n + m) m:辺の本数 class SCCGraph { private int _n; private List<(int from, int to)> edges; public SCCGraph(int n) { _n = n; edges = new List<(int, int)>(); } public int NumVertices() { return _n; } public void AddEdge(int from, int to) { edges.Add((from, to )); } public (int, int[]) SCCIds() { var g = new CSR(_n, edges); var nowOrd = 0; var groupNum = 0; var visited = new List(_n); var low = new int[_n]; var ord = Enumerable.Repeat(-1, _n).ToArray(); var ids = new int[_n]; void DFS(int v) { low[v] = ord[v] = nowOrd++; visited.Add(v); for (var i = g.Start[v]; i < g.Start[v + 1]; ++i) { var to = g.EList[i]; if (ord[to] == -1) { DFS(to); low[v] = Math.Min(low[v], low[to]); } else low[v] = Math.Min(low[v], ord[to]); } if (low[v] == ord[v]) { while (true) { var u = visited.Last(); visited.RemoveAt(visited.Count - 1); ord[u] = _n; ids[u] = groupNum; if (u == v) break; } ++groupNum; } } for (var i = 0; i < _n; ++i) if (ord[i] == -1) DFS(i); for (var i = 0; i < ids.Length; ++i) ids[i] = groupNum - 1 - ids[i]; return (groupNum, ids); } public List[] SCC() { var (groupNum, list) = SCCIds(); var counts = new int[groupNum]; foreach (var x in list) ++counts[x]; var groups = new List[groupNum]; for (var i = 0; i < groups.Length; ++i) groups[i] = new List(counts[i]); for (var i = 0; i < _n; ++i) groups[list[i]].Add(i); return groups; } } // 有向辺のリスト class CSR { public int[] Start { get; private set; } public E[] EList { get; private set; } public CSR(int n, List<(int, E)> edges) { Start = new int[n + 1]; EList = new E[edges.Count]; foreach (var e in edges) ++Start[e.Item1 + 1]; for (var i = 1; i <= n; ++i) Start[i] += Start[i - 1]; var counter = (int[])Start.Clone(); foreach (var e in edges) { EList[counter[e.Item1]++] = e.Item2; } } } /// SCCの応用:2-SAT /// /// Xi == true, Xi == false に対応する頂点を用意し、 /// (Xi == true) or (Xj == false) を (Xi == false) -> (Xj == false), (Xj == true) -> (Xi == true) に変換して /// グラフを作成し、SCCを求める /// Xi == true と Xi == false が同じ連結成分にあったら実現不可 /// そうでないなら Xi == true と Xi == false のうちSCCIdの小さいほうを真とすればいい /// class TwoSat { private int N; private SCCGraph scc; public TwoSat(int n) { N = n; scc = new SCCGraph(n * 2); } public void AddOrClause(int xi, bool fi, int xj, bool fj) { scc.AddEdge(xi * 2 + (fi ? 1 : 0), xj * 2 + (fj ? 0 : 1)); scc.AddEdge(xj * 2 + (fj ? 1 : 0), xi * 2 + (fi ? 0 : 1)); } public (bool res, bool[] ans) Solve() { var ans = new bool[N]; var (_, sccid) = scc.SCCIds(); for (var i = 0; i < N; ++i) { if (sccid[i * 2] == sccid[i * 2 + 1]) return (false, ans); ans[i] = sccid[i * 2] < sccid[i * 2 + 1]; } return (true, ans); } } }