Problem:
Score : 600 points

Problem Statement

Given are an integer N and arrays S, T, U, and V, each of length N.
Construct an N×N matrix a that satisfy the following conditions:

a_{i,j} is an integer.

0 \leq a_{i,j} \lt 2^{64}.

If S_{i} = 0, the bitwise AND of the elements in the i-th row is U_{i}.

If S_{i} = 1, the bitwise OR of the elements in the i-th row is U_{i}.

If T_{i} = 0, the bitwise AND of the elements in the i-th column is V_{i}.

If T_{i} = 1, the bitwise OR of the elements in the i-th column is V_{i}.

However, there may be cases where no matrix satisfies the conditions.

Constraints

All values in input are integers.

1 \leq N \leq 500

0 \leq S_{i} \leq 1

0 \leq T_{i} \leq 1

0 \leq U_{i} \lt 2^{64}

0 \leq V_{i} \lt 2^{64}

Input

Input is given from Standard Input in the following format:

N
S_{1} S_{2} ... S_{N}
T_{1} T_{2} ... T_{N}
U_{1} U_{2} ... U_{N}
V_{1} V_{2} ... V_{N}

Output

If there exists a matrix that satisfies the conditions, print one such matrix in the following format:

a_{1,1} ... a_{1,N}
:
a_{N,1} ... a_{N,N}

Note that any matrix satisfying the conditions is accepted.

If no matrix satisfies the conditions, print -1.

Sample Input 1

2
0 1
1 0
1 1
1 0

Sample Output 1

1 1
1 0

In Sample Input 1, we need to find a matrix such that:

the bitwise AND of the elements in the 1-st row is 1;

the bitwise OR of the elements in the 2-nd row is 1;

the bitwise OR of the elements in the 1-st column is 1;

the bitwise AND of the elements in the 2-nd column is 0.

Sample Input 2

2
1 1
1 0
15 15
15 11

Sample Output 2

15 11
15 11

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

#region いつもの
using AtCoderProject;
using System;
using System.Collections.Generic;
using System.Linq;
using static AtCoderProject.Global;
using BigInteger = System.Numerics.BigInteger;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using StringBuilder = System.Text.StringBuilder;
using Unsafe = System.Runtime.CompilerServices.Unsafe;

namespace AtCoderProject { using System.IO; using System.Text; using System.Diagnostics; using System.Runtime.CompilerServices; public static class Global { public static T[] NewArray<T>(int len0, T value) => new T[len0].Fill(value); public static T[] NewArray<T>(int len0, Func<T> factory) { var arr = new T[len0]; for (int i = 0; i < arr.Length; i++) arr[i] = factory(); return arr; } public static T[][] NewArray<T>(int len0, int len1, T value) where T : struct { var arr = new T[len0][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, value); return arr; } public static T[][] NewArray<T>(int len0, int len1, Func<T> factory) { var arr = new T[len0][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, factory); return arr; } public static T[][][] NewArray<T>(int len0, int len1, int len2, T value) where T : struct { var arr = new T[len0][][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, value); return arr; } public static T[][][] NewArray<T>(int len0, int len1, int len2, Func<T> factory) { var arr = new T[len0][][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, factory); return arr; } public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, T value) where T : struct { var arr = new T[len0][][][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, value); return arr; } public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, Func<T> factory) { var arr = new T[len0][][][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, factory); return arr; } public static int Pow(int x, int y) { int res = 1; for (; y > 0; y >>= 1) { if ((y & 1) == 1) res *= x; x *= x; } return res; } public static BigInteger ParseBigInteger(ReadOnlySpan<char> s) { /* 自前実装の方が速い */ BigInteger res; if (s.Length % 9 == 0) res = 0; else { res = new BigInteger(int.Parse(s.Slice(0, s.Length % 9))); s = s.Slice(s.Length % 9); } while (s.Length > 0) { var sp = s.Slice(0, 9); res *= 1000_000_000; res += int.Parse(sp); s = s.Slice(9); } return res; } public static int BitCount(int x) { x -= (x >> 1) & 0x55555555; x = (x & 0x33333333) + ((x >> 2) & 0x33333333); x = (x + (x >> 4)) & 0x0f0f0f0f; x += x >> 8; x += x >> 16; return x & 0x3f; } public static int BitCount(long x) { x -= (x >> 1) & 0x5555555555555555; x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333); x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f; x += x >> 8; x += x >> 16; x += x >> 32; return (int)(x & 0x0000007f); } public static int MSB(int x) { x |= x >> 1; x |= x >> 2; x |= x >> 4; x |= x >> 8; x |= x >> 16; return BitCount(x) - 1; } public static int MSB(long x) { x |= x >> 1; x |= x >> 2; x |= x >> 4; x |= x >> 8; x |= x >> 16; x |= x >> 32; return BitCount(x) - 1; } public static int LSB(int x) { x |= x << 1; x |= x << 2; x |= x << 4; x |= x << 8; x |= x << 16; return 32 - BitCount(x); } public static int LSB(long x) { x |= x << 1; x |= x << 2; x |= x << 4; x |= x << 8; x |= x << 16; x |= x << 32; return 64 - BitCount(x); } } public static class Ext { public static bool UpdateMax(this ref int r, int val) { if (r < val) { r = val; return true; } return false; } public static bool UpdateMax(this ref long r, long val) { if (r < val) { r = val; return true; } return false; } public static bool UpdateMin(this ref int r, int val) { if (r > val) { r = val; return true; } return false; } public static bool UpdateMin(this ref long r, long val) { if (r > val) { r = val; return true; } return false; } public static long ToLong(this int i) => i; public static T[] Fill<T>(this T[] arr, T value) { Array.Fill(arr, value); return arr; } public static T[] Sort<T>(this T[] arr) { Array.Sort(arr); return arr; } public static string[] Sort(this string[] arr) => Sort(arr, StringComparer.OrdinalIgnoreCase); public static T[] Sort<T, U>(this T[] arr, Func<T, U> selector) where U : IComparable<U> => Sort(arr, (a, b) => selector(a).CompareTo(selector(b))); public static T[] Sort<T>(this T[] arr, Comparison<T> comparison) { Array.Sort(arr, comparison); return arr; } public static T[] Sort<T>(this T[] arr, IComparer<T> comparer) { Array.Sort(arr, comparer); return arr; } public static T[] Reverse<T>(this T[] arr) { Array.Reverse(arr); return arr; } public static (int index, T max) MaxBy<T>(this T[] arr) where T : IComparable<T> { T max = arr[0]; int maxIndex = 0; for (int i = 0; i < arr.Length; i++) { if (max.CompareTo(arr[i]) < 0) { max = arr[i]; maxIndex = i; } } return (maxIndex, max); } public static (TSource item, TMax max) MaxBy<TSource, TMax>(this IEnumerable<TSource> source, Func<TSource, TMax> maxBySelector) where TMax : IComparable<TMax> { TMax max; TSource maxByItem; var e = source.GetEnumerator(); e.MoveNext(); maxByItem = e.Current; max = maxBySelector(maxByItem); while (e.MoveNext()) { var item = e.Current; var next = maxBySelector(item); if (max.CompareTo(next) < 0) { max = next; maxByItem = item; } } return (maxByItem, max); } public static (int index, T min) MinBy<T>(this T[] arr) where T : IComparable<T> { T min = arr[0]; int minIndex = 0; for (int i = 0; i < arr.Length; i++) { if (min.CompareTo(arr[i]) > 0) { min = arr[i]; minIndex = i; } } return (minIndex, min); } public static (TSource item, TMin min) MinBy<TSource, TMin>(this IEnumerable<TSource> source, Func<TSource, TMin> minBySelector) where TMin : IComparable<TMin> { TMin min; TSource minByItem; var e = source.GetEnumerator(); e.MoveNext(); minByItem = e.Current; min = minBySelector(minByItem); while (e.MoveNext()) { var item = e.Current; var next = minBySelector(item); if (min.CompareTo(next) > 0) { min = next; minByItem = item; } } return (minByItem, min); } public static IComparer<T> Reverse<T>(this IComparer<T> comparer) => Comparer<T>.Create((x, y) => comparer.Compare(y, x)); public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count()); public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i); public static TValue Get<TKey, TValue>(this Dictionary<TKey, TValue> dic, TKey key) { dic.TryGetValue(key, out var v); return v; } public static TValue GetOrInit<TKey, TValue>(this Dictionary<TKey, TValue> dic, TKey key, TValue value) { if (dic.TryGetValue(key, out var v)) return v; return dic[key] = value; } } public class ReverseComparer<T> : Comparer<T> where T : IComparable<T> { private static ReverseComparer<T> defaultComparer; public static new IComparer<T> Default => defaultComparer ??= new ReverseComparer<T>(); public override int Compare(T y, T x) => x.CompareTo(y); public override bool Equals(object obj) => obj != null && GetType() == obj.GetType(); public override int GetHashCode() => GetType().GetHashCode(); } public class ΔDebugView<T> { private IEnumerable<T> collection; public ΔDebugView(IEnumerable<T> collection) { this.collection = collection ?? throw new ArgumentNullException(nameof(collection)); }[DebuggerBrowsable(DebuggerBrowsableState.RootHidden)] public T[] Items => collection.ToArray(); }[DebuggerStepThrough] public class ConsoleReader { const int BufSize = 1 << 12; private readonly byte[] buffer = new byte[BufSize]; private readonly Stream input; private readonly Encoding encoding; private int pos = 0; private int len = 0; public ConsoleReader(Stream input, Encoding encoding) { this.input = input; this.encoding = encoding; } public ConsoleReader(Stream input) : this(input, Console.InputEncoding) { } private void MoveNext() { if (++pos >= len) { len = input.Read(buffer, 0, buffer.Length); if (len == 0) { buffer[0] = 10; } pos = 0; } } public int Int { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { int res = 0; bool neg = false; while (buffer[pos] < 48) { neg = buffer[pos] == 45; MoveNext(); } do { res = checked(res * 10 + (buffer[pos] ^ 48)); MoveNext(); } while (48 <= buffer[pos]); return neg ? -res : res; } } public int Int0 => this.Int - 1; public long Long { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { long res = 0; bool neg = false; while (buffer[pos] < 48) { neg = buffer[pos] == 45; MoveNext(); } do { res = res * 10 + (buffer[pos] ^ 48); MoveNext(); } while (48 <= buffer[pos]); return neg ? -res : res; } } public long Long0 => this.Long - 1; public string String { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { var sb = new List<byte>(); while (buffer[pos] <= 32) MoveNext(); do { sb.Add(buffer[pos]); MoveNext(); } while (32 < buffer[pos]); return this.encoding.GetString(sb.ToArray()); } } public string Ascii { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { var sb = new StringBuilder(); while (buffer[pos] <= 32) MoveNext(); do { sb.Append((char)buffer[pos]); MoveNext(); } while (32 < buffer[pos]); return sb.ToString(); } } public string Line { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { var sb = new List<byte>(); while (buffer[pos] < 32) MoveNext(); do { sb.Add(buffer[pos]); MoveNext(); } while (buffer[pos] != 10 && buffer[pos] != 13); return this.encoding.GetString(sb.ToArray()); } } public char Char { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { while (buffer[pos] < 32) MoveNext(); char res = (char)buffer[pos]; MoveNext(); return res; } } public double Double => double.Parse(this.Ascii);[DebuggerStepThrough] public struct RepeatReader { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public T[] Select<T>(Func<ConsoleReader, T> factory) { var arr = new T[count]; for (var i = 0; i < count; i++) arr[i] = factory(cr); return arr; } public T[] Select<T>(Func<ConsoleReader, int, T> factory) { var arr = new T[count]; for (var i = 0; i < count; i++) arr[i] = factory(cr, i); return arr; } public string[] Line { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.Line; return arr; } } public string[] String { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.String; return arr; } } public string[] Ascii { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.Ascii; return arr; } } public int[] Int { get { var arr = new int[count]; for (var i = 0; i < count; i++) arr[i] = cr.Int; return arr; } } public int[] Int0 { get { var arr = new int[count]; for (var i = 0; i < count; i++) arr[i] = cr.Int0; return arr; } } public long[] Long { get { var arr = new long[count]; for (var i = 0; i < count; i++) arr[i] = cr.Long; return arr; } } public long[] Long0 { get { var arr = new long[count]; for (var i = 0; i < count; i++) arr[i] = cr.Long0; return arr; } } public double[] Double { get { var arr = new double[count]; for (var i = 0; i < count; i++) arr[i] = cr.Double; return arr; } } public static implicit operator int[](RepeatReader rr) => rr.Int; public static implicit operator long[](RepeatReader rr) => rr.Long; public static implicit operator double[](RepeatReader rr) => rr.Double; public static implicit operator string[](RepeatReader rr) => rr.Ascii; } public RepeatReader Repeat(int count) => new RepeatReader(this, count);[DebuggerStepThrough] public struct SplitReader { ConsoleReader cr; public SplitReader(ConsoleReader cr) { this.cr = cr; } public string[] String { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<string>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.String); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public string[] Ascii { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<string>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Ascii); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public int[] Int { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<int>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Int); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public int[] Int0 { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<int>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Int0); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public long[] Long { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<long>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Long); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public long[] Long0 { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<long>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Long0); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public double[] Double { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<double>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Double); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public static implicit operator int[](SplitReader sr) => sr.Int; public static implicit operator long[](SplitReader sr) => sr.Long; public static implicit operator double[](SplitReader sr) => sr.Double; public static implicit operator string[](SplitReader sr) => sr.Ascii; } public SplitReader Split => new SplitReader(this); public static implicit operator int(ConsoleReader cr) => cr.Int; public static implicit operator long(ConsoleReader cr) => cr.Long; public static implicit operator double(ConsoleReader cr) => cr.Double; public static implicit operator string(ConsoleReader cr) => cr.Ascii; public void Deconstruct(out ConsoleReader o1, out ConsoleReader o2) => (o1, o2) = (this, this); public void Deconstruct(out ConsoleReader o1, out ConsoleReader o2, out ConsoleReader o3) => (o1, o2, o3) = (this, this, this); public void Deconstruct(out ConsoleReader o1, out ConsoleReader o2, out ConsoleReader o3, out ConsoleReader o4) => (o1, o2, o3, o4) = (this, this, this, this); public void Deconstruct(out ConsoleReader o1, out ConsoleReader o2, out ConsoleReader o3, out ConsoleReader o4, out ConsoleReader o5) => (o1, o2, o3, o4, o5) = (this, this, this, this, this); public void Deconstruct(out ConsoleReader o1, out ConsoleReader o2, out ConsoleReader o3, out ConsoleReader o4, out ConsoleReader o5, out ConsoleReader o6) => (o1, o2, o3, o4, o5, o6) = (this, this, this, this, this, this); public void Deconstruct(out ConsoleReader o1, out ConsoleReader o2, out ConsoleReader o3, out ConsoleReader o4, out ConsoleReader o5, out ConsoleReader o6, out ConsoleReader o7) => (o1, o2, o3, o4, o5, o6, o7) = (this, this, this, this, this, this, this); public void Deconstruct(out ConsoleReader o1, out ConsoleReader o2, out ConsoleReader o3, out ConsoleReader o4, out ConsoleReader o5, out ConsoleReader o6, out ConsoleReader o7, out ConsoleReader o8) => (o1, o2, o3, o4, o5, o6, o7, o8) = (this, this, this, this, this, this, this, this); }[DebuggerStepThrough] public class ConsoleWriter { private readonly StreamWriter sw; public ConsoleWriter(Stream output) : this(output, Console.OutputEncoding) { } public ConsoleWriter(Stream output, Encoding encoding) { sw = new StreamWriter(output, encoding); } public void Flush() => sw.Flush(); public ConsoleWriter WriteLine<T>(T obj) { sw.WriteLine(obj.ToString()); return this; } public ConsoleWriter WriteLineJoin<T>(IEnumerable<T> col) => WriteMany(' ', col); public ConsoleWriter WriteLines<T>(IEnumerable<T> col) => WriteMany('\n', col); public ConsoleWriter WriteLineGrid<T>(IEnumerable<IEnumerable<T>> cols) { var en = cols.GetEnumerator(); while (en.MoveNext()) WriteLineJoin(en.Current); return this; } private ConsoleWriter WriteMany<T>(char sep, IEnumerable<T> col) { var en = col.GetEnumerator(); if (!en.MoveNext()) return this; sw.Write(en.Current.ToString()); while (en.MoveNext()) { sw.Write(sep); sw.Write(en.Current.ToString()); } sw.WriteLine(); return this; } } }
public partial class Program {[System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] public ConsoleReader cr;[System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] public ConsoleWriter cw; public Program(ConsoleReader reader, ConsoleWriter writer) { this.cr = reader; this.cw = writer; System.Globalization.CultureInfo.CurrentCulture = System.Globalization.CultureInfo.InvariantCulture; } static void Main() => new Program(new ConsoleReader(Console.OpenStandardInput()), new ConsoleWriter(Console.OpenStandardOutput())).Run(); public void Run() { var res = Calc(); if (res is double) cw.WriteLine(Result((double)res)); else if (res is bool) cw.WriteLine(Result((bool)res)); else if (res != null) cw.WriteLine(res.ToString()); cw.Flush(); } }
public partial class Program
{
    public static string Result(double d) => d.ToString("0.####################", System.Globalization.CultureInfo.InvariantCulture);
    #endregion
    public static string Result(bool b) => b ? "Yes" : "No";
    private object Calc()
    {
        N = cr;
        S = cr.Repeat(N).Select(cr => cr.Int == 1);
        T = cr.Repeat(N).Select(cr => cr.Int == 1);
        U = cr.Repeat(N).Select(cr => unchecked((ulong)cr.Long));
        V = cr.Repeat(N).Select(cr => unchecked((ulong)cr.Long));
        ulong[][] res = NewArray(N, N, 0UL);
        for (int b = 0; b < 64; b++)
        {
            var r = Calc(b);
            for (int i = 0; i < N; i++)
                for (int j = 0; j < N; j++)
                    if (r[i][j] == St.One)
                        res[i][j] |= 1UL << b;
        }

        var mU = new ulong[N];
        var mV = new ulong[N];
        for (int i = 0; i < N; i++)
        {
            if (S[i])
            {
                for (int j = 0; j < N; j++)
                    mU[i] |= res[i][j];
            }
            else
            {
                mU[i] = 0xFFFFFFFFFFFFFFFF;
                for (int j = 0; j < N; j++)
                    mU[i] &= res[i][j];
            }
            if (T[i])
            {
                for (int j = 0; j < N; j++)
                    mV[i] |= res[j][i];
            }
            else
            {
                mV[i] = 0xFFFFFFFFFFFFFFFF;
                for (int j = 0; j < N; j++)
                    mV[i] &= res[j][i];
            }
        }
        if (mV.SequenceEqual(V) && mU.SequenceEqual(U))
            cw.WriteLineGrid(res);
        else
            return -1;
        return null;
    }
    St[][] Calc(int v)
    {
        var row = NewArray(N, 5, 0);
        var col = NewArray(N, 5, 0);
        var st = NewArray(N, N, St.None);
        for (int i = 0; i < N; i++)
            for (int j = 0; j < N; j++)
            {
                if (S[i])
                {
                    if (U[i].On(v))
                    {
                        if (T[j])
                        {
                            if (V[j].On(v))
                            {
                                row[i][(int)St.One]++;
                                col[j][(int)St.One]++;
                                st[i][j] = St.One;
                            }
                            else
                            {
                                row[i][(int)St.Zero]++;
                                col[j][(int)St.Zero]++;
                                st[i][j] = St.Zero;
                            }
                        }
                        else
                        {
                            if (V[j].On(v))
                            {
                                row[i][(int)St.One]++;
                                col[j][(int)St.One]++;
                                st[i][j] = St.One;
                            }
                            else
                            {
                                row[i][(int)St.WantRowOneColZero]++;
                                col[j][(int)St.WantRowOneColZero]++;
                                st[i][j] = St.WantRowOneColZero;
                            }
                        }
                    }
                    else
                    {
                        row[i][(int)St.Zero]++;
                        col[j][(int)St.Zero]++;
                        st[i][j] = St.Zero;
                        if (!T[j] && V[j].On(v))
                            return st;
                    }
                }
                else
                {
                    if (U[i].On(v))
                    {
                        row[i][(int)St.One]++;
                        col[j][(int)St.One]++;
                        st[i][j] = St.One;
                        if (T[j] && !V[j].On(v))
                            return st;
                    }
                    else
                    {
                        if (T[j])
                        {
                            if (V[j].On(v))
                            {
                                row[i][(int)St.WantRowZeroColOne]++;
                                col[j][(int)St.WantRowZeroColOne]++;
                                st[i][j] = St.WantRowZeroColOne;
                            }
                            else
                            {
                                row[i][(int)St.Zero]++;
                                col[j][(int)St.Zero]++;
                                st[i][j] = St.Zero;
                            }
                        }
                        else
                        {
                            if (V[j].On(v))
                            {
                                row[i][(int)St.One]++;
                                col[j][(int)St.One]++;
                                st[i][j] = St.One;
                            }
                            else
                            {
                                row[i][(int)St.Zero]++;
                                col[j][(int)St.Zero]++;
                                st[i][j] = St.Zero;
                            }
                        }
                    }
                }
            }

        var nokori = row.Sum(rr => rr[3] + rr[4]);

        while (nokori > 0)
        {
            var pn = nokori;
            for (int i = 0; i < N; i++)
                for (int j = 0; j < N; j++)
                {
                    if (st[i][j] == St.WantRowOneColZero)
                    {
                        if (row[i][(int)St.One] > 0)
                        {
                            row[i][(int)St.WantRowOneColZero]--;
                            col[j][(int)St.WantRowOneColZero]--;
                            row[i][(int)St.Zero]++;
                            col[j][(int)St.Zero]++;
                            st[i][j] = St.Zero;
                            nokori--;
                        }
                        else if (col[j][(int)St.Zero] > 0)
                        {
                            row[i][(int)St.WantRowOneColZero]--;
                            col[j][(int)St.WantRowOneColZero]--;
                            row[i][(int)St.One]++;
                            col[j][(int)St.One]++;
                            st[i][j] = St.One;
                            nokori--;
                        }
                        else if (row[i][(int)St.WantRowOneColZero] == 1)
                        {
                            row[i][(int)St.WantRowOneColZero]--;
                            col[j][(int)St.WantRowOneColZero]--;
                            row[i][(int)St.One]++;
                            col[j][(int)St.One]++;
                            st[i][j] = St.One;
                            nokori--;
                        }
                        else if (col[j][(int)St.WantRowOneColZero] == 1)
                        {
                            row[i][(int)St.WantRowOneColZero]--;
                            col[j][(int)St.WantRowOneColZero]--;
                            row[i][(int)St.Zero]++;
                            col[j][(int)St.Zero]++;
                            st[i][j] = St.Zero;
                            nokori--;
                        }
                    }
                    else if (st[i][j] == St.WantRowZeroColOne)
                    {
                        if (row[i][(int)St.Zero] > 0)
                        {
                            row[i][(int)St.WantRowZeroColOne]--;
                            col[j][(int)St.WantRowZeroColOne]--;
                            row[i][(int)St.One]++;
                            col[j][(int)St.One]++;
                            st[i][j] = St.One;
                            nokori--;
                        }
                        else if (col[j][(int)St.One] > 0)
                        {
                            row[i][(int)St.WantRowZeroColOne]--;
                            col[j][(int)St.WantRowZeroColOne]--;
                            row[i][(int)St.Zero]++;
                            col[j][(int)St.Zero]++;
                            st[i][j] = St.Zero;
                            nokori--;
                        }
                        else if (row[i][(int)St.WantRowZeroColOne] == 1)
                        {
                            row[i][(int)St.WantRowZeroColOne]--;
                            col[j][(int)St.WantRowZeroColOne]--;
                            row[i][(int)St.Zero]++;
                            col[j][(int)St.Zero]++;
                            st[i][j] = St.Zero;
                            nokori--;
                        }
                        else if (col[j][(int)St.WantRowZeroColOne] == 1)
                        {
                            row[i][(int)St.WantRowZeroColOne]--;
                            col[j][(int)St.WantRowZeroColOne]--;
                            row[i][(int)St.One]++;
                            col[j][(int)St.One]++;
                            st[i][j] = St.One;
                            nokori--;
                        }
                    }
                }

            if (nokori == pn)
            {
                for (int i = 0; i < N; i++)
                    for (int j = 0; j < N; j++)
                    {
                        var stl = st[i][j];
                        if (!stl.IsFixed())
                        {
                            row[i][(int)stl]--;
                            col[j][(int)stl]--;
                            row[i][(int)St.One]++;
                            col[j][(int)St.One]++;
                            st[i][j] = St.One;
                            nokori--;
                            goto END;
                        }
                    }
                END: { }
            }
        }

        return st;
    }

    bool[] S;
    bool[] T;
    ulong[] U;
    ulong[] V;
    int N;
}

static class Bit { public static string ToBitString(this int num, int padLeft = sizeof(int) * 8) => Convert.ToString(num, 2).PadLeft(padLeft, '0'); public static string ToBitString(this long num, int padLeft = sizeof(long) * 8) => Convert.ToString(num, 2).PadLeft(padLeft, '0'); public static string ToBitString(this ulong num, int padLeft = sizeof(ulong) * 8) => Convert.ToString(unchecked((long)num), 2).PadLeft(padLeft, '0'); public static bool On(this int num, int index) => ((num >> index) & 1) != 0; public static bool On(this long num, int index) => ((num >> index) & 1) != 0; public static bool On(this ulong num, int index) => ((num >> index) & 1) != 0; public static IEnumerable<int> Bits(this int num) { for (var i = 0; num > 0; i++, num >>= 1) if ((num & 1) == 1) yield return i; } public static IEnumerable<int> Bits(this long num) { for (var i = 0; num > 0; i++, num >>= 1) if ((num & 1) == 1) yield return i; } public static IEnumerable<int> Bits(this ulong num) { for (var i = 0; num > 0; i++, num >>= 1) if ((num & 1) == 1) yield return i; } }
[Flags]
enum St
{
    None,
    Zero,
    One,
    WantRowOneColZero,
    WantRowZeroColOne,
}
static class StExt { public static bool IsFixed(this St st) => st == St.Zero || st == St.One; }