// Sokoban map generator (mask-based, reverse search from solved state)
// - Uses small hand-made masks (Microban/Novoban 스타일) to shape the outer walls.
// - Places goals/boxes in solved state, then pulls boxes away from goals (reverse of push) to guarantee solvability.
// - Run: `dotnet run > output.json` (defaults use band config). Optional: `dotnet run <seed> [startId] [endId]`.
// Legend: '#' wall, '.' floor, '0' void, 'G' goal, '$' box, '@' player.

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text.Json;

internal static class Program
{
    private static readonly LevelBandConfig[] LevelBands =
    {
        new LevelBandConfig
        {
            StartId = 3,
            EndId = 20,
            BoxCountLow = 1,
            BoxCountHigh = 2,
            MinAllowedPushes = 4,
            MinAllowedTurns = 2,
            ShapeMasks = MaskLibrary.Microban.Take(8).ToList()
        },
        new LevelBandConfig
        {
            StartId = 21,
            EndId = 40,
            BoxCountLow = 1,
            BoxCountHigh = 2,
            MinAllowedPushes = 7,
            MinAllowedTurns = 3,
            ShapeMasks = MaskLibrary.Microban.ToList()
        },
        new LevelBandConfig
        {
            StartId = 41,
            EndId = 60,
            BoxCountLow = 2,
            BoxCountHigh = 3,
            MinAllowedPushes = 9,
            MinAllowedTurns = 4,
            ShapeMasks = MaskLibrary.Microban.ToList()
        }
    };

    private static readonly GenerationTuning Tuning = new GenerationTuning
    {
        MaxAttemptsPerLevel = 2000,
        MaxMillisecondsPerLevel = 40_000,
        PushLimitPadding = 2,
        PushLimitScale = 0.35,
        DynamicGrowthWindow = 12,
        DynamicPushIncrement = 2,
        ReverseSearchMaxDepth = 120,
        ReverseSearchBreadth = 800,
        ApplyMaskTransforms = true,
        MaskWallJitter = 2
    };

    private const int DefaultSeed = 12345;

    public static void Main(string[] args)
    {
        var seed = DefaultSeed;
        if (args.Length > 0 && int.TryParse(args[0], out var parsedSeed))
        {
            seed = parsedSeed;
        }

        var rng = new Random(seed);
        var generator = new LevelGenerator(rng, Tuning, LevelBands);

        var startId = LevelBands.Min(b => b.StartId);
        var endId = LevelBands.Max(b => b.EndId);

        if (args.Length >= 2 && int.TryParse(args[1], out var requestedStart))
        {
            startId = requestedStart;
        }

        if (args.Length >= 3 && int.TryParse(args[2], out var requestedEnd))
        {
            endId = requestedEnd;
        }

        if (startId > endId)
        {
            (startId, endId) = (endId, startId);
        }

        var levels = generator.BuildRange(startId, endId);
        var options = new JsonSerializerOptions
        {
            WriteIndented = true,
            PropertyNamingPolicy = JsonNamingPolicy.CamelCase
        };

        Console.WriteLine(JsonSerializer.Serialize(levels, options));
    }
}

internal sealed class LevelGenerator
{
    private readonly Random _rng;
    private readonly GenerationTuning _tuning;
    private readonly IReadOnlyList<LevelBandConfig> _bands;
    private readonly bool _trace;
    private readonly HashSet<string> _seenLayouts = new();

    public LevelGenerator(Random rng, GenerationTuning tuning, IReadOnlyList<LevelBandConfig> bands)
    {
        _rng = rng;
        _tuning = tuning;
        _bands = bands;
        _trace = Environment.GetEnvironmentVariable("NEKOBAN_DEBUG") == "1";
    }

    public List<GeneratedLevel> BuildRange(int startId, int endId)
    {
        foreach (var band in _bands)
        {
            if (band.ShapeMasksExpanded == null || band.ShapeMasksExpanded.Count == 0)
            {
                var baseMasks = band.ShapeMasks.Count > 0 ? band.ShapeMasks : MaskLibrary.Microban;
                band.ShapeMasksExpanded = MaskLibrary.ExpandWithTransforms(baseMasks);
            }
        }

        var output = new List<GeneratedLevel>();
        for (var id = startId; id <= endId; id++)
        {
            var band = ResolveBand(id);
            var level = BuildSingle(id, band);
            output.Add(level);
        }

        return output;
    }

    private GeneratedLevel BuildSingle(int id, LevelBandConfig band)
    {
        var stopwatch = Stopwatch.StartNew();
        var attempts = 0;
        var failReasons = _trace ? new Dictionary<string, int>() : null;

        while (attempts < _tuning.MaxAttemptsPerLevel &&
               stopwatch.ElapsedMilliseconds < _tuning.MaxMillisecondsPerLevel)
        {
            attempts++;

            var baseMasks = band.ShapeMasks.Count > 0 ? band.ShapeMasks : MaskLibrary.Microban;
            var prepped = band.ShapeMasksExpanded ?? MaskLibrary.ExpandWithTransforms(baseMasks);
            band.ShapeMasksExpanded ??= prepped;
            var mask = MaskLibrary.CreateVariant(
                MaskLibrary.PickRandom(_rng, prepped),
                _rng,
                _tuning.ApplyMaskTransforms,
                _tuning.MaskWallJitter);

            var canvas = LayoutFactory.FromMask(mask, _rng, _tuning);

            var boxCount = _rng.Next(band.BoxCountLow, band.BoxCountHigh + 1);
            if (boxCount <= 0)
            {
                boxCount = 1;
            }

            if (!PiecePlacer.TryPlace(canvas, _rng, boxCount, out var goals, out var boxes, out var player))
            {
                NoteFail(failReasons, "place");
                continue;
            }

            var board = Board.FromCanvas(canvas);
            var reverse = new ReverseSearch(board, _tuning.ReverseSearchMaxDepth, _tuning.ReverseSearchBreadth);
            var startState = reverse.FindStartState(goals, band.MinAllowedPushes, _rng);
            if (startState == null)
            {
                NoteFail(failReasons, "reverse_not_found");
                continue;
            }

            var solver = new SokobanSolver(board);
            var solve = solver.SolveDetailed(startState.Player, startState.Boxes, goals);
            if (solve.IsFail)
            {
                NoteFail(failReasons, "verify_unsolvable");
                continue;
            }

            if (solve.Pushes < band.MinAllowedPushes || solve.Turns < band.MinAllowedTurns || solve.Branching < band.MinAllowedBranching)
            {
                NoteFail(failReasons, "too_easy");
                continue;
            }

            var pushLimit = solve.Pushes + Math.Max(_tuning.PushLimitPadding,
                                                  (int)Math.Ceiling(solve.Pushes * _tuning.PushLimitScale));

            canvas.ClearDynamic();
            canvas.Overlay(goals, 'G');
            canvas.Overlay(startState.Boxes, '$');
            canvas.Set(startState.Player, '@');

            // Final wall normalization; reject if tokens end up on the edge.
            if (!LayoutFactory.NormalizeOuterWallsStrict(canvas, failOnTokens: true))
            {
                NoteFail(failReasons, "boundary");
                continue;
            }

            var lines = canvas.ToLines();
            var layoutKey = string.Join("|", lines);
            if (_seenLayouts.Contains(layoutKey))
            {
                NoteFail(failReasons, "duplicate");
                continue;
            }
            _seenLayouts.Add(layoutKey);

            return new GeneratedLevel
            {
                Id = id,
                Grid = lines,
                LowestPush = solve.Pushes,
                PushLimit = pushLimit
            };
        }

        if (_trace && failReasons != null)
        {
            Console.Error.WriteLine($"[trace] level {id} failed. Reasons:");
            foreach (var kv in failReasons.OrderByDescending(kv => kv.Value))
            {
                Console.Error.WriteLine($" - {kv.Key}: {kv.Value}");
            }
        }

        throw new InvalidOperationException($"레벨 {id} 생성 실패 (attempts {attempts}).");
    }

    private LevelBandConfig ResolveBand(int id)
    {
        foreach (var band in _bands)
        {
            if (id >= band.StartId && id <= band.EndId)
            {
                return band;
            }
        }

        var last = _bands.Last();
        var delta = id - last.EndId;
        var growthStep = Math.Max(1, delta / Math.Max(1, _tuning.DynamicGrowthWindow) + 1);
        return new LevelBandConfig
        {
            StartId = id,
            EndId = id,
            BoxCountLow = last.BoxCountLow + growthStep / 2,
            BoxCountHigh = last.BoxCountHigh + growthStep / 2,
            MinAllowedPushes = last.MinAllowedPushes + growthStep * _tuning.DynamicPushIncrement,
            ShapeMasks = last.ShapeMasks
        };
    }

    private static void NoteFail(IDictionary<string, int>? sink, string reason)
    {
        if (sink == null) return;
        sink[reason] = sink.TryGetValue(reason, out var count) ? count + 1 : 1;
    }
}

internal sealed class GeneratedLevel
{
    public int Id { get; init; }
    public List<string> Grid { get; init; } = new();
    public int LowestPush { get; init; }
    public int PushLimit { get; init; }
}

internal sealed class LevelBandConfig
{
    public int StartId { get; init; }
    public int EndId { get; init; }
    public int BoxCountLow { get; init; }
    public int BoxCountHigh { get; init; }
    public int MinAllowedPushes { get; init; }
    public int MinAllowedTurns { get; init; } = 0;
    public int MinAllowedBranching { get; init; } = 0;
    public List<string[]> ShapeMasks { get; init; } = new();
    public List<string[]>? ShapeMasksExpanded { get; set; }
}

internal sealed class GenerationTuning
{
    public int MaxAttemptsPerLevel { get; init; }
    public int MaxMillisecondsPerLevel { get; init; }
    public int PushLimitPadding { get; init; }
    public double PushLimitScale { get; init; }
    public int DynamicGrowthWindow { get; init; }
    public int DynamicPushIncrement { get; init; }
    public int ReverseSearchMaxDepth { get; init; }
    public int ReverseSearchBreadth { get; init; }
    public bool ApplyMaskTransforms { get; init; }
    public int MaskWallJitter { get; init; }
    public int PocketCarveMin { get; init; } = 0;
    public int PocketCarveMax { get; init; } = 0;
    public int PocketMaxRadius { get; init; } = 1;
}

internal sealed class GridCanvas
{
    private readonly char[] _cells;

    public GridCanvas(int width, int height)
    {
        Width = width;
        Height = height;
        _cells = Enumerable.Repeat('0', width * height).ToArray();
    }

    public int Width { get; }
    public int Height { get; }

    public void Fill(char c) => Array.Fill(_cells, c);

    public void Set(int x, int y, char c)
    {
        if (!InBounds(x, y)) return;
        _cells[y * Width + x] = c;
    }

    public void Set(int index, char c)
    {
        if (index < 0 || index >= _cells.Length) return;
        _cells[index] = c;
    }

    public char Get(int x, int y) => _cells[y * Width + x];
    public char Get(int index) => _cells[index];

    public bool InBounds(int x, int y) => x >= 0 && y >= 0 && x < Width && y < Height;

    public void Overlay(IEnumerable<int> indices, char c)
    {
        foreach (var idx in indices)
        {
            Set(idx, c);
        }
    }

    public void ClearDynamic()
    {
        for (var i = 0; i < _cells.Length; i++)
        {
            if (_cells[i] == '@' || _cells[i] == '$')
            {
                _cells[i] = '.';
            }
        }
    }

    public List<string> ToLines()
    {
        var lines = new List<string>(Height);
        for (var y = 0; y < Height; y++)
        {
            lines.Add(new string(_cells, y * Width, Width));
        }
        return lines;
    }
}

internal static class LayoutFactory
{
    public static GridCanvas FromMask(string[] mask, Random rng, GenerationTuning tuning)
    {
        var height = mask.Length;
        var width = mask.Max(row => row.Length);
        var canvas = new GridCanvas(width, height);
        canvas.Fill('0');

        for (var y = 0; y < height; y++)
        {
            var row = mask[y];
            for (var x = 0; x < row.Length; x++)
            {
                canvas.Set(x, y, row[x]);
            }
        }

        NormalizeOuterWalls(canvas);

        if (tuning.PocketCarveMax > 0)
        {
            AddPockets(canvas, rng, tuning);
            NormalizeOuterWalls(canvas);
        }

        return canvas;
    }

    // Enforce: inside the bounding box of non-void tiles, edges are walls, interior voids become walls.
    private static void NormalizeOuterWalls(GridCanvas canvas)
    {
        var w = canvas.Width;
        var h = canvas.Height;

        var minX = w;
        var minY = h;
        var maxX = -1;
        var maxY = -1;

        for (var y = 0; y < h; y++)
        {
            for (var x = 0; x < w; x++)
            {
                var c = canvas.Get(x, y);
                if (c == '0') continue;
                if (x < minX) minX = x;
                if (y < minY) minY = y;
                if (x > maxX) maxX = x;
                if (y > maxY) maxY = y;
            }
        }

        if (maxX < minX || maxY < minY)
        {
            return; // nothing to normalize
        }

        for (var y = minY; y <= maxY; y++)
        {
            for (var x = minX; x <= maxX; x++)
            {
                var isEdge = x == minX || x == maxX || y == minY || y == maxY;
                if (isEdge)
                {
                    canvas.Set(x, y, '#');
                }
                else if (canvas.Get(x, y) == '0')
                {
                    canvas.Set(x, y, '#');
                }
            }
        }

        // Outside bounding box remains void.
    }

    public static bool NormalizeOuterWallsStrict(GridCanvas canvas, bool failOnTokens)
    {
        var w = canvas.Width;
        var h = canvas.Height;

        var minX = w;
        var minY = h;
        var maxX = -1;
        var maxY = -1;

        for (var y = 0; y < h; y++)
        {
            for (var x = 0; x < w; x++)
            {
                var c = canvas.Get(x, y);
                if (c == '0') continue;
                if (x < minX) minX = x;
                if (y < minY) minY = y;
                if (x > maxX) maxX = x;
                if (y > maxY) maxY = y;
            }
        }

        if (maxX < minX || maxY < minY)
        {
            return false;
        }

        for (var y = minY; y <= maxY; y++)
        {
            for (var x = minX; x <= maxX; x++)
            {
                var isEdge = x == minX || x == maxX || y == minY || y == maxY;
                var c = canvas.Get(x, y);
                if (isEdge)
                {
                    if (failOnTokens && (c == 'G' || c == '$' || c == '@'))
                    {
                        return false;
                    }
                    canvas.Set(x, y, '#');
                }
                else if (c == '0')
                {
                    canvas.Set(x, y, '#');
                }
            }
        }

        return true;
    }

    private static void AddPockets(GridCanvas canvas, Random rng, GenerationTuning tuning)
    {
        var pockets = rng.Next(tuning.PocketCarveMin, tuning.PocketCarveMax + 1);
        for (var i = 0; i < pockets; i++)
        {
            var radius = rng.Next(1, tuning.PocketMaxRadius + 1);
            var x = rng.Next(1, canvas.Width - 1);
            var y = rng.Next(1, canvas.Height - 1);
            for (var yy = y - radius; yy <= y + radius; yy++)
            {
                for (var xx = x - radius; xx <= x + radius; xx++)
                {
                    if (!canvas.InBounds(xx, yy)) continue;
                    if (xx == 0 || yy == 0 || xx == canvas.Width - 1 || yy == canvas.Height - 1) continue;
                    var dx = xx - x;
                    var dy = yy - y;
                    if (dx * dx + dy * dy <= radius * radius)
                    {
                        if (canvas.Get(xx, yy) == '#')
                        {
                            canvas.Set(xx, yy, '.');
                        }
                    }
                }
            }
        }
    }
}

internal static class PiecePlacer
{
    public static bool TryPlace(GridCanvas canvas, Random rng, int boxCount, out HashSet<int> goals, out int[] boxes, out int player)
    {
        goals = new HashSet<int>();
        boxes = Array.Empty<int>();
        player = -1;

        var candidates = Walkable(canvas).ToList();
        var minRequired = boxCount + 2;
        if (candidates.Count < minRequired)
        {
            return false;
        }

        Shuffle(candidates, rng);

        var softGoals = new List<int>();
        foreach (var idx in candidates)
        {
            if (IsDeadCorner(canvas, idx))
            {
                softGoals.Add(idx);
                continue;
            }
            goals.Add(idx);
            if (goals.Count == boxCount) break;
        }

        if (goals.Count != boxCount)
        {
            foreach (var idx in softGoals)
            {
                goals.Add(idx);
                if (goals.Count == boxCount) break;
            }
        }

        if (goals.Count != boxCount) return false;

        var goalSet = new HashSet<int>(goals);
        var nonGoals = candidates.Where(i => !goalSet.Contains(i)).ToList();
        Shuffle(nonGoals, rng);

        boxes = goals.ToArray();
        Array.Sort(boxes);

        if (nonGoals.Count == 0) return false;

        var reachable = FloodFrom(goalSet.First(), canvas, Array.Empty<int>());
        if (goalSet.Any(g => !reachable.Contains(g))) return false;

        var playerOptions = nonGoals.Where(reachable.Contains).ToList();
        if (playerOptions.Count == 0) return false;

        player = playerOptions[rng.Next(playerOptions.Count)];
        return true;
    }

    private static HashSet<int> FloodFrom(int start, GridCanvas canvas, int[] boxes)
    {
        var visited = new HashSet<int>();
        if (IsSolid(canvas.Get(start)) || Array.BinarySearch(boxes, start) >= 0) return visited;

        var queue = new Queue<int>();
        visited.Add(start);
        queue.Enqueue(start);

        while (queue.Count > 0)
        {
            var current = queue.Dequeue();
            foreach (var next in NeighborIndices(current, canvas.Width, canvas.Height))
            {
                if (next < 0 || next >= canvas.Width * canvas.Height) continue;
                if (visited.Contains(next)) continue;

                var tile = canvas.Get(next);
                if (IsSolid(tile) || Array.BinarySearch(boxes, next) >= 0) continue;

                visited.Add(next);
                queue.Enqueue(next);
            }
        }

        return visited;
    }

    private static IEnumerable<int> Walkable(GridCanvas canvas)
    {
        for (var i = 0; i < canvas.Width * canvas.Height; i++)
        {
            var tile = canvas.Get(i);
            if (!IsSolid(tile))
            {
                yield return i;
            }
        }
    }

    private static IEnumerable<int> NeighborIndices(int index, int width, int height)
    {
        var x = index % width;
        var y = index / width;

        if (y > 0) yield return index - width;
        if (y < height - 1) yield return index + width;
        if (x > 0) yield return index - 1;
        if (x < width - 1) yield return index + 1;
    }

    private static bool IsDeadCorner(GridCanvas canvas, int idx)
    {
        var w = canvas.Width;
        var h = canvas.Height;
        var x = idx % w;
        var y = idx / w;

        var solidNorth = y == 0 || IsSolid(canvas.Get(x, y - 1));
        var solidSouth = y == h - 1 || IsSolid(canvas.Get(x, y + 1));
        var solidWest = x == 0 || IsSolid(canvas.Get(x - 1, y));
        var solidEast = x == w - 1 || IsSolid(canvas.Get(x + 1, y));

        var verticalBlocked = (solidNorth && solidSouth);
        var horizontalBlocked = (solidWest && solidEast);
        if (verticalBlocked || horizontalBlocked) return true;

        var cornerNW = solidNorth && solidWest;
        var cornerNE = solidNorth && solidEast;
        var cornerSW = solidSouth && solidWest;
        var cornerSE = solidSouth && solidEast;
        return cornerNW || cornerNE || cornerSW || cornerSE;
    }

    private static bool IsSolid(char tile) => tile == '#' || tile == '0';

    private static void Shuffle<T>(IList<T> list, Random rng)
    {
        for (var i = list.Count - 1; i > 0; i--)
        {
            var j = rng.Next(i + 1);
            (list[i], list[j]) = (list[j], list[i]);
        }
    }
}

internal sealed class Board
{
    private readonly bool[] _walls;

    private Board(int width, int height, bool[] walls)
    {
        Width = width;
        Height = height;
        _walls = walls;
    }

    public int Width { get; }
    public int Height { get; }
    public int Size => Width * Height;

    public static Board FromCanvas(GridCanvas canvas)
    {
        var walls = new bool[canvas.Width * canvas.Height];
        for (var i = 0; i < walls.Length; i++)
        {
            var tile = canvas.Get(i);
            walls[i] = tile == '#' || tile == '0';
        }

        return new Board(canvas.Width, canvas.Height, walls);
    }

    public bool IsSolid(int index) => _walls[index];
}

internal sealed class ReverseSearch
{
    private readonly Board _board;
    private readonly int _maxDepth;
    private readonly int _breadth;
    private readonly int[] _dirs;

    public ReverseSearch(Board board, int maxDepth, int breadth)
    {
        _board = board;
        _maxDepth = maxDepth;
        _breadth = breadth;
        _dirs = new[] { -board.Width, board.Width, -1, 1 };
    }

    public ScrambledState? FindStartState(HashSet<int> goals, int minPush, Random rng)
    {
        var boxes = goals.ToArray();
        Array.Sort(boxes);

        var playerStart = FirstFloorNotGoal(goals);
        if (playerStart < 0) return null;

        var start = new SolverState(playerStart, boxes);
        var queue = new Queue<(SolverState State, int Pushes)>();
        var visited = new HashSet<SolverState>(new StateComparer()) { start };
        queue.Enqueue((start, 0));

        ScrambledState? best = null;
        var bestPush = -1;

        while (queue.Count > 0 && visited.Count < _breadth)
        {
            var (state, pushes) = queue.Dequeue();
            if (pushes >= minPush && pushes > bestPush)
            {
                bestPush = pushes;
                best = new ScrambledState(state.Player, state.Boxes);
            }

            if (pushes >= _maxDepth) continue;

            foreach (var next in Expand(state))
            {
                var nextPushes = pushes + (next.Item2 ? 1 : 0);
                if (nextPushes > _maxDepth) continue;

                var nextState = next.Item1;
                if (visited.Add(nextState))
                {
                    queue.Enqueue((nextState, nextPushes));
                }
            }
        }

        return best;
    }

    private int FirstFloorNotGoal(HashSet<int> goals)
    {
        for (var i = 0; i < _board.Size; i++)
        {
            if (_board.IsSolid(i)) continue;
            if (goals.Contains(i)) continue;
            return i;
        }
        return -1;
    }

    // Returns (state, isPull) where isPull indicates a box move (counts as push)
    private IEnumerable<(SolverState, bool)> Expand(SolverState state)
    {
        foreach (var dir in _dirs)
        {
            var step = state.Player + dir;
            if (!IndexInBounds(step) || _board.IsSolid(step) || Array.BinarySearch(state.Boxes, step) >= 0)
            {
                // pull candidate?
                var boxPos = state.Player + dir;
                var behind = state.Player - dir;
                if (!IndexInBounds(boxPos) || !IndexInBounds(behind)) continue;
                var boxIndex = Array.BinarySearch(state.Boxes, boxPos);
                if (boxIndex < 0) continue;
                if (_board.IsSolid(behind) || Array.BinarySearch(state.Boxes, behind) >= 0) continue;

                var nextBoxes = state.Boxes.ToArray();
                nextBoxes[boxIndex] = state.Player;
                Array.Sort(nextBoxes);
                yield return (new SolverState(behind, nextBoxes), true);
                continue;
            }

            // player walk
            yield return (new SolverState(step, state.Boxes), false);
        }
    }

    private bool IndexInBounds(int idx) => idx >= 0 && idx < _board.Size;
}

internal sealed class SokobanSolver
{
    private readonly Board _board;
    private readonly StateComparer _comparer = new();
    private readonly int[] _dirs;

    public SokobanSolver(Board board)
    {
        _board = board;
        _dirs = new[] { -board.Width, board.Width, -1, 1 };
    }

    public SolveResult SolveDetailed(int player, int[] boxes, HashSet<int> goals)
    {
        Array.Sort(boxes);
        var start = new SolverState(player, boxes);
        var visited = new HashSet<SolverState>(_comparer) { start };
        var parents = new Dictionary<SolverState, (SolverState Parent, int Dir)>(_comparer);
        var queue = new Queue<SolverState>();
        queue.Enqueue(start);

        while (queue.Count > 0)
        {
            var state = queue.Dequeue();
            if (IsSolved(state.Boxes, goals))
            {
                return BuildResult(state, parents);
            }

            foreach (var (next, dir) in Expand(state))
            {
                if (visited.Add(next))
                {
                    parents[next] = (state, dir);
                    queue.Enqueue(next);
                }
            }
        }

        return SolveResult.Fail;
    }

    private IEnumerable<(SolverState State, int Dir)> Expand(SolverState state)
    {
        var reachable = ReachableWithoutPushing(state.Player, state.Boxes);
        foreach (var pos in reachable)
        {
            foreach (var dir in _dirs)
            {
                var boxPos = pos + dir;
                var landing = boxPos + dir;
                if (!IndexInBounds(boxPos) || !IndexInBounds(landing)) continue;

                var boxIndex = Array.BinarySearch(state.Boxes, boxPos);
                if (boxIndex < 0) continue;
                if (_board.IsSolid(landing) || Array.BinarySearch(state.Boxes, landing) >= 0) continue;

                var nextBoxes = state.Boxes.ToArray();
                nextBoxes[boxIndex] = landing;
                Array.Sort(nextBoxes);
                yield return (new SolverState(boxPos, nextBoxes), dir);
            }
        }
    }

    private SolveResult BuildResult(SolverState solved, Dictionary<SolverState, (SolverState Parent, int Dir)> parents)
    {
        var pushes = 0;
        var turns = 0;
        var branching = 0;

        var path = new List<(SolverState State, int Dir)>();
        var current = solved;
        while (parents.TryGetValue(current, out var entry))
        {
            path.Add((current, entry.Dir));
            current = entry.Parent;
        }
        path.Reverse();

        var prevDir = 0;
        foreach (var (_, dir) in path)
        {
            pushes++;
            if (prevDir != 0 && dir != prevDir) turns++;
            prevDir = dir;
        }

        // branching: count states along path that had more than one push option
        current = solved;
        while (parents.TryGetValue(current, out var entry2))
        {
            var pushOptions = Expand(entry2.Parent).Count();
            if (pushOptions > 1) branching++;
            current = entry2.Parent;
        }

        return new SolveResult(pushes, turns, branching);
    }

    private List<int> ReachableWithoutPushing(int start, int[] boxes)
    {
        var visited = new bool[_board.Size];
        var queue = new Queue<int>();
        var output = new List<int>();

        if (_board.IsSolid(start) || Array.BinarySearch(boxes, start) >= 0) return output;

        visited[start] = true;
        queue.Enqueue(start);
        output.Add(start);

        while (queue.Count > 0)
        {
            var current = queue.Dequeue();
            foreach (var dir in _dirs)
            {
                var next = current + dir;
                if (!IndexInBounds(next)) continue;
                if (visited[next]) continue;
                if (_board.IsSolid(next) || Array.BinarySearch(boxes, next) >= 0) continue;
                visited[next] = true;
                queue.Enqueue(next);
                output.Add(next);
            }
        }

        return output;
    }

    private bool IsSolved(int[] boxes, HashSet<int> goals)
    {
        foreach (var b in boxes)
        {
            if (!goals.Contains(b)) return false;
        }
        return true;
    }

    private bool IndexInBounds(int idx) => idx >= 0 && idx < _board.Size;
}

internal readonly record struct SolverState(int Player, int[] Boxes);

internal readonly record struct SolveResult(int Pushes, int Turns, int Branching)
{
    public static SolveResult Fail => new(-1, -1, -1);
    public bool IsFail => Pushes < 0;
}

internal sealed class StateComparer : IEqualityComparer<SolverState>
{
    public bool Equals(SolverState x, SolverState y)
    {
        if (x.Player != y.Player) return false;
        var a = x.Boxes;
        var b = y.Boxes;
        if (a.Length != b.Length) return false;
        for (var i = 0; i < a.Length; i++)
        {
            if (a[i] != b[i]) return false;
        }
        return true;
    }

    public int GetHashCode(SolverState obj)
    {
        var hash = obj.Player * 397 ^ obj.Boxes.Length;
        unchecked
        {
            for (var i = 0; i < obj.Boxes.Length; i++)
            {
                hash = hash * 31 + obj.Boxes[i];
            }
        }
        return hash;
    }
}

internal sealed record ScrambledState(int Player, int[] Boxes);