using System;
using System.Collections.Generic;
using System.Text;

namespace ConsoleApplication {
    internal class Program {
        private static readonly Stack<Point> OccupyHistory = new Stack<Point>();

        public static void Main(string[] args) {
            var chessTable = new ChessTable();
            var combinationsCount = GetCombinationsCount(chessTable, 8);
            Console.WriteLine("Combinations count: " + combinationsCount);
        }

        private static int GetCombinationsCount(ChessTable table, int figures) {
            var count = 0;
            for (var i = 0; i < ChessTable.Rows; i++) {
                count += StartPlacingAt(table, new Point(0, i), 1, figures);
                table.Clear();
            }

            return count;
        }

        private static int StartPlacingAt(ChessTable table, Point point, int current, int max) {
            if (current == max)
                return 1;

            FigureOccupyTablePoint(table, point);

            var count = 0;
            for (var j = 0; j < ChessTable.Rows; j++) {
                var cell = table[current, j];
                if (cell.IsOccupied || cell.Attacked > 0)
                    continue;

                count += StartPlacingAt(table, new Point(current, j), current + 1, max);
            }

            RollbackOccupyPoint(table);
            return count;
        }

        private static void FigureOccupyTablePoint(ChessTable table, Point point) {
            OccupyHistory.Push(point);
            table[point].IsOccupied = true;
            SetAttacked(table, point, true);
        }

        private static void RollbackOccupyPoint(ChessTable table) {
            var point = OccupyHistory.Pop();
            table[point].IsOccupied = false;
            SetAttacked(table, point, false);
        }

        private static void SetAttacked(ChessTable table, Point point, bool isAttacked) {
            AttackCast(table, point, isAttacked, p => p + Point.Up);
            AttackCast(table, point, isAttacked, p => p + Point.Down);
            AttackCast(table, point, isAttacked, p => p + Point.Right);
            AttackCast(table, point, isAttacked, p => p + Point.Left);
            AttackCast(table, point, isAttacked, p => p + Point.Up + Point.Left);
            AttackCast(table, point, isAttacked, p => p + Point.Down + Point.Left);
            AttackCast(table, point, isAttacked, p => p + Point.Up + Point.Right);
            AttackCast(table, point, isAttacked, p => p + Point.Down + Point.Right);
        }

        private static void AttackCast(ChessTable table, Point start, bool isAttack, Func<Point, Point> move) {
            while (true) {
                start = move(start);
                if (!table.PointInRange(start))
                    return;
                table[start].Attacked += isAttack ? 1 : -1;
            }
        }

        public class ChessTable {
            public const int Rows = 8;

            private readonly Cell[,] _table = new Cell[Rows, Rows];

            public ChessTable() {
                Clear();
            }

            public Cell this[int i, int j] => _table[i, j];
            public Cell this[Point point] => _table[point.X, point.Y];

            public bool PointInRange(Point point)
                => point.X > -1 && point.X < Rows && point.Y > -1 && point.Y < Rows;

            public void Clear() {
                for (var i = 0; i < Rows; i++)
                for (var j = 0; j < Rows; j++)
                    _table[i, j] = new Cell();
            }

            public class Cell {
                public int Attacked;
                public bool IsOccupied;
            }

            public override string ToString() {
                var builder = new StringBuilder();

                for (var i = 0; i < ChessTable.Rows; i++) {
                    for (var j = 0; j < ChessTable.Rows; j++) {
                        var cell = _table[i, j];
                        if (cell.IsOccupied)
                            builder.Append("@");
                        else if (cell.Attacked > 0)
                            builder.Append("X");
                        else
                            builder.Append("O");
                    }

                    builder.Append("\r");
                }

                return builder.ToString();
            }
        }


        public struct Point {
            public static readonly Point Up = new Point(0, 1);
            public static readonly Point Down = new Point(0, -1);
            public static readonly Point Right = new Point(1, 0);
            public static readonly Point Left = new Point(-1, 0);
            public static readonly Point Zero = new Point(0, 0);

            public int X;
            public int Y;

            public Point(int x, int y) {
                X = x;
                Y = y;
            }

            public static Point operator +(Point a, Point b) {
                return new Point(a.X + b.X, a.Y + b.Y);
            }

            public static Point operator -(Point a, Point b) {
                return new Point(a.X - b.X, a.Y - b.Y);
            }

            public override string ToString() => "X: " + X + " Y: " + Y;
        }
    }
}