import java.util.Scanner;
import java.io.*;

public class KPuzzle
{
	//a 2-d array of the cages, cages that are more than 1 square will have alieases on all of the squares.
	KCage[] p;//The puzzle
	int size;
	boolean[] p2; //The possiblilities for every square - 3D
	public KPuzzle()
	{

	}
	public KPuzzle(String filename)
	{
		parsePuzzle(filename);
		makePossible();
		checkCages();
	}
	private void checkCages()
	{
		for(int i = 0; i < p.length; i++)
		{
			KCage c = p[i];
			if(c.getNumCells() == 1)
			{
				Cell cell = c.getCell(0);
				this.putNumber(cell.getX(),cell.getY(),c.getTargNumber());
				System.out.println("After putting " + c.getTargNumber() + " into (" + cell.getX() + "," + cell.getY() + ") Possibilities are:");
				this.printPossibilities();
				return;
			}
		}
	}
	public Cell getCell(int x, int y)
	{
		KCage k = p[y*size + x];
		for(int  i = 0; i < k.getNumCells();i++)
		{
			Cell c = k.getCell(i);
			if(c.getX() == x && c.getY() == y)
			{
				return c;
			}
		}
		return null;
	}
	public boolean isComplete()
	{
		for(int i = 0; i < size; i++)
		{
			for(int j = 0; j < size; j++)
			{
				int possibilitiesForCell = 0;
				for(int k = 0; k < size; k++)
				{
					if(p2[(i*size*size)+(j*size)+k])
					{
						possibilitiesForCell++;
					}
				}
				if(possibilitiesForCell != 1)
				{
					return false;
				}
			}
		}
		return true;
	}
	public boolean[] getPossibilities(int xn, int yn)
	{
		boolean[] output = new boolean[size];
		for(int i = 0; i < size; i++)
		{
			output[i] = p2[(yn*size*size)+(xn*size)+i];
		}
		return output;
	}
	public void removePossibility(int xn, int yn, int num)
	{
		p2[(yn*size*size)+(xn*size)+num-1] = false;
	}
	public void addPossibility(int xn, int yn, int num)
	{
		p2[(yn*size*size)+(xn*size)+num-1] = true;
	}
	public void putNumber(int xn, int yn, int num)
	{
		System.out.println("putting " + num + " in (" + xn + "," + yn + ")");
		for(int y = 0; y < size; y++)
		{
			for(int z = 0; z < size; z++)
			{
				if(z == num-1)
				{
					//System.out.println("Setting (" + xn + "," + y + "," + z + ") to false");
					p2[(y*size*size)+(xn*size)+z] = false;
				}
			}
		}
		for(int x = 0; x < size; x++)
		{
			for(int z = 0; z < size; z++)
			{
				if(z == num-1)
					p2[(yn*size*size)+(x*size)+z] = false;
			}
		}
		for(int z = 0; z < size; z++)
		{
			p2[(yn*size*size)+(xn*size)+z] = false;
		}
		System.out.println("Setting (" + xn + "," + yn + "," + (num-1) + ") to true");
		p2[(yn*size*size)+(xn*size)+num-1] = true;
	}
	public void takeNumber(int xn, int yn)
	{
		int thisnum = -1;
		for(int z = 0; z < size; z++)
		{
			if(p2[(yn*size*size)+(xn*size)+z])
				thisnum = z;
		}
		if(thisnum == -1)
		{
			System.out.println("I couldn't find a number there!");
			return;
		}
		for(int y = 0; y < size; y++)
		{
			for(int z = 0; z < size; z++)
			{
				if(z == thisnum)
				{
					System.out.println("Setting (" + xn + "," + y + "," + z + ") to true");
					p2[(y*size*size)+(xn*size)+z] = true;
				}
			}
		}
		for(int x = 0; x < size; x++)
		{
			for(int z = 0; z < size; z++)
			{
				if(z == thisnum)
					p2[(yn*size*size)+(x*size)+z] = true;
			}
		}
		for(int z = 0; z < size; z++)
		{
			p2[(yn*size*size)+(xn*size)+z] = true;
		}
	}
	public void printPossibilities()
	{
		for(int y = 0; y < size; y++)
		{
			for(int x = 0; x < size; x++)
			{
				System.out.print("Possibilities for (" + x + "," + y + ") are: ");
				for(int z = 0; z < size; z++)
				{
					if(p2[(y*size*size)+(x*size)+z])
					{
						System.out.print(z+1);
					}
				}
				System.out.println("");
			}
		}
	}
	private void makePossible()
	{
		p2 = new boolean[size*size*size];
		//System.out.println("Makeing possibilities:");
		for(int i = 0; i < size; i++)
		{
			for(int j = 0; j < size; j++)
			{
				for(int k = 0; k < size; k++)
				{
					p2[(i*size*size)+(j*size)+k] = true;
					//System.out.print(p2[(i*size*size)+(j*size)+k] + " ");
				}
				//System.out.print("\t");
			}
			//System.out.println("");
		}
	}
	private void parsePuzzle(String filename)
	{
		Scanner s = null;
		try
		{
			s = new Scanner(new FileInputStream(filename));
		}
		catch (Exception e)
		{
			System.out.println("Something went terribly wrong!\n" + e);
		}
		size = Integer.parseInt(s.nextLine().replaceAll("\n",""));
		p = new KCage[size*size];
		//System.out.println("Puzzle size: " + size + " Cages: " + p.length);
		for(int i = 0; s.hasNextLine();i++)
		{
			String t1 = s.nextLine();
			//System.out.println("Praseing: " + t1);
			String[] t2 = t1.split(",");
			//System.out.println("Parts length: " + t2.length);
			if(t2.length > 1)
			{
				Cell[] allcells = new Cell[Integer.parseInt(t2[2])];
				for(int j = 0; j < Integer.parseInt(t2[2]);j++)
				{
					String[] coords = s.nextLine().split(",");
					allcells[j] = new Cell(Integer.parseInt(coords[0]),Integer.parseInt(coords[1]));
				}
				for(Cell c : allcells)
				{
					p[c.getY()*size + c.getX()] = new KCage(Integer.parseInt(t2[0]),getOp(t2[1]),allcells);
				}
				//p[i] = new KCage(Integer.parseInt(t2[0]),getOp(t2[1]),allcells);
				//System.out.println("Created " + p[i]);
			}
		}
	}
	public KCage getCage(int i)
	{
		return p[i];
	}
	public int getNumCages()
	{
		return p.length;
	}
	public String toString()
	{
		String output = "Puzzle{\n\t";
		if(p.length == 0)
			return output+"}";
		output += p[0];
		for(int i = 1; i < p.length; i++)
		{
			output += ",\n\t"+p[i];
		}
		return output + "\n}";
	}
	private static Operator getOp(String s)
	{
		switch(s)
		{
			case "+":
				return Operator.PLUS;
			case "-":
				return Operator.MINUS;
			case "*":
				return Operator.MULTIPLY;
			case "/":
				return Operator.DIVIDE;
			case " ":
				return Operator.NONE;
			default:
				return Operator.NULL;
		}
	}
}