public static boolean isValidPosition(int i, int j){
		if(i < 4) return (j > -1 && j < 4);
		else if(i > 3 && i < 7) return (j > -1 && j < 3);
		else if(i > 6 && i < 9) return (j > -1 && j < 2);
		else if(i == 9) return (j == 0);
		else System.out.println("invalid Position dected. i="+i+", j="+j); return false;
	}