In the center of 2015*2015 grid is placed a common dice with the numbers 1,2,3,4,5,6 written on its sides, so that two numbers on opposite sides add up to 7.
A move by a player consists of 3 steps:
First step: A player is now allowed to rotate the dice, so that any of its numbers shows top.
Second step: The dice is then moved either left or right, which way, that's up to the player's decision, by the number that shows top from the dice.
Third step: The dice is then moved either up or down, which way is also up to the player's decision, by the number that is hidden underneath the cube.
A move that would lead outside the grid is not legal.
How many points on the grid are possible to reach after a finite number of moves?