Chocolate Bar Game

Dia and Ruby take turns playing a game with an $n \times n$ square chocolate bar. Ruby goes first. On each turn, the current player must do one of the following:

1. Select a prime number $p$ that no player has selected in a previous round. Then choose a $p \times p$ square on the bar that contains no empty squares (X), and eat every chocolate square inside it.
2. Eat any one $1 \times 1$ chocolate square.

The player who eats the last chocolate square wins. Some squares are already eaten at the start. If both players play optimally, who wins? Note: "optimally" means that if a player has a strategy that wins no matter how the opponent responds, that player makes a move that keeps that strategy.

The first line contains a single integer $n$ ($1 \le n \le 2000$), the size of the chocolate bar. The next $n$ lines each contain $n$ characters. Each character is either X (an empty square) or - (a chocolate square).

Print RUBY if Ruby wins, or DIA if Dia wins.