IG won the S championship and many people are excited, ii and gg are no exception. After watching the game, the two of them also want to play a game.

There is now an infinite chessboard with only one piece. Initially the pieces are placed at the $(x, y)$ position (the board coordinates are counted from 0). They took turns to move the pieces. ii moves first.
There are three ways to move

1. Move the piece to the left by one space (from $(x, y)$ to $(x-1, y)$).
2. Move the piece down one space (from $(x, y)$ to $(x, y-1)$).
3. Move the piece to the lower left by one space (from $(x, y)$ to $(x-1, y-1)$).

It should be noted that the pieces cannot be removed from the board.
The first person who can not operate is judged negative (in other words, the first person who moves the piece to $(0,0)$ wins).

Now give the initial coordinates $x, y$ of the piece. Under the premise that both take the optimal strategy, please output the name of the winner (ii or gg).

The input contains only one line. Enter two integers $x\ y$ to represent the initial coordinates of the piece. $(0≤x, y≤1000)$.

The winner's name (ii or gg).