Flukehn is a well-known god in Eastern and he is invincible with 5 ranks in Go. To challenge the legend of god
Flukehn in Eastern, you decided to compose a modified Shogi (the Japanese variant of chess) match with
Flukehn. The chess board can be viewed as an infinite two-dimensional plane. Initially you have

Pawns uniquely occupying an integral point on the board, and
Flukehn has one Gold general occupying an integral point either.
The game is turn-based. At each turn,
- you shall pick a Pawn and move it down one unit. More formally, you can move one Pawn with original coordinate
to
. Noted that you can't have two Pawns on the same point at any moment. - Then Flukehn shall choose his Gold general to move up, down, left, right, up-left or up-right to the nearest integral point. More formally, with original coordinate
, Flukehn shall choose his Gold general to move to
,
,
,
,
or
.
No one can skip his own turn.
At any moment when Gold general and a Pawn are on the same integral point, the Pawn is considered defeated by \textsf{Flukehn} and should be picked out from the board (Even if it is on your turn). The initial coordinate of
Flukehn's Gold general is on
)
.
There is no limitation on turns of the game.
You aim to minimize the number of defeated Pawns while
Flukehn aim to maximize it and you both play
optimally in the game.
What is final number of Pawns defeated in finite number of turns?