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After decades of shadowy demonstrations and delays from the game’s maker,
Chess 2 has finally been released. You waited in line all night to be one of
the first to purchase an example of the hot sequel to the classic original,
and now you are finally getting a chance to open up your new investment and
take a look inside. What you find is slightly puzzling; in addition to the
traditional pieces, the game has been expanded to contain a number of pieces
that are not actually original.
The best-known piece that has been added to the game is the nightrider. The
nightrider can make any number of knight moves in a single direction, i.e.,
its offset from its initial position will be 2***m** in one dimension and
**m** in the other for some nonzero integer **m**. Like other "sliding"
pieces, if one of the knight moves would cause it to take another piece it is
not able to traverse beyond that point
The archbishop is also part of Chess 2. The archbishop can simply make any
move that a knight or bishop could legally make.
The strangest new piece is the kraken. The kraken can move to any square on
the board, regardless of the position of any other pieces, including its own
current position.
You don't feel like reading the manual to learn about how the new pieces fit
into the standard chess opening positions, so instead you place some of the
pieces randomly on the board. The game you’ve decided to play is simply to
count how many pieces on the board are currently being threatened. A piece is
threatened if another piece is able to move into its cell and take it (note
that if the kraken moves into its own cell it does not take itself).
## Input
Your input file will consist of a single integer **N** followed by **N** test
cases. Each case will consist of, all separated by whitespace, an integer
**P** followed by the identities and positions of **P** Chess 2 pieces. Pieces
are described by a single character **C** to denote their type (see
specification below) followed by two integers **R** and **F**, the 1-based
rank and file, respectively, of the piece.
You've decided to ignore the colors of the pieces in this game. The color of
the pieces will not be reflected in the input and so cannot affect your
output.
To make room for the new pieces, the Chess 2 board is a 16 by 16 grid. No
specified pieces will fall outside the board, and no two pieces will occupy
the same position.
The types of pieces will be specified as follows, and no entries not present
in this table will appear on the board:
Piece
Abbreviation
King
K
Queen
Q
Rook
R
Bishop
B
Knight
N
Nightrider
S
Archbishop
A
Kraken
E
## Output
Output a single integer, the number of threatened pieces on the board, for
each test case separated by whitespace.
## Constraints
**N** = 20
3 ≤ **P** ≤ 64
1 ≤ **R, F** ≤ 16
**C** will be one of {K, Q, R, B, N, S, A, E}
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