Mate in one P76591

Given several chess positions, tell if white can checkmate in one movement. The given positions always follow these properties:

• It is white’s turn.
• Black has only the king.
• White does not have any pawns.
• White cannot castle.

Please remember these rules:

• A king can never move into an attacked position.
• In particular, both kings cannot be in adjacent cells.
• A king can eat an adjacent enemy piece if it is not defended by any other piece.
• A position is checkmate if the king is threatened and it has no valid movement.
• A king can checkmate by moving, if by this another piece attacks the enemy king.

Input

Input consists of several cases. Each case begins with the position of the black king, followed by the number n of white pieces (between 2 and 16), followed by the position of the white pieces. Positions are codified with the kind of piece (‘K’ for king, ‘Q’ for queen, ‘B’ for bishop, ‘N’ for knight, ‘R’ for rook), followed by the column (between ‘a’ and ‘h’), followed by the row (between 1 and 8). There are no two pieces on the same cell, and no piece is threatening the black king.

Output

For every case, print the only movement that checkmates the black king: the kind of piece, and the position to move to. If it is impossible to checkmate in one, print “NO”. If there is more than one movement that checkmates in one, print “>1”.