Igor has been into chess for a long time and now he is sick of the game by the ordinary rules. He is going to think of new rules of the game and become world famous.

Igor's chessboard is a square of size n×n cells. Igor decided that simple rules guarantee success, that's why his game will have only one type of pieces. Besides, all pieces in his game are of the same color. The possible moves of a piece are described by a set of shift vectors. The next passage contains a formal description of available moves.

Let the rows of the board be numbered from top to bottom and the columns be numbered from left to right from 1 to n. Let's assign to each square a pair of integers (x,y)− the number of the corresponding column and row. Each of the possible moves of the piece is defined by a pair of integers (dx,dy); using this move, the piece moves from the field (x,y) to the field (x+dx,y+dy). You can perform the move if the cell (x+dx,y+dy) is within the boundaries of the board and doesn't contain another piece. Pieces that stand on the cells other than (x,y) and (x+dx,y+dy) are not important when considering the possibility of making the given move (for example, like when a knight moves in usual chess).

Igor offers you to find out what moves his chess piece can make. He placed several pieces on the board and for each unoccupied square he told you whether it is attacked by any present piece (i.e. whether some of the pieces on the field can move to that cell). Restore a possible set of shift vectors of the piece, or else determine that Igor has made a mistake and such situation is impossible for any set of shift vectors.