The Travel of the Queen

Once Alice and Bob decided to play chess, but they found out that a lot of chessmen are missing. Then they invented another game. They needed only chess-clock, chessboard and the queen. The rules of the game are quite easy. The first player puts the queen at any field of the chessboard. Then the players move the queen in turn, starting from the second player. If the player puts the queen on the field, where it has already been, he loses. The game can be completed in a draw, only if the queen has already been on every field of the chessboard, but the player may move the queen on the starting field. The queen can move on any number of fields horizontally, vertically or diagonally.

Suppose, that the game is completed in a draw, and all moves of the first player are known. Restore the moves of the second player.

The input file contains one line with the moves of the first player, separated by one space. Verticals are designated by letters from a through h, and horizontals by numerals.

Write into the output file in the same form the moves made by the second player so, that the game is ended in a draw. If there exist a number of variants, then write any one of them.

a8 a7 c4 d1 b4 a1 a3 c2 b3 b8 c5 d8 b7 c7 d2 d3 h5 e1 h1 f3 f2 g2 e6 f4 g6 e4 f8 g7 e8 g5 h2 h3

a5 a6 a4 b1 c3 a2 c1 b2 b5 d6 b6 c8 c6 d7 d4 d5 e5 h4 f1 e2 g1 g4 e3 g3 f5 e7 f6 f7 g8 h6 h7 h8