The chess endgame "a king and a queen versus a king" is known to be easy victory for the side that has a queen.

The position in such an endgame is described by the locations of three figures: the white king, the white queen, and the black king. Locations are written in a usual chess notation, constructed from a letter from "a" to "h", which determine vertical line, and the digit from 1 to 8, which determine horizontal line of the location.

Given the position described, you are find a move for the white queen by which the black king will be checkmated, or determine that no such a move exists.

The input contains three two-character locations for the white king, white queen, and black king, in that order, separated by spaces.
The input position is a valid chess position for the white's turn, i.e. all figures occupy different spaces, kings are not located in the neighboring squares, and the black king is not under the check.

Output file must contain the two-character location — destination square for the white queen's move. If checkmating move does not exist, output file must contain the string "no". If there is more than one checkmating move, output the one with the smallest vertical position then with the smallest horizontal postion.

a3 g2 a1

a2

Move rules:
The queen may move in any straight line, horizontal, vertical, or diagonal.
The king moves one square in any direction, horizontally, vertically, or diagonally.

Northeastern Europe 2001, Far-Eastern Subregion