Problem E
Mengi

News have spread of a competition to be held within the university, one centered around the board game Mengi. Someone has to make sure that every move made is legal and there isn’t enough manpower to do so, so a program to find every legal move given a particular board state has to be made.

The game is played with $12$ cards on the table at any given time. The players have to find $3$ cards that together make a Mengi. Each card has $4$ properties. The first property is colour, which can be red (R), blue (B) or green (G). Next is the number of shapes on the card which can be one ($1$), two ($2$) or three ($3$). Next is the shape on the card which can be diamonds (D), ellipses (E) or squares (S). Finally there is the background which can be full colour (F), half colour (H) or transparent (T).

Cards will be represented with colour first, next number, then shape and finally background. As an example R2ST is a red card with two transparent squares.

Three cards constitute a Mengi if for each of these four properties the cards are either all the same or no two are the same. As an example, the three cards all have to be the same colour or have to be of three different colours, then the same for the other properties. The internal order of the cards does not matter, a permutation of three cards that make up a Mengi is still the same Mengi.

Input

The input contains $12$ lines, each with one card that is on the table. No two cards are identical.

Output

Print one line for each possible Mengi. The cards in each Mengi are to be written in internal alphabetical order and printed together on one line with spaces between the cards. The Mengi themselves should also be ordered alphabetically in the output. If no Mengi can be formed from the cards in the input, print “Engin Mengi” instead.

B3SF
G3ET
R3DH
B1ET
G3SF
G3DH
G2SF
R1EH
B3EH
G2SH
B2DH
R3SH

B1ET B2DH B3SF
B1ET G2SF R3DH
B3EH G3DH R3SH
B3SF G3ET R3DH
G3DH G3ET G3SF

G1DH
R1DH
G3DH
B1EH
B2DF
B3EH
R2ST
R1DF
G2EF
G1EF
B3SH
B2SH

Engin Mengi