Given a list of variable constraints of the form \(x < y\), you are to write a program that prints all orderings of the variables that are consistent with the constraints.

For example, given the constraints \(x < y\) and \(x < z\) there are two orderings of the variables \(x\), \(y\), and \(z\) that are consistent with these constraints: \(xyz\) and \(xzy\).

Input

• The input consists of a sequence of constraint specifications. A specification consists of two lines: a list of variables on one line followed by a list of constraints on the next line. A constraint is given by a pair of variables, where \(x y\) indicates that \(x < y\).

• All variables are single character, lower-case letters. There will be at least two variables, and no more than \(20\) variables in a specification. There will be at least one constraint, and no more than \(50\) constraints in a specification. There will be at least one, and no more than \(300\) orderings consistent with the constraints in a specification.
• Input is terminated by end-of-file.

Output

• For each constraint specification, all orderings consistent with the constraints should be printed. Orderings are printed in lexicographical (alphabetical) order, one per line. Output for different constraint specifications is separated by a blank line.

Example

Sample input

a b f g
a b b f

v w x y z
v y x v z v w v

Sample output

abfg
abgf
agbf
gabf

wxzvy
wzxvy
xwzvy
xzwvy
zwxvy
zxwvy