Unique Decipherability of Substitution Rules

Given 26 strings s_a, s_b, ..., s_z each consisting only of lowercase English letters. For any string t (also containing only lowercase letters), we define its substitution t' by replacing every letter x in t with the corresponding string s_x.

For example, if s_a = \(\mathtt{ana}\) and s_b = \(\mathtt{ban}\), then for t = \(\mathtt{baba}\) we have:

[ \mathtt{baba} \implies \mathtt{ban},\mathtt{ana},\mathtt{ban},\mathtt{ana} ]

The substitution rule is said to be bad (i.e. not uniquely decodable) if there exist two distinct strings \(p\) and \(q\) such that \(p \neq q\) but \(p' = q'\). Otherwise, the rule is called good.

Your task is to determine whether the given substitution rule is good or bad.

Note: All formulas are in \( \LaTeX \) format.

inputFormat

The input consists of 26 lines. The i-th line contains a non-empty string \(s\) (only lowercase letters), corresponding to the mapping for the letter \(\mathtt{chr}(i+96)\).

outputFormat

Output a single line containing either good if the substitution rule is uniquely decodable, or bad otherwise.

sample

ana
ban
c
d
e
f
g
h
i
j
k
l
m
n
o
p
q
r
s
t
u
v
w
x
y
z

good