Genotypes

Memory limit: 32 MB

Genotype is a finite sequence of genes. It can be described by words built of capital letters A–Z of the English alphabet. Different letters denote different kinds of genes. A gene can bud and in effect transform into a pair of new genes. Such transformations are controlled by a finite set of rules. Every rule of budding can be described by three capital letters . Such a description means that gene can transform into the pair of genes .

We are using to denote the special kind of genes called supergenes. The breeding of a genotype begins from a sequence of supergenes and it consists in controlled budding of chosen genes according to the given rules.

Task

Write a program that:

• reads from the standard input a finite set of budding rules and a sequence of words describing genotypes which we want to breed,
• for every given genotype checks if it can be bred from a certain finite sequence of supergenes according to the given budding rules and if so finds the minimal length of such a sequence,
• writes the result to the standard output.

Input

In the first line of the standard output there is one integer , . In each of the following n lines there is one budding rule. Such a rule is described by a word consisting of three capital letters A–Z. We allow budding rules in which the second or the third character denotes a supergene.

In the next line there is written one integer , . In each of the following lines there is one genotype. Such a genotype is described by a non-empty word consisting of at most letters A–Z.

Output

In the -th of lines of the standard output there should be written:

• one positive integer — the minimal length of a sequence of supergenes needed to breed the -th of the given genotypes, or
• the word NIE (which means “no” in Polish), if such a genotype cannot be bred.

Example

For the input data:

6
SAB
SBC
SAA
ACA
BCC
CBC
3
ABBCAAABCA
CCC
BA

the correct result is:

3
1
NIE

Task author: Przemyslawa Kanarek.