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 A₁A₂A₃. Such a description means that gene A₁ can transform into the pair of genes A₂A₃.

We are using S 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

• reads from the text file GEN.IN 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 text file GEN.OUT.

Input

In the next line there is written one integer k, 1 <= k <= 10000. In each of the following k lines there is one genotype. Such a genotype is described by a non-empty word consisting of at most 100 letters A - Z.

Output

• one positive integer - the minimal length of a sequence of supergenes needed to breed the i-th of the given genotypes, or
• the word NIE (which means NO in Polish), if such a genotype can not be bred.

Example

6
SAB
SBC
SAA
ACA
BCC
CBC
3
ABBCAAABCA
CCC
BA

3
1
NIE