Algorithm title: UVA 620 Cellular Structure (DP)

Cellular Structure

A chain of connected cells of two types A and B composes a cellular structure of some microorganisms of species.

If no mutation had happened during growth of a organism, its cellular chain would take one of the following forms:

Sample notation O = OA means that if we added to chain of a healthy organism a cell a from the right hand side, we would E nd up also with a chain of healthy organism. It would grow by one cell A.

A laboratory researches a cluster of these organisms. Your task is to write a program which could find out a current stage of growth and health of a organism, given its Cellul AR chain sequence.

Input

A integer n being a number of cellular chains to test, and then n consecutive lines containing chains of tested organisms.

Output

For each tested chain give (in separate lines) proper answers:

If a organism were in two stages of growth on the same time the ' I ' from the list above should to given as an Swer.

Sample Input

4
A
AAB
Baab
Baaba

Sample Output

Simple
fully-grown
mutant
mutagenic