<s>[INST] This problem is based on a combination of Roman Coin Classification, and long short-term memory (LSTM) network algorithm. 

In problems related to Roman coin classification, we use the surface roughness of the coins to determine if a coin is genuine or counterfeit. A multi-class LSTM classification model is proposed. The prepared surface roughness data set along with other information about coins such as weight and date of issue will be used. 

The weights of the coins are measured in grams and range between 1.50 g and 3.20 g. We assume that the data set provided to us only has the measurement of two genuine along with one counterfeit coins with the weight of 2.00 g, 2.199 g, and 1.88 g. I need some formulas, equations and some ideas and insights on selecting a certain parameters.

For this problem, you can consider that we have 3 classes for Roman coins classification based on their surface roughness with three classes: rough, smooth, and medium.

First i would like to know What is the maximum number of samples you would expect to have for your data set and also what is the size of the training set in both balanced and imbalanced scenarios?[/INST]