Metric to measure top 3 predictions in a multi-class classification problem


I have a multi- class text classification task where I have used the label-smoothing as the loss function to train a model and make predictions on the test data. For each prediction, I got the top 3 predictions classes

What would be a good performance metric to use if the requirement for the model is to make the correct prediction in any of the top 2 or 3 options?

So, Y is a matrix of size n * 1 where as Y_hat is a matrix of n * 3 for top 3 predictions or n * 2 for only the top 2 predictions.