terrific! thank you so much. This makes me think how one may likely approximate a good value for parameter "okay" So that the number of clusters in the data is what it should be instead of what I want it to be? quite, What if if I dont know how many cuts I intent to make because I dont know how many clusters there are in the data. That is indeed what I am verifying that is to say the number of clusters and the elements within each cluster.

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