Setting different color for each series in scatter plot on matplotlib

Suppose I have three data sets:

X = [1,2,3,4]
Y1 = [4,8,12,16]
Y2 = [1,4,9,16]

I can scatter plot this:

from matplotlib import pyplot as plt
plt.scatter(X,Y1,color="red")
plt.scatter(X,Y2,color="blue")
plt.show()

How can I do this with 10 sets?

I searched for this and could find any reference to what I’m asking.

Edit: clarifying (hopefully) my question

If I call scatter multiple times, I can only set the same color on each scatter. Also, I know I can set a color array manually but I’m sure there is a better way to do this.
My question is then, “How can I automatically scatter-plot my several data sets, each with a different color.

If that helps, I can easily assign a unique number to each data set.

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