Square the Square #4th power

If nn is a perfect square, and n2k(mod10){ n }^{ 2 }\equiv k(mod\quad 10) what is the sum of all the possible values of kk and the number of values of kk

Example: Suppose kk has 22 values, 33 and 44. Then the answer would be 2+3+4=92+3+4=9

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