Counting in 2D Matrix

Filling Matrix

https://www.codechef.com/VIT32020/problems/CCVITR31

The question asks us to :

Find the number of combinations in which at least one column or one row contains balls of only one color.

So we have N rows and N columns and if we select any row or column and color it with one color of the 3 color and the remaining boxes any color that should give us the answer.
My Formula :C(2N,1)*C(3,1)*3^(N * N - N).
But this approach is not matching with the input test cases?

Problem say’s at least one column or one row (not exactly one).

@marksman I don’t know how to do that?