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Excel Countif with matrix

Hi, I have the following table and I would like to count the amount of rows in which either column x, y OR z has a value greater than 0. I'm assuming this has to be done with an array formule as I do not want to create a helper column. In the example below, the result of this calculation is 5 (rows A, C, D, F and G have a value in one of the 3 columns greater than 0). A B C D E F G Does anyone know how to do this?

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