Add Countif to Array Formula (Subtotal) in Excel

I am new to array formulae and have noticed that while SUBTOTAL includes many functions, it does not feature COUNTIF (only COUNT and COUNTA).

I'm trying to figure out how I can integrate a COUNTIF-like feature to my array formula.

I have a matrix, a small subset of which looks like:

A   B   C   D   E
48  53  46  64  66
48      66  89
40  38  42  49  44

37  33  35  39  41

Thanks to the help of @Tom Shape in this post, I (he) was able to average the sum of each row in the matrix provided it had complete data (so rows 2 and 4 in the example above would not be included).

Now I would like to count the number of rows with complete data (so rows 2 and 4 would be ignored) which include at least one value above a given threshold (say 45).

In the current example, the result would be 2, since row 1 has 5/5 values > 45, and row 3 has 1 value > 45. Row 5 has values < 45 and rows 2 and 3 have partially or fully missing data, respectively.

I have recently discovered the SUMPRODUCT function and think that perhaps SUMPRODUCT(--(A1:E1 >= 45 could be useful but I'm not sure how to integrate it within Tom Sharpe's elegant code, e.g.,

=AVERAGE(IF(SUBTOTAL(2,OFFSET(A1,ROW(A1:A5)-ROW(A1),0,1,COLUMNS(A1:E1)))=COLUMNS(A1:E1),SUBTOTAL(9,OFFSET(A1,ROW(A1:A5)-ROW(A1),0,1,COLUMNS(A1:E1))),""))

Remember, I am no longer looking for the average: I want to filter rows for whether they have full data, and if they do, I want to count rows with at least 1 entry > 45.

Try the following. Enter as array formula.

=COUNT(IF(SUBTOTAL(4,OFFSET(A1,ROW(A1:A5)-ROW(A1),0,1,COLUMNS(A1:E1)))>45,IF(SUBTOTAL(2,OFFSET(A1,ROW(A1:A5)-ROW(A1),0,1,COLUMNS(A1:E1)))=COLUMNS(A1:E1),SUBTOTAL(9,OFFSET(A1,ROW(A1:A5)-ROW(A1),0,1,COLUMNS(A1:E1))))))

Data