Counting cells that contain formulas when the formulas contain the result I want to count

Attendance sample.xlsx

In the attached spreadsheet, I want a formula for cell H27 that counts the number of students with perfect attendance, i.e. 5, without using and hiding an additional column. I have tried several ways of doing this using COUNTIF and other functions. However, because all of the formulas in column H use asterisks, *, the simple =COUNTIF(H2:H26,"*") returns 25, not 5.

Feel free to change the other formulas in column H, so long as an asterisk, *, is displayed for a student with perfect attendance and nothing (either blank or the null string, "") is displayed for a student without perfect attendance. (I don't want to see TRUEs and FALSEs or 1's and 0's.)

Please help.

Thank you, MarvinP.