google sheets – Using countifs with Index function and (OR) criteria

I’m using this formula to count rows that has either of the following text (SCD,SCA,Sickl).
First I indexed two columns to be one column (E & G)
Then I asked to count any row that has any one of the following texts (SCD or SCA or sickl). if the column has two of three of those texts, It will all return same count 1 as one row only.

=ArrayFormula(sum(countif(index(admissions!E9:E58 & admissions!G9:G58),{"*SCD*","*SCA*","*Sickl*"})))

https://docs.google.com/spreadsheets/d/1OUk3hUwL2CcePR4aKXU746DQTVdTVE5_lICpYSKBLpg/edit?usp=sharing

This is the link, the formula gives back a result of 6 while it should have given 4 only.