How to calculate TP, FP, TN, FN using only N and 4 relationships between the cells?

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Is there an easy way to calculate TP, FP, TN, FN using only the total number of participants and the relationships Sensitivity, Specificity, PPV, and NPV?

I'm doing a meta-analysis on the diagnostic accuracy of various cancer screening tests and I need the MADA counts for a program I wrote to easily compare the treatments and display the ROC curves.

I'd like to find the counts but the author only gives the relations and the total number of participants.

I could simply guess and check the cells until I get a close answer, or I could exhaustively simply do the algebra because I think it's solvable.

I'd simply like to know if there is a package in R or some other language that would simply solves this problem for me.

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