I have piped unknown length sequences into makeblastdb. Now I want to know total length of those sequences (BLAST database size).

Example:

 # "cat" is used as an example
 # My "real" sequences are piped from "make random length sequences" command
 cat unknown_length_sequences
     >Seq1
     AA --//-- TG
     >Seq2
     GG --//-- TA
     >Seq3
     AC --//-- CC
     ...

 cat unknown_length_sequences | 
     makeblastdb \ 
         -in - \
         -dbtype 'nucl' \
         -parse_seqids \
         -out random_seq \
         -title "random_seq"

  Output files look like this:  
     random_seq.nhr
     random_seq.nin
     random_seq.nog
     random_seq.nsd
     random_seq.nsi
     random_seq.nsq

My question is - How to get BLAST database size (length of all the sequences)?
Result should be the same as using:
grep -v '>' INPUT | tr -d '\n' | wc

Edit
I want to achieve this without making intermediate files.