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PROBLEM

You will be given a list of nucleotides which represent a gene. You know also that there is exactly 3 exons and 2 introns. The gene starts with an exon and ends with an exon. You don't know where the intermediate exon is located. You also know that the both of the introns are non-empty. Since exons are sequences of codons (three nucleotides together) they are a multiple of 3. This is not so for introns, since they are garbage their length has not to be a multiple of 3.

Here is an example of such a gene:

(T C T G C A G C A G A G G G G C C G T C G G C A G A A G G A G 
 G G C T C G G G C A G G C T C T G C G A C T C G T A G G C A C 
 C A G G C G T G A G A C C T G T A G C C C C C G A T C A C C A 
 T G T A C A G C T T C A T G G G T G G T G G C C T G T T C T G 
 T G C C T G G G T G G G G A C C A T C C T C C T G G T G G T G 
 G C C A T G G C A A C A G A C G G G G C C A A G G A C A C C T 
 G T A T T C C A G A T G G A G A A C T C T G C G G C T C A A A 
 G A G G G A A A G G G A G C A A C C C A A G G T C A C T C A G 
 C G G A G G C T G A C T C C T G G T C C T A G G C T G G A A G 
 G A G G A A G A A T A G G G C C C A T G G G A G G G A G C T G 
 A G A A G A C T)
You will also be given a protein (as a list of amino acids). Which is something like:
(ARG ARG ARG LEU PRO GLY SER ARG LEU PRO PRO GLU PRO VAL ARG ASP ALA GLU
 LEU VAL VAL HIS VAL GLU VAL PRO THR THR GLY GLN ASP THR ASP PRO PRO LEU
 VAL GLY GLY PRO PRO PRO VAL PRO LEU SER PRO PRO THR GLU ASP GLN ASP PRO
 THR PHE LEU LEU LEU ILE PRO GLY THR LEU PRO ARG LEU PHE stop)
You are expected to find the introns' start and end positions. The answer will be given a list of two lists. Where each inner list is a pair of two positions.

\begin{displaymath}
\mbox{\tt (} 
\mbox{\tt (} 
intron_{1_{start}}\;\;\;\; intro...
 ...{2_{start}}\;\;\;\; intron_{2_{end}}
\mbox{\tt )}
\mbox{\tt )} \end{displaymath}

If you discover that this protein is not the product of the gene given, then you shall return an empty list.

Name your function that takes the gene list as its first argument and the protein list as the second, as locate_intron

The answer for the above example shall be:

((55 85) (170 249))


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