Please solve in R program language. NOT C++ or Python!!!!

DNAseq.txt

ATGGCAATAACCCCCCGTTTCTACTTCTAGAGGAGAAAAGTATTGACATGAGCGCTCCCGGCACAAGGGCCAAAGAAGTCTCCAATTTCTTATTTCCGAATGACATGCGTCTCCTTGCGGGTAAATCACCGACCGCAATTCATAGAAGCCTGGGGGAACAGATAGGTCTAATTAGCTTAAGAGAGTAAATCCTGGGATCATTCAGTAGTAACCATAAACTTACGCTGGGGCTTCTTCGGCGGATTTTTACAGTTACCAACCAGGAGATTTGAAGTAAATCAGTTGAGGATTTAGCCGCGCTATCCGGTAATCTCCAAATTAAAACATACCGTTCCATGAAGGCTAGAATTACTTACCGGCCTTTTCCATGCCTGCGCTATACCCCCCCACTCTCCCGCTTATCCGTCCGAGCGGAGGCAGTGCGATCCTCCGTTAAGATATTCTTACGTGTGACGTAGCTATGTATTTTGCAGAGCTGGCGAACGCGTTGAACACTTCACAGATGGTAGGGATTCGGGTAAAGGGCGTATAATTGGGGACTAACATAGGCGTAGACTACGATGGCGCCAACTCAATCGCAGCTCGAGCGCCCTGAATAACGTACTCATCTCAACTCATTCTCGGCAATCTACCGAGCGACTCGATTATCAACGGCTGTCTAGCAGTTCTAATCTTTTGCCAGCATCGTAATAGCCTCCAAGAGATTGATGATAGCTATCGGCACAGAACTGAGACGGCGCCGATGGATAGCGGACTTTCGGTCAACCACAATTCCCCACGGGACAGGTCCTGCGGTGCGCATCACTCTGAATGTACAAGCAACCCAAGTGGGCCGAGCCTGGACTCAGCTGGTTCCTGCGTGAGCTCGAGACTCGGGATGACAGCTCTTTAAACATAGAGCGGGGGCGTCGAACGGTCGAGAAAGTCATAGTACCTCGGGTACCAACTTACTCAGGTTATTGCTTGAAGCTGTACTATTTTAGGGGGGGAGCGCTGAAGGTCTCTTCTTCTCATGACTGAACTCGCGAGGGTCGTGAAGTCGGTTCCTTCAATGGTTAAAAAACAAAGGCTTACTGTGCGCAGAGGAACGCCCATCTAGCGGCTGGCGTCTTGAATGCTCGGTCCCCTTTGTCATTCCGGATTAATCCATTTCCCTCATTCACGAGCTTGCGAAGTCTACATTGGTATATGAATGCGACCTAGAAGAGGGCGCTTAAAATTGGCAGTGGTTGATGCTCTAAACTCCATTTGGTTTACTCGTGCATCACCGCGATAGGCTGACAAAGGTTTAACATTGAATAGCAAGGCACTTCCGGTCTCAATGAACGGCCGGGAAAGGTACGCGCGCGGTATGGGAGGATCAAGGGGCCAATAGAGAGGCTCCTCTCTCACTCGCTAGGAGGCAAATGTAAAACAATGGTTACTGCATCGATACATAAAACATGTCCATCGGTTGCCCAAAGTGTTAAGTGTCTATCACCCCTAGGGCCGTTTCCCGCATATAAACGCCAGGTTGTATCCGCATTTGATGCTACCGTGGATGAGTCTGCGTCGAGCGCGCCGCACGAATGTTGCAATGTATTGCATGAGTAGGGTTGACTAAGAGCCGTTAGATGCGTCGCTGTACTAATAGTTGTCGACAGACCGTCGAGATTAGAAAATGGTACCAGCATTTTCGGAGGTTCTCTAACTAGTATGGATTGCGGTGTCTTCACTGTGCTGCGGCTACCCATCGCCTGAAATCCAGCTGGTGTCAAGCCATCCCCTCTCCGGGACGCCGCATGTAGTGAAACATATACGTTGCACGGGTTCACCGCGGTCCGTTCTGAGTCGACCAAGGACACAATCGAGCTCCGATCCGTACCCTCGACAAACTTGTACCCGACCCCCGGAGCTTGCCAGCTCCTCGGGTATCATGGAGCCTGTGGTTCATCGCGTCCGATATCAAACTTCGTCATGATAAAGTCCCCCCCTCGGGAGTACCAGAGAAGATGACTACTGAGTTGTGCGAT

(i) Write a function that accepts a DNA sequence (as a single string consisting of A, G, C, T characters only) and a user-given number n>=2, and returns a matrix containing the starting position of each match along with the actual number of codons between the start and the end for each match. (A "match" is a DNA subsequence (as string) that starts with triplet ("codon") "AAA" or "GAA" and ends with triplet ("codon") "AGT" and has at least 2 and at most " n " other triplets ("codons") between the start and the end.) E.g. for "GAACCCACTAGTATAAAATTTGGGAGTCCCAAACCCTTTGGGAGT" and n=10, the answer is Apply the function for several values of n of your choice on the DNA sequence in file DNAseq.txt (posted in D2L). Make sure that the columns are named as shown and that the empty matrix displays properly. (ii) Write a function that accepts a DNA sequence (as a single string) and returns a matrix that contains (without duplicates) all possible occurrences (whether overlapping, partially overlapping or not) of DNA subsequences that start with codon "AAA" or "GAA" and end with codon "AGT" and have at least 2 other codons between the start and the end. The first column of the matrix should contain the starting point of the subsequence in the given DNA sequence and the second column should contain the number of the codons between the first and last codon in each subsequence. The matrix should be in sorted increasing order of start and codon count. (The function may call the function in (i). Also function union() that applies to data frames (dplyr package) might be useful. Also at most one loop is allowed. Apply the function on the DNA sequence in file DNAseq.txt (posted in D2L)