In this problem, we explore some common DNA problems that arise in Biology.

Given two strings of characters X $($of length n$)$ and Y $($of length m$),$ we care

to compute the length of their longest common subsequence. If there is no

common subsequence, the answer is of course $0.$

A subsequence of a string is a new string generated from the original

string with some characters deleted without changing the relative order of the

remaining characters. A common subsequence of two strings is a subsequence

that is common to both strings.

Examples: $$ace$$ is a subsequence of $$abcde$.$ Another example is that

$$abc$,$abg$,$bdf$,$aeg$,$acefg$,$ all are subsequences of $$abcdefg$$