Longest Common Subsequence
For given two sequences X and Y, a sequence Z is a common subsequence of XX and YY if Z is a subsequence of both X and Y. For example, if X={a,b,c,b,d,a,b} and Y={b,d,c,a,b,a}, the sequence{b,c,a} is a common subsequence of both X and Y. On the other hand, the sequence {b,c,a} is not a longest common subsequence (LCS) of X and Y, since it has length 3 and the sequence {b,c,b,a}, which is also common to both X and Y, has length 4. The sequence{b,c,b,a} is an LCS of X and Y, since there is no common subsequence of length 5 or greater.
Write a program which finds the length of LCS of given two sequences X and Y. The sequence consists of alphabetical characters.