A proper substring of a string is a substring which is not equal to the string itself. For

example, $$LUCK$$ is a substring of the string $$LUCK$,$ but $$LUCK$$ is not a proper substring of the

string $$LUCK$.$

Given a string, the fingerprint F$($S$)$ of a string S is its longest proper substring which is a prefix

of S and is also equal to a suffix of S$.$ Note that the prefix and suffix could be overlapped. For

example, given a string $$XYXYX$,$ its fingerprint is $$XYX$.$ The length is $3.$

Given a string $$WXYZWXYZWX$,$

$(1)$ give the length of its fingerprint. $(2)$ design an O$($n$)$ algorithm to find the length of the fingerprint. Give the pseudo code.

$(3)$ illustrate your algorithm by the given string