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A *prefix* of a string S is any leading contiguous part of S. A *suffix* of the string S is any trailing contiguous part of S. For example, "`c`" and "`cod`" are prefixes, and "`ty`" and "`ity`" are suffixes of the string "`codility`". For simplicity, we require prefixes and suffixes to be non-empty and shorter than the whole string S.

A *border* of a string S is any string that is both a prefix and a suffix. For example, "`cut`" is a border of a string "`cutletcut`", and a string "`barbararhubarb`" has two borders: "`b`" and "`barb`".

We are looking for such borders of S that have at least three non-overlapping occurrences; that is, for some string that occurs as a prefix, as a suffix and elsewhere in between. For example, for S = "`barbararhubarb`", the only such string is "`b`".

In this problem we consider only strings that consist of lower-case English letters (`a`−`z`).

Write a function:

class Solution { public int solution(String S); }

that, given a string S consisting of N characters, returns the length of its longest border that has at least three non-overlapping occurrences in the given string. If there is no such border in S, the function should return 0.

For example, given a string S as follows:

- if S = "
barbararhubarb" the function should return 1, as explained above;- if S = "
ababab" the function should return 2, as "ab" and "abab" are both borders of S, but only "ab" has three non-overlapping occurrences;- if S = "
baaab" the function should return 0, as its only border "b" occurs only twice.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [0..1,000,000];
- string S is made only of lowercase letters (
a−z).

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