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ambitious

Find the maximal product of string prefixes.

Programming language:

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

The *product* of prefix P of string S is the number of occurrences of P multiplied by the length of P. More precisely, if prefix P consists of K characters and P occurs exactly T times in S, then the product equals K * T.

For example, S = "`abababa`" has the following prefixes:

- "
a", whose product equals 1 * 4 = 4,- "
ab", whose product equals 2 * 3 = 6,- "
aba", whose product equals 3 * 3 = 9,- "
abab", whose product equals 4 * 2 = 8,- "
ababa", whose product equals 5 * 2 = 10,- "
ababab", whose product equals 6 * 1 = 6,- "
abababa", whose product equals 7 * 1 = 7.

The longest prefix is identical to the original string. The goal is to choose such a prefix as maximizes the value of the product. In above example the maximal product is 10.

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 maximal product of any prefix of the given string. If the product is greater than 1,000,000,000 the function should return 1,000,000,000.

For example, for a string:

- S = "
abababa" the function should return 10, as explained above,- S = "
aaa" the function should return 4, as the product of the prefix "aa" is maximal.

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

- N is an integer within the range [1..300,000];
- string S consists only of lowercase letters (
a−z).

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