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December 2010

PrefixSet edition (2010-10)

Find the maximal product of string prefixes.

Spoken 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

int solution(char *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 is made only of lowercase letters (
a−z).

Copyright 2009–2024 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

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

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 is made only of lowercase letters (
a−z).

Copyright 2009–2024 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

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

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 is made only of lowercase letters (
a−z).

Copyright 2009–2024 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

*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.

*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.

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); }

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

int solution(String S);

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

func Solution(S string) int

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 is made only of lowercase letters (
a−z).

*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.

*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.

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); }

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 is made only of lowercase letters (
a−z).

*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.

*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.

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); }

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

function solution(S);

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

fun solution(S: String): Int

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

function solution(S)

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

int solution(NSString *S);

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

function solution(S: PChar): longint;

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

function solution($S);

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

sub solution { my ($S) = @_; ... }

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

def solution(S)

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

def solution(s)

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

object Solution { def solution(s: String): Int }

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

public func solution(_ S : inout String) -> Int

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

function solution(S: string): number;

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 is made only of lowercase letters (
a−z).

*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.

*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.

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

Write a function

Private Function solution(S As String) As Integer

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 is made only of lowercase letters (
a−z).