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Count the palindromic subwords of given string.

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

A string is a *palindrome* if it reads exactly the same from left to right as it does from right to left. For example, these strings are palindromes:

azaabbaabacaba

These strings are not palindromes:

zazaabcdabacada

Given a string S of length N, a *slice* of S is a substring of S specified by a pair of integers (p, q), such that 0 ≤ p < q < N. A slice (p, q) of string S is *palindromic* if the string consisting of letters S[p], S[p+1], ..., S[q] is a palindrome. For example, in a string S = `abbacada`:

- slice (0, 3) is palindromic because
abbais a palindrome,- slice (6, 7) is not palindromic because
dais not a palindrome,- slice (2, 5) is not palindromic because
bacais not a palindrome,- slice (1, 2) is palindromic because
bbis a palindrome.

Write a function

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

that, given a string S of length N letters, returns the number of palindromic slices of S. The function should return −1 if this number is greater than 100,000,000.

For example, for string S = `baababa` the function should return 6, because exactly six of its slices are palindromic; namely: (0, 3), (1, 2), (2, 4), (2, 6), (3, 5), (4, 6).

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

- N is an integer within the range [0..20,000];
- string S is made only of lowercase letters (
a−z).

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