Harry and magic string

Harry got a string T, he wanted to know the number of T’s disjoint palindrome substring pairs. A string is considered to be palindrome if and only if it reads the same backward or forward. For two substrings of $T: \, x = T[a_1 \ldots b_1], \, y = T[a_2 \ldots b_2]$(where a1 is the beginning index of $x, b_1$ is the ending index of x. $a_2, b_2$ as the same of y), if both x and y are palindromes and $b_1 < a_2 \text{ or } b_2 < a_1$ then we consider (x, y) to be a disjoint palindrome substring pair of T.

There are several cases.
For each test case, there is a string T in the first line, which is composed by lowercase characters. The length of T is in the range of [1,100000].

For each test case, output one number in a line, indecates the answer.

aca
aaaa

3
15

For the first test case there are 4 palindrome substrings of T.
They are:
S1=T[0,0]
S2=T[0,2]
S3=T[1,1]
S4=T[2,2]
And there are 3 disjoint palindrome substring pairs.
They are:
(S1,S3) (S1,S4) (S3,S4).
So the answer is 3.

BestCoder Round #25