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D. Palindrome pairs

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a non-empty string *s* consisting of lowercase letters. Find the number of pairs of non-overlapping palindromic substrings of this string.

In a more formal way, you have to find the quantity of tuples (*a*, *b*, *x*, *y*) such that 1 ≤ *a* ≤ *b* < *x* ≤ *y* ≤ |*s*| and substrings *s*[*a*... *b*], *s*[*x*... *y*] are palindromes.

A palindrome is a string that can be read the same way from left to right and from right to left. For example, "abacaba", "z", "abba" are palindromes.

A substring *s*[*i*... *j*] (1 ≤ *i* ≤ *j* ≤ |*s*|) of string *s* = *s*_{1}*s*_{2}... *s*_{|s|} is a string *s*_{i}*s*_{i + 1}... *s*_{j}. For example, substring *s*[2...4] of string *s* = "abacaba" equals "bac".

Input

The first line of input contains a non-empty string *s* which consists of lowercase letters ('a'...'z'), *s* contains at most 2000 characters.

Output

Output a single number — the quantity of pairs of non-overlapping palindromic substrings of *s*.

Please do not use the %lld format specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d format specifier.

Examples

Input

aa

Output

1

Input

aaa

Output

5

Input

abacaba

Output

36

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