Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

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

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/24/2019 23:49:08 (f2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|