Problem: You 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 = s1s2... s|s| is a string sisi + 1... sj. 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

Solution (in PYTHON3):

Solution:
import re
import itertools
from collections import Counter, deque

class Task:
    s = ""
    answer = ""
	
    def getData(self):
        self.s = input()
        #inFile = open('input.txt', 'r')
        #inFile.readline().rstrip()
        #self.childs = inFile.readline().rstrip()

    def solve(self):
        s = self.s
        pairs = [0] * len(s)
        palindroms = [0] * len(s)
        palindroms[0] = 1
        isPalindrome = [[False for i in range(0, len(s))] \
                for j in range(0, len(s))]
        for i in range(0, len(s)):
            for delta in range(0, min(i, len(s) - i - 1) + 1):
                if s[i - delta] != s[i + delta]:
                    break
                isPalindrome[i - delta][i + delta] = True
        for i in range(0, len(s) - 1):
            if s[i] != s[i + 1]:
                continue
            for delta in range(0, min(i, len(s) - i - 2) + 1):
                if s[i - delta] != s[i + 1 + delta]:
                    break
                isPalindrome[i - delta][i + 1 + delta] = True
        
        for i in range(1, len(s)):
            newPalindromsCounter = 0
            for j in range(1, i + 1):
                if isPalindrome[j][i]:
                    pairs[i] += palindroms[j - 1]
                    newPalindromsCounter += 1
            if isPalindrome[0][i]:
                newPalindromsCounter += 1
            pairs[i] += pairs[i - 1]
            palindroms[i] = palindroms[i - 1] + newPalindromsCounter
        self.answer = pairs[len(s) - 1]

    def printAnswer(self):
        print(self.answer)
        #outFile = open('output.txt', 'w')
        #outFile.write(self.answer)

task = Task()
task.getData()
task.solve()
task.printAnswer()