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:
from os import path;import sys,time
mod = int(1e9 + 7) ;maxx = float('inf')
import sys,time, collections as c , math as m , pprint as p , bisect as bs
I = lambda :int(sys.stdin.buffer.readline())
lint = lambda :[int(x) for x in sys.stdin.buffer.readline().split()]
S = lambda: sys.stdin.readline().strip('\n')
nCr = lambda n, r: reduce(mul, range(n - r + 1, n + 1), 1) // factorial(r)
ceill = lambda n , x: (n+x -1 )//x
T =0
def solve():
	s = S() ; n = len(s)
	l , r  , ans = [0]*n , [0]*n , 0
	a = [(i,i) for i in range(n)] + [(i,i+1) for i in range(n-1) if s[i] == s[i+1]]	
	for i , j in a:
		while i >=0 and j < n and s[i] == s[j]:
			l[j]+=1 ; r[i]+=1
			j+=1 ; i-=1
	for i in range(n):
		for j in range(i+1 , n ):
			ans+=l[i]*r[j]
	print(ans)


				







def run():
    if (path.exists('input.txt')):
        sys.stdin=open('input.txt','r')
        sys.stdout=open('output.txt','w')

run()
T = I() if T else 1
for _ in range(T):
    solve()