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 sys
input=sys.stdin.readline
s=list(input().rstrip())
n=len(s)
l=[0]*n # [0,i]
r=[0]*n # [i,n-1]
for i in range(n):
  j=0
  while 0<=i-j and i+j<n and s[i-j]==s[i+j]:
    l[i+j]+=1
    r[i-j]+=1
    j+=1
  j=1
  while 0<=i-j+1 and i+j<n and s[i-j+1]==s[i+j]:
    l[i+j]+=1
    r[i-j+1]+=1
    j+=1
ans=0
for i in range(n):
  for j in range(i+1,n):
    ans+=l[i]*r[j]
print(ans)