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:
# cook your dish here
from sys import stdin
from sys import stdout
a=stdin.readline()
n=len(a)-1
a=list(a)[:n]
dp=[[0 for j in range(n)] for i in range(n)]
for i in range(n):
    dp[i][i]=1
for l in range(2,n+1):
    for i in range(n-l+1):
        j=i+l-1
            # print(i,j)
        if(j-i==1 and a[i]==a[j]):
            dp[i][j]=1
        else:
            temp=dp[i+1][j-1]*(a[i]==a[j])
            dp[i][j]=temp
dpr=[[0 for j in range(n)] for i in range(n)]
for i in range(n):
    dpr[i][i]=1
s=a[::-1]
for l in range(2,n+1):
    for i in range(n-l+1):
        j=i+l-1
            # print(i,j)
        if(j-i==1 and s[i]==s[j]):
            dpr[i][j]=1
        else:
            temp=dpr[i+1][j-1]*(s[i]==s[j])
            dpr[i][j]=temp
 
s=[]
 
for i in range(n):
    tempy=0
    for j in range(i,n):
        tempy=tempy+dp[i][j]
    s.append(tempy)
r=[]
for i in range(n):
    tempy=0
    for j in range(i,n):
        tempy=tempy+dpr[i][j]
    r.append(tempy)
# print(s)
# print(r)
# s=s[::-1]
tot=sum(s)
right=[]
 
for i in range(n):
    right.append(tot)
    tot=tot-r[i]
s=s[::-1]
# print(s)
# print(right)
ans=0
for i in range(n):
    j=i+1
    if(j<n):
        ans=ans+s[i]*right[j]
stdout.write(str(ans))