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 JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.BigInteger; 
public class Palindrome_pairs
{
	public static void main(String[] args) throws IOException 
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw=new PrintWriter(System.out);

		int t=1;

		while(t-->0)
		{

			char a[]=("#"+br.readLine()).trim().toCharArray();
			int n=a.length;
			
			long b[]=new long[n+1];
			long c[]=new long[n+1];
			for(int i=1;i<n;i++)
			{
				long count=0;
				for(int j=i;j<n;j++)
				{
					if(check(i,j,a))
					{
						b[j]++;
						count++;
					}
				}

				c[i]=count;
			}
			for(int i=1;i<n;i++)
			{
				b[i]+=b[i-1];
			}
			/*for(long x:b)
				System.out.print(x+" ");
			System.out.println();

			for(long x:c)
				System.out.print(x+" ");
			System.out.println();*/

			BigInteger ans=new BigInteger("0");
			//BigInteger temp;
			for(int i=1;i<n;i++)
			{
				ans=ans.add(new BigInteger(""+(c[i]*b[i-1])));
			}

			pw.println(ans.toString());
		}
		pw.flush();
	}

	public static boolean check(int s,int e,char a[])
	{
		while(s<=e)
		{
			if(a[s]!=a[e])
			{
				return false;
			}
			else
			{
				s++;
				e--;
			}
		}

		return true;
	}
}