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 VkQ2D{
    static BufferedReader br;
    public static void main(String args[])throws Exception{
        br=new BufferedReader(new InputStreamReader(System.in));
        String st=toStr();
        int n=st.length();

        int d1[] = new int[n];
        int l = 0;
        int r = -1;
        for (int i = 0; i < n; ++i) {
            int k = (i > r ? 0 : Math.min(d1[l + r - i], r - i)) + 1;
            while (i + k < n && i - k >= 0 && st.charAt(i + k) == st.charAt(i - k)) {
                ++k;
            }
            d1[i] = --k;
            if (i + k > r) {
                l = i - k;
                r = i + k;
            }
        }
        int d2[] = new int[n];
        l = 0;
        r = -1;
        for (int i = 0; i < n; ++i) {
            int k = (i > r ? 0 : Math.min(d2[l + r - i + 1], r - i + 1)) + 1;
            while (i + k - 1 < n && i - k >= 0 && st.charAt(i + k - 1) == st.charAt(i - k)) {
                ++k;
            }
            d2[i] = --k;
            if (i + k - 1 > r) {
                l = i - k;
                r = i + k - 1;
            }
        }

        long left[]=new long[n];
        long right[]=new long[n];
        
        for(int i=0;i<n;i++){
            left[i]=i+1;
            right[i]=n-i-1;
            for(int j=0;j<n;j++){
                if(d1[j]>0){
                    int m=Math.min(d1[j],i-j);
                    if(m>0)left[i]+=m;
                }
                if(d2[j]>0){
                    int m=Math.min(i-j+1,d2[j]);
                    if(m>0)left[i]+=m;
           
                }
                if(d1[j]>0){
                    int m=Math.min(j-i-1,d1[j]);
                    if(m>0){
                        right[i]+=m;
                    }
                }
                if(d2[j]>0){
                    int m=Math.min(j-i-1,d2[j]);
                    if(m>0){
                        right[i]+=m;
                    }
                }
            }
        }
        for(int i=n-1;i>0;i--){
            left[i]=left[i]-left[i-1];
        }
        long res=0;
        for(int i=0;i<n;i++){
            res+=left[i]*right[i];
        }
        System.out.println(res);


    }


    /****************************************************************/
    public static int[] toIntArray()throws Exception{
       String str[]=br.readLine().split(" ");
       int k[]=new int[str.length];
       for(int i=0;i<str.length;i++){
            k[i]=Integer.parseInt(str[i]);
       }
       return k;
    }
    public static int toInt()throws Exception{
       return Integer.parseInt(br.readLine());
    }
    public static long[] toLongArray()throws Exception{
       String str[]=br.readLine().split(" ");
       long k[]=new long[str.length];
       for(int i=0;i<str.length;i++){
            k[i]=Long.parseLong(str[i]);
       }
       return k;
    }
    public static long toLong()throws Exception{
       return Long.parseLong(br.readLine());
    }
    public static double[] toDoubleArray()throws Exception{
       String str[]=br.readLine().split(" ");
       double k[]=new double[str.length];
       for(int i=0;i<str.length;i++){
            k[i]=Double.parseDouble(str[i]);
       }
       return k;
    }
    public static double toDouble()throws Exception{
       return Double.parseDouble(br.readLine());
    }
    public static String toStr()throws Exception{
       return br.readLine();
    }
    public static String[] toStrArray()throws Exception{
       String str[]=br.readLine().split(" ");
       return str;
    }
    /****************************************************************/

}