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.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;

public class Coder{
	
	static class FastScanner{
		BufferedReader s;
		StringTokenizer st;
		
		public FastScanner(){
			st = new StringTokenizer("");
			s = new BufferedReader(new InputStreamReader(System.in));
		}
		
		public FastScanner(File f) throws FileNotFoundException{
			st = new StringTokenizer("");
			s = new BufferedReader (new FileReader(f));
		}
		
		public int nextInt() throws IOException{
			if(st.hasMoreTokens())
				return Integer.parseInt(st.nextToken());
			else{
				st = new StringTokenizer(s.readLine());
				return nextInt();
			}
		}
		public String nextString() throws IOException{
			if(st.hasMoreTokens())
				return st.nextToken();
			else{
				st = new StringTokenizer(s.readLine());
				return nextString();
			}
			
		}
		public String readLine() throws IOException{
			return s.readLine();
		}
		
		public void close() throws IOException{
			s.close();
		}
	}
	
	
	public static void main(String[] args) throws IOException{
	/*  	FastScanner s = new FastScanner(new File("input.txt"));
		PrintWriter ww = new PrintWriter(new FileWriter("output.txt"));
	*/    FastScanner in = new FastScanner();   
	    PrintWriter ww = new PrintWriter(new OutputStreamWriter(System.out));
	    
	    char[] word = in.nextString().toCharArray();
		long total = 0;
		long paliBefore = 0;
		long[] paliEndedBy = new long[word.length];
		for (int i = 0; i < word.length; i++) {
			long pali = 0;
			outer: for (int j = i; j < word.length; j++) {
				int a = i, b = j;
				while (b > a) {
					if (word[a++] != word[b--])
						continue outer;
				}
				pali++;
				paliEndedBy[j]++;
			}
	//		System.out.println(pali+" "+paliBefore);
			total += pali * paliBefore;
			paliBefore += paliEndedBy[i];
		}
		
//		for(int i=0;i<word.length;i++) System.out.print(paliEndedBy[i]+" ");
//		System.out.println();
		
		System.out.println(total);
	    
        in.close();
		ww.close();
	}
}