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.*;
public class D159 {
	
	class InputReader {

		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream));
			tokenizer = null;
		}

		public InputReader() throws FileNotFoundException {
			reader = new BufferedReader(new FileReader("d:/input.txt"));
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

	}
	
	public void run(){
		
		InputReader reader = new InputReader(System.in);
		String str = reader.next();
		char s[] = str.toCharArray();
		boolean p[][] = new boolean[s.length][s.length];
		for(int i = 0 ; i < s.length ; i ++){
			for(int j = 0 ; j < s.length ; j ++){
				if(i != j) p[i][j] = false;
				else p[i][j] = true;
			}
		}
		for(int i = s.length-1 ;i >= 0 ; i --){
			for(int j = i+1 ; j < s.length ; j ++){
				if(s[i] == s[j]){
					if(j -i == 1) p[i][j] = true;
					else{
						p[i][j] = p[i+1][j-1];
					}
				}else{
					p[i][j] = false;
				}
			}
		}
		long a[] = new long[s.length];
		long sum[] = new long[s.length];
		for(int i = 0 ; i < s.length ; i ++){
			for(int j = 0 ; j < s.length; j ++){
				if(p[i][j]) a[i] ++;
			}
		}
		for(int i = s.length-1 ; i >= 0  ; i --){
			if(i == s.length-1) sum[i] = a[i];
			else sum[i] = sum[i+1]+a[i];
		}
		long ans = 0;
		for(int i = 0 ; i < s.length ; i ++){
			for(int j = i ; j < s.length ; j ++){
				if(p[i][j]){
					if(j+1==s.length) continue;
					else ans += sum[j+1];
				}
			}
		}
		System.out.println(ans);
		
	}
	
	public static void main(String[] args) {
		new D159().run();
	}

}