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.*;
import java.util.*;

public class D {
	public static List<int[]> pos = new ArrayList<>();
	
	public static void findpals(String s , int[] left , int[] right,int start , int end ) {
		
		while(start >= 0 && end < s.length() && s.charAt(start) == s.charAt(end)) {
			left[start]++;
			right[end]++;
			start--;
			end++;
		}
		
	}
	
	public static void main(String[] args) {
		// TODO Auto-generated method stub
			FastScanner sc = new FastScanner();
			
			String s = sc.next();
			
			int[] left = new int[s.length()];
			int[] right = new int[s.length()];
			
			for(int i = 0 ;i < s.length() ; i++) {
				findpals(s ,left , right ,i , i);
				findpals(s , left , right , i, i + 1);
			}
			long res = 0;
			
			
			for(int i = 0 ; i < pos.size(); i++) {
				int[] curr = pos.get(i);
				
				System.out.println(curr[0] + " " + curr[1]);
			}
			for(int i = 0 ;i < s.length() - 1  ; i++) {
				
				for(int j = i + 1 ; j < s.length() ; j++) {
					
					res += left[j] * right[i];
					
					
				}
				
				
			}
			System.out.println(res);
			
			
			

	}
	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}

}