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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {
    
    static String s;
    
    static Boolean[][] dpPal;
    static Integer[][] dp;
    
    static boolean isPalindrome(int l, int r) {
        if (l >= r)
            return true;
        
        if (dpPal[l][r] != null)
            return dpPal[l][r];
        
        return dpPal[l][r] = s.charAt(l) == s.charAt(r) && isPalindrome(l + 1, r - 1);
    }
    
    static int go(int l, int r) {
        if (l > r)
            return 0;
        if (l == r)
            return 1;
        
        if (dp[l][r] != null)
            return dp[l][r];
        
        return dp[l][r] = (isPalindrome(l, r) ? 1 : 0) + go(l + 1, r) + go(l, r - 1) - go(l + 1, r - 1);
    }
    
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        
        s = in.next();
        dpPal = new Boolean[s.length() + 1][s.length() + 1];
        dp = new Integer[s.length() + 1][s.length() + 1];
        
        long ans = 0;
        for (int i = 0; i < s.length(); ++i)
            for (int j = i; j < s.length(); ++j)
                if (i > 0 && isPalindrome(i, j))
                    ans += go(0, i - 1);
        
        System.out.println(ans);
    }
    
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

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

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

        public int nextInt() {
            return Integer.parseInt(next());
        }
        
        public double nextDouble() {
            return Double.parseDouble(next());
        }
        
        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}