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.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author lwc626
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyInputReader in = new MyInputReader(inputStream);
        MyOutputWriter out = new MyOutputWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskD {
    public void solve(int testNumber, MyInputReader in, MyOutputWriter out) {
        String str = in.next() ;
        int len = str.length() ;
        int[ ] left = new int[ len ], right = new int[ len ] ;
        Arrays.fill( left , 0 );
        Arrays.fill( right , 0 );
        
        for( int i = 0 ; i < len ; i ++ ){
            int j = 0 ;
            while ( i - j >= 0 && i + j < len && str.charAt( i - j ) == str.charAt( i + j )){
                left[ i + j  ] ++ ;
                right[ i - j ] ++ ;
                j ++ ;
            }
            j = 1;
            while ( i - j + 1 >= 0 && i + j < len && str.charAt( i - j + 1 ) == str.charAt( i + j ) ){
                left[ i + j ] ++ ;
                right[ i - j + 1] ++ ;
                j ++ ;
            }
        }
        //for( int i = 0 ; i < len ; i ++ )
        for( int i = len - 2 ; i >= 0 ; i -- )
            right[i] += right[i+1];
        
        long ret = 0 ;
        for( int i = 0 ; i < len-1 ; i ++ )
            ret += (long)left[i] * right[i+1];
        out.printLine( ret );
        
    }
}

class MyInputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public MyInputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        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();
    }

    }

class MyOutputWriter {
    private final PrintWriter writer;

    public MyOutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(outputStream);
    }

    public MyOutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object...objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }

    public void printLine(Object...objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }

}