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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

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

    static class TaskD {
        public void solve(int testNumber, FastReader in, PrintWriter out) {
            char[] s = in.nextString().toCharArray();
            int n = s.length;
            int[][] dp = new int[n + 1][n + 1];
            boolean[][] isPalin = new boolean[n][n];
            for (int len = 1; len <= n; ++len) {
                for (int start = 0, end = start + len - 1; end < n; ++start, ++end) {
                    if (len == 1) {
                        isPalin[start][end] = true;
                        dp[start][end] = 1;
                    } else if (len == 2) {
                        dp[start][end] = 2;
                        if (s[start] == s[end]) {
                            isPalin[start][end] = true;
                            ++dp[start][end];
                        }
                    } else {
                        if (s[start] == s[end] && isPalin[start + 1][end - 1])
                            isPalin[start][end] = true;
                        dp[start][end] = dp[start + 1][end] + dp[start][end - 1] - dp[start + 1][end - 1];
                        if (isPalin[start][end]) ++dp[start][end];
                    }
                }
            }
            long res = 0;
            for (int len = 1; len <= n; ++len) {
                for (int start = 1, end = start + len - 1; end < n; ++start, ++end) {
                    if (isPalin[start][end]) res += dp[0][start - 1];
                }
            }
            out.println(res);
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int pnumChars;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        private int pread() {
            if (pnumChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= pnumChars) {
                curChar = 0;
                try {
                    pnumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (pnumChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public String nextString() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = pread();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}