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.*;
import java.math.*;


public class Main {
	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer tok;

	static void solve() throws Exception {
		char[] s = next().toCharArray();
		int n = s.length;
		int[] begins = new int[n];
		int[] ends = new int[n];
		for (int i = 0; i < n; i++) {
			int l = i;
			int r = i;
			while (l >= 0 && r < n && s[l] == s[r]) {
				begins[l--]++;
				ends[r++]++;
			}
			l = i;
			r = i+1;
			while (l >= 0 && r < n && s[l] == s[r]) {
				begins[l--]++;
				ends[r++]++;
			}
		}
		long res = 0;
		for (int i = 0; i < n; i++) {
			for (int j = i+1; j < n; j++) {
				res += (long)ends[i] * begins[j];
			}
		}
		out.println(res);
	}

	static int sqr(int x) {
		return x*x;
	}
	
	static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	static long nextLong() throws IOException {
		return Long.parseLong(next());
	}

	static double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	static BigInteger nextBigInteger() throws IOException {
		return new BigInteger(next());
	}
	
	static String next() throws IOException {
		while (tok == null || !tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}
	
	static String nextLine() throws IOException {
		tok = new StringTokenizer("");
		return in.readLine();
	}

	static boolean hasNext() throws IOException {
		while (tok == null || !tok.hasMoreTokens()) {
			String s = in.readLine();
			if (s == null) {
				return false;
			}
			tok = new StringTokenizer(s);
		}
		return true;
	}

	public static void main(String args[]) {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(new OutputStreamWriter(System.out));
			//in = new BufferedReader(new FileReader("1.in"));
			//out = new PrintWriter(new FileWriter("1.out"));
			solve();
			in.close();
			out.close();
		} catch (Throwable e) {
			e.printStackTrace();
			java.lang.System.exit(1);
		}
	}
}