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.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Collection;
import java.util.Locale;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) throws IOException {
		new Thread(null, new Runnable() {
			public void run() {
				try {
					long prevTime = System.currentTimeMillis();
					new Main().run();
					System.err.println("Total time: "
							+ (System.currentTimeMillis() - prevTime) + " ms");
					System.err.println("Memory status: " + memoryStatus());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
		}, "1", 1L << 24).start();
	}

	void run() throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		Object o = solve();
		if (o != null)
			out.println(o);
		out.close();
		in.close();
	}

	private Object solve() throws IOException {
		String s = in.readLine();
		int n = s.length();
		Boolean[][] pal = new Boolean[n][n];
		for (int i = 0; i < n; i++)
			pal[i][i] = true;
		for (int i = 0; i < n; i++)
			for (int j = i + 1; j < n; j++)
				pal[i][j] = go(s, pal, i, j);
		long[] start = new long[n];
		long[] end = new long[n];
		for (int i = 0; i < n; i++)
			for (int j = i; j < n; j++)
				if (pal[i][j]) {
					start[i]++;
					end[j]++;
				}
		for (int i = n - 1; i > 0; i--)
			start[i - 1] += start[i];
		
		long ret = 0;
		for (int i = 0; i < n-1; i++)
			ret += end[i] * start[i+1];

		return ret;
	}

	private Boolean go(String s, Boolean[][] pal, int i, int j) {
		if(pal[i][j]!=null)
			return pal[i][j];
		
		if (i + 1 == j){
			pal[i][j] = s.charAt(i) == s.charAt(j);
			return pal[i][j];
		}
		if (s.charAt(i) == s.charAt(j)) {
			pal[i][j] = go(s, pal, i + 1, j - 1);
		} else {
			pal[i][j] = false;
		}
		return pal[i][j];
	}

	BufferedReader in;
	PrintWriter out;
	StringTokenizer st = new StringTokenizer("");

	String nextToken() throws IOException {
		while (!st.hasMoreTokens())
			st = new StringTokenizer(in.readLine());
		return st.nextToken();
	}

	int ni() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nl() throws IOException {
		return Long.parseLong(nextToken());
	}

	double nd() throws IOException {
		return Double.parseDouble(nextToken());
	}

	int[] nia(int size) throws IOException {
		int[] ret = new int[size];
		for (int i = 0; i < size; i++)
			ret[i] = ni();
		return ret;
	}

	long[] nla(int size) throws IOException {
		long[] ret = new long[size];
		for (int i = 0; i < size; i++)
			ret[i] = nl();
		return ret;
	}

	double[] nda(int size) throws IOException {
		double[] ret = new double[size];
		for (int i = 0; i < size; i++)
			ret[i] = nd();
		return ret;
	}

	String nextLine() throws IOException {
		st = new StringTokenizer("");
		return in.readLine();
	}

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

	void printRepeat(String s, int count) {
		for (int i = 0; i < count; i++)
			out.print(s);
	}

	void printArray(int[] array) {
		for (int i = 0; i < array.length; i++) {
			if (i > 0)
				out.print(' ');
			out.print(array[i]);
		}
		out.println();
	}

	void printArray(long[] array) {
		for (int i = 0; i < array.length; i++) {
			if (i > 0)
				out.print(' ');
			out.print(array[i]);
		}
		out.println();
	}

	void printArray(double[] array) {
		for (int i = 0; i < array.length; i++) {
			if (i > 0)
				out.print(' ');
			out.print(array[i]);
		}
		out.println();
	}

	void printArray(double[] array, String spec) {
		for (int i = 0; i < array.length; i++) {
			if (i > 0)
				out.print(' ');
			out.printf(Locale.US, spec, array[i]);
		}
		out.println();
	}

	void printArray(Object[] array) {
		boolean blank = false;
		for (Object x : array) {
			if (blank)
				out.print(' ');
			else
				blank = true;
			out.print(x);
		}
		out.println();
	}

	@SuppressWarnings("rawtypes")
	void printCollection(Collection collection) {
		boolean blank = false;
		for (Object x : collection) {
			if (blank)
				out.print(' ');
			else
				blank = true;
			out.print(x);
		}
		out.println();
	}

	static String memoryStatus() {
		return (Runtime.getRuntime().totalMemory()
				- Runtime.getRuntime().freeMemory() >> 20)
				+ "/" + (Runtime.getRuntime().totalMemory() >> 20) + " MB";
	}
}