You've got a string s = s1s2... s|s| of length |s|, consisting of lowercase English letters. There also are q queries, each query is described by two integers li, ri (1 ≤ li ≤ ri ≤ |s|). The answer to the query is the number of substrings of string s[li... ri], which are palindromes.

String s[l... r] = slsl + 1... sr (1 ≤ l ≤ r ≤ |s|) is a substring of string s = s1s2... s|s|.

String t is called a palindrome, if it reads the same from left to right and from right to left. Formally, if t = t1t2... t|t| = t|t|t|t| - 1... t1.

Input

The first line contains string s (1 ≤ |s| ≤ 5000). The second line contains a single integer q (1 ≤ q ≤ 106) — the number of queries. Next q lines contain the queries. The i-th of these lines contains two space-separated integers li, ri (1 ≤ li ≤ ri ≤ |s|) — the description of the i-th query.

It is guaranteed that the given string consists only of lowercase English letters.

Output

Print q integers — the answers to the queries. Print the answers in the order, in which the queries are given in the input. Separate the printed numbers by whitespaces.

Examples

Input

caaaba
5
1 1
1 4
2 3
4 6
4 5


Output

1
7
3
4
2

Note

Consider the fourth query in the first test case. String s[4... 6] = «aba». Its palindrome substrings are: «a», «b», «a», «aba».
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;


public class Main {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		InputReader r = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		char[] a = r.next().toCharArray();
		
		boolean[][] P = new boolean[a.length][a.length];
		for(int i = 0; i < a.length; i++)
			P[i][i] = true;
		
		for(int l = 2; l <= a.length; l++)
		for(int i = 0; i + l - 1 < a.length; i++){
			int j = i + l - 1;
			if(a[i] != a[j])P[i][j] = false;
			else {
				if(l == 2)P[i][j] = true;
				else P[i][j] = P[i + 1][j - 1];
			}
		}
		int[] s = new int[a.length + 1];
		s[1] = a.length;
		for(int i = 2; i <= a.length; i++)
			s[i] = s[i - 1] + a.length - (i - 1);
		
		int[] DP = new int[s[a.length] + 1];
		for(int i = 0; i < a.length; i++)
			DP[s[i] + 0] = 1;
		
		for(int l = 2; l <= a.length; l++)
		for(int i = 0; i + l - 1 < a.length; i++){
			int j = i + l - 1;
			if(P[i][j])DP[s[i] + (j - i)] = 1;
//			System.out.println((i + 1) + ", " + s[i + 1] + ", " + j);
			DP[s[i] + (j - i)] += DP[s[i + 1] + (j - (i + 1))] + DP[s[i] + j - 1 - i] - (l - 2 > 0 ? DP[s[i + 1] + j - 1 - (i + 1)] : 0);
		}
		
		int Q = r.nextInt();
		for(int k = 0; k < Q; k++){
			int i = r.nextInt() - 1;
			int j = r.nextInt() - 1;
			
			out.println(DP[s[i] + j - i]);
		}
		out.close();
	}
	static class InputReader {
	    private BufferedReader reader;
	    private StringTokenizer tokenizer;

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

	    public String nextLine(){
	    	try {
				return reader.readLine();
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
				return 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();
	    }

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