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.*;

public class Main {
	public static void main(String[] args) throws IOException{
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		String line = reader.readLine();
		final int n = line.length();
		boolean [][] palindrome = new boolean[n + 1][n + 1];
		int [][] count = new int[n][n];
		for (int i = 0; i < n; ++i){
			count[i][i] = 1;
			palindrome[i][i] = palindrome[i + 1][i] = true;
		}
		for (int l = 1; l < n; ++l){
			for (int i = 0; i + l < n; ++i){
				palindrome[i][i + l] = line.charAt(i) == line.charAt(i + l) && palindrome[i + 1][i + l - 1];
				count[i][i + l] = count[i + 1][i + l] + count[i][i + l - 1] - count[i + 1][i + l - 1] + (palindrome[i][i + l] ? 1 : 0); 
			}
		}
		final int m = Integer.parseInt(reader.readLine());
		for (int i = 0; i < m; ++i){
			String[] items = reader.readLine().split(" ");
			System.out.println(count[Integer.parseInt(items[0]) - 1][Integer.parseInt(items[1]) - 1]);
		}
	}
}
