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.util.*;
import java.io.*;
public class H245 {
	public static void main(String[] args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		String line = br.readLine();
		int n = line.length();
		int[][] ans = new int[n][n];
		for(int i = 0;i<n;i++){
			int left = i;
			int right = i;
			while(left >= 0 && right < n && line.charAt(left) == line.charAt(right)){
				ans[left][right] = 1;
				left--;
				right++;
			}
			left = i;
			right = i+1;
			while(left >= 0 && right < n && line.charAt(left) == line.charAt(right)){
				ans[left][right] = 1;
				left--;
				right++;
			}
		}
		for(int i = 0;i<n;i++){
			int count = 0;
			for(int j = i;j<n;j++){
				count+=ans[i][j];
				ans[i][j] = count;
				if(i != 0){
					ans[i][j]+=ans[i-1][j];
				}
			}
		}
		
		int q = Integer.parseInt(br.readLine());
		
		for(int i = 0;i<q;i++){
			StringTokenizer st = new StringTokenizer(br.readLine(), " ");
			int left = Integer.parseInt(st.nextToken())-1;
			int right = Integer.parseInt(st.nextToken())-1;
			out.println(ans[right][right] - (left == 0 ? 0 : ans[left-1][right]));
		}
		out.close();
	}
}
