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 queriesforpalindromes {

	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
		char[] s = br.readLine().toCharArray();
		int n = s.length;
		int[][] tab = new int[n][n];

		for(int i = 0; i < n; i++) {
			tab[i][i] = 1;
			int k = 1;
			while((i-k>=0) & (i+k<n)) {
				if(s[i-k] == s[i+k]) {
		            tab[i-k][i+k] = 1;
		            k += 1;
				}
		        else {
		            break;
		        }
			}
				        
		}

		for(int i = 0; i < n; i++) {
			int k = 1;
			while((i-k+1>=0) & (i+k<n)) {
				if(s[i-k+1] == s[i+k]) {
					tab[i-k+1][i+k] = 1;
				    k += 1;
				}
				else {
					break;
				}
			}
		}
		        
		int[][] acc = new int[n][n];

		acc[0][0] = tab[0][0];
		for(int i = 1; i < n; i++) {
		    acc[0][i] = acc[0][i-1] + tab[0][i];
		}

		for(int i = 1; i < n; i++) {
		    acc[i][0] = acc[i-1][0] + tab[i][0];
		    for(int j = 1; j < n; j++) {
		        acc[i][j] = acc[i-1][j] + acc[i][j-1] - acc[i-1][j-1] + tab[i][j];
		    }
		}
		        
		int q = Integer.parseInt(br.readLine());
		
		for(int i = 0; i < q; i++) {
			StringTokenizer st = new StringTokenizer(br.readLine());
		    int a = Integer.parseInt(st.nextToken());
			int b = Integer.parseInt(st.nextToken());
		    if(b == 1) {
		        bw.write("1");
		    }
		    else if(a == 1){
		    	bw.write(""+acc[b-1][b-1]);
		    }
		    else {
		    	bw.write(""+(acc[b-1][b-1] - acc[b-1][a-2] - acc[a-2][b-1] + acc[a-2][a-2]));
		    }
		    bw.write("\n");
		}
		bw.flush();
	}

}
