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.lang.*;
import java.io.*;

public class NewClass {
	public static void main (String[] args) throws IOException{
		//code
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
                BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
                StringTokenizer st;
		//int t = Integer.parseInt(in.readLine());
		String s = in.readLine();
                int s_len = s.length();
                int dp[][] = new int[s_len][s_len];
                int is_palin[][] = new int[s_len][s_len];
                
                for(int i = 0; i < s_len; i++){
                
                    for(int j = 0; j < s_len; j++){
                    
                        dp[i][i] = 1;
                        is_palin[i][i] = 1;
                        
                        if(j < i)
                            is_palin[i][j] = 1;
                    }
                }
		
                for(int j = 1; j < s_len; j++){
                
                    for(int i = j-1; i >= 0; i--){
                    
                        if((is_palin[i+1][j-1] == 1) && (s.charAt(i) == s.charAt(j)))
                            is_palin[i][j] = 1;
                        dp[i][j] = dp[i+1][j] + dp[i][j-1] - dp[i+1][j-1] + is_palin[i][j];
                    }
                }
                
                int q = Integer.parseInt(in.readLine());
                
                for(int i = 0; i < q; i++){
                
                    st = new StringTokenizer(in.readLine());
                    int l = Integer.parseInt(st.nextToken());
                    int r = Integer.parseInt(st.nextToken());
                    out.write(dp[l-1][r-1]+"\n");
                }
                out.flush();
	}
}