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 Palindrome {
    public static void main(String[] args)throws Exception{
        FastScanner sc= new FastScanner("baldhfa", true);
        FastWriter pw= new FastWriter("andfaklf", true);
        String s= sc.next();
        s=' '+s;
        int[][] matrix= new int[s.length()][s.length()];
        int[][] pre= new int[matrix.length][matrix.length];
        // fill in matrix
        for (int x=1; x<s.length(); x++){
            matrix[x][x]=1;
        }
        for (int x=1; x<s.length()-1; x++){
            if (s.charAt(x)== s.charAt(x+1)){
                matrix[x][x+1]=1;
            }
        }
        for (int len=0; len<s.length()-2; len++){
            for (int x=1; x<s.length()-len-1; x++){
                if (matrix[x][x+len]==1 && s.charAt(x-1)== s.charAt(x+len+1)){
                    matrix[x-1][x+len+1]=1;
                }
            }
        }
        for (int x=1; x<s.length(); x++){
            for (int y=1; y<s.length(); y++){
                pre[x][y]= matrix[x][y]+ pre[x-1][y]+ pre[x][y-1]-pre[x-1][y-1];
            }
        }
        int q= sc.ni();
        while (q-->0){
            int a= sc.ni();
            int b= sc.ni();
            int res= pre[b][b]- pre[a-1][b]- pre[b][a-1]+ pre[a-1][a-1];
            pw.pl(res);
        }
        pw.close();



    }


    static class FastWriter{
        public PrintWriter pw;
        public FastWriter(String name, boolean debug) throws IOException {
            if (debug){
                pw= new PrintWriter(System.out);
            }
            else {
                pw = new PrintWriter(new BufferedWriter(new FileWriter(new File(name))));
            }
        }
        public void pl(Object text){
            pw.println(text);
        }
        public void p( Object text){
            pw.print(text);
        }
        public void close(){
            pw.close();
        }
    }
    static class FastScanner {
        public BufferedReader br;
        public StringTokenizer st;
        public InputStream is;
        public FastScanner(String name, boolean debug) throws IOException {
            if (debug){
                is= System.in;
            }
            else{
                is= new FileInputStream(name);
            }
            br = new BufferedReader(new InputStreamReader(is),32768);
            st = null;
        }


        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int ni() {
            return Integer.parseInt(next());
        }

        public long nl() {
            return Long.parseLong(next());
        }

        public double nd() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return str;
        }
    }
}
