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.*;
import java.util.*;

public class H_QueriesForNumberOfPalindromes {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();
    }

    private static class Solver {
        private void solve(InputReader inp, PrintWriter out) {
            char[] s = inp.next().toCharArray();
            int n = s.length;

            // store whether i..j is a palindrome
            boolean[][] p = new boolean[n][n];
            for (int i = 0; i < n; i++) p[i][i] = true;
            for (int len = 2; len <= n; len++) {
                for (int start = 0; start + len - 1 < n; start++) {
                    // [start, start + len - 1]
                    if (len >= 3) {
                        p[start][start + len - 1] = p[start+1][start+len-2] && s[start] == s[start + len - 1];
                    } else {
                        p[start][start + len - 1] = s[start] == s[start + 1];
                    }
                    // [start + 1, start + len - 2] should be palindrome
                    // s[start] == s[start + len - 1]
                }
            }

            int[][] dp = new int[n][n];
            for (int i = 0; i < n; i++) dp[i][i] = 1;
            for (int len = 2; len <= n; len++) {
                for (int start = 0; start + len - 1 < n; start++) {
                    // [start, start + len - 1]
                    // add [start, start + len - 2]
                    // add [start + 1, start + len - 1]
                    // sub [start + 1, start + len - 2] (0 for length = 2)
                    // add 1 if p[start][start + len - 1]
                    int total = dp[start][start + len - 2];
                    total += dp[start + 1][start + len - 1];
                    if (len >= 3) total -= dp[start + 1][start + len - 2];
                    if (p[start][start + len - 1]) total++;
                    dp[start][start + len - 1] = total;
                }
            }

            int q = inp.nextInt();
            for (int i = 0; i < q; i++) {
                out.println(dp[inp.nextInt() - 1][inp.nextInt() - 1]);
            }
        }
    }

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

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

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}