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.StringTokenizer;

public class Template {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));

        // Start writing your solution here. -------------------------------------


        String s = sc.nextLine();       // read whole line as String
        int N = s.length();
        s = " " + s;
        int[][] pal = new int[5001][5001];
        int[][] pre = new int[5001][5001];

        for (int i = 1; i <= N; i++) {
            pal[i][i] = 1;
        }

        for (int i = 1; i < N; i++) {
            if (s.charAt(i) == s.charAt(i + 1)) {
                pal[i][i + 1] = 1;
            }
        }

        for (int len = 0; len < N - 2; len++) {
            for (int i = 1; i < N - len; i++) {
                if (pal[i][i + len] == 1 && s.charAt(i - 1) == s.charAt(i + len + 1)) {
                    pal[i - 1][i + len + 1] = 1;
                }
            }
        }

        for (int i = 1; i <= N; i++) {
            for (int j = 1; j <= N; j++) {
                pre[i][j] = pal[i][j] + pre[i - 1][j] + pre[i][j - 1] - pre[i - 1][j - 1];
            }
        }

        int Q = sc.nextInt();

        for (int i = 0; i < Q; i++) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            int answer = pre[b][b] - pre[a - 1][b] - pre[b][a - 1] + pre[a - 1][a - 1];
            out.println(answer);
        }


        // Stop writing your solution here. -------------------------------------
        out.close();
    }

    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

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

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
}
