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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Solve6 {

    public static void main(String[] args) {
        PrintWriter pw = new PrintWriter(System.out);
        new Solve6().solve(pw);
        pw.flush();
        pw.close();
    }

    public void solve(PrintWriter pw) {
        FastReader sc = new FastReader();
        char[] c = sc.next().toCharArray();
//        char[] c = new char[5000];
//        for (int i = 0; i < 5000; i++) {
//            c[i] = 'a';
//        }
        final long MOD = (long) 1E9 + 7;
        final long base = 39;
        int n = c.length;
        long[] power = new long[n];
        power[0] = 1;
        for (int i = 1; i < n; i++) {
            power[i] = (power[i - 1] * base) % MOD;
        }
        long[] prefix = new long[n];
        for (int i = 0; i < n; i++) {
            prefix[i] = ((i == 0 ? 0 : prefix[i - 1]) + power[i] * (c[i] - 'a' + 7)) % MOD;
        }
        int[][] temp = new int[n][n];
        for (int i = n - 1; i >= 0; i--) {
            long hash = 0;
            for (int j = i; j >= 0; j--) {
                hash = (power[i - j] * (c[j] - 'a' + 7) + hash) % MOD;
                if (j < i) {
                    temp[i][j] = temp[i][j + 1];
                }
                if ((hash * power[n - 1]) % MOD == ((prefix[i] - (j == 0 ? 0 : prefix[j - 1]) + MOD) * power[n - 1 - j]) % MOD) {
                    ++temp[i][j];
                }
            }
        }
        int[][] ans = new int[n][n];
        for (int i = 0; i < n; i++) {
            for (int j = i; j < n; j++) {
                ans[i][j] = (j > i ? ans[i][j - 1] : 0) + temp[j][i];
            }
        }
        int q = sc.nextInt();
        while (q-- > 0) {
            int l = sc.nextInt() - 1, r = sc.nextInt() - 1;
            pw.println(ans[l][r]);
        }
    }

    long mult(long a, long b, long c) {
        if (a < b) {
            a = b + a - (b = a);
        }
        long r = 0, m = a;
        for (int i = 0; i < 64; ++i) {
            if ((1L << i) > b) {
                break;
            }
            if ((b & 1L << i) != 0) {
                r = (r + m) % c;
            }
            m = (m * 2) % c;
        }
        return r;
    }

    static class FastReader {

        BufferedReader br;
        StringTokenizer st;

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

        public FastReader(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
            }
        }

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

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

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public boolean hasNext() throws IOException {
            if (st != null && st.hasMoreTokens()) {
                return true;
            }
            String s = br.readLine();
            if (s == null || s.isEmpty()) {
                return false;
            }
            st = new StringTokenizer(s);
            return true;
        }
    }
}
