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.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class H {
    static BufferedReader br = new BufferedReader(new InputStreamReader(
            System.in));
    static StringTokenizer st = new StringTokenizer("");

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

    static String next() throws Exception {
        while (true) {
            if (st.hasMoreTokens()) {
                return st.nextToken();
            }
            String s = br.readLine();
            if (s == null) {
                return null;
            }
            st = new StringTokenizer(s);
        }
    }

    public static void main(String[] args) throws Exception {
        String str = next();
        int[][] count = new int[str.length()][str.length()];
        for (int i = 0; i < str.length(); i++) {
            for (int j = 0; j + i < str.length(); j++) {
                int next = j + i;
                if (j == next) {
                    count[j][j] = 1;
                } else {
                    if (str.charAt(j) == str.charAt(next)) {
                        if (j + 1 <= next - 1) {
                            count[j][next] = count[j + 1][next - 1];
                        } else {
                            count[j][next] = 1;
                        }
                    }
                }
            }
        }
        for (int i = 0; i < str.length(); i++) {
            for (int j = 0; j + i < str.length(); j++) {
                int next = j + i;
                if (j == next) {
                    count[j][j] = 1;
                } else {
                    count[j][next] += count[j + 1][next] + count[j][next - 1];
                    if (j + 1 <= next - 1) {
                        count[j][next] -= count[j + 1][next - 1];
                    }
                }
            }
        }
        PrintWriter out=new PrintWriter(System.out);
        int qCnt = nextInt();
        for (int i = 0; i < qCnt; i++) {
            out.println(count[nextInt() - 1][nextInt() - 1]);
            if(i%100==0){
                out.flush();
            }
        }
        out.flush();
    }
}
