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 CFR {
    static final int UNCALC = -1;
    static final int INF = (int) 1e9;

    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        char[] s = sc.next().toCharArray();
        int n = s.length;
        boolean[][] pal = new boolean[n][n];
        int[][] dp = new int[n][n];
        for (int i = 0; i < n; i++) {
            pal[i][i] = true;
            dp[i][i] = 1;
        }
        for (int len = 2; len <= n; len++)
            for (int i = 0; i + len - 1 < n; i++) {
                int j = i + len - 1;
                if (len == 2) {
                    if (s[i] == s[j]) pal[i][j] = true;
                    continue;
                }
                if (s[i] == s[j] && pal[i + 1][j - 1]) pal[i][j] = true;
            }
        for (int len = 2; len <= n; len++)
            for (int i = 0; i + len - 1 < n; i++) {
                int j = i + len - 1;
                dp[i][j] = dp[i][j - 1] + dp[i + 1][j] - dp[i + 1][j - 1];
                if (pal[i][j]) dp[i][j]++;
            }
        int q = sc.nextInt();
        while (q-- > 0) out.println(dp[sc.nextInt() - 1][sc.nextInt() - 1]);
        out.flush();
        out.close();
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }

        public Scanner(String file) throws Exception {
            br = new BufferedReader(new FileReader(file));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

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

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

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

        public boolean ready() throws IOException {
            return br.ready();
        }

        public void waitForInput() throws InterruptedException {
            Thread.sleep(3000);
        }

    }
}