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.BufferedWriter;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;


public class cf245h {
  public static void main(String[] args) {
    FastIO in = new FastIO(), out = in;
    String s = in.next().trim();
    int n = s.length();
    int[][] dp = new int[n][n];
    for(int i=0; i<n; i++)
      dp[i][i] = 1;
    for(int i=1; i<n; i++)
      if(s.charAt(i-1) == s.charAt(i))
        dp[i-1][i] = 1;
    for(int d=2; d<=n; d++)
      for(int i=0; i+d<n; i++)
        if(s.charAt(i)==s.charAt(i+d))
          dp[i][i+d] = dp[i+1][i+d-1];
    for(int i=0; i<n; i++)
      for(int j=0; j<n; j++) {
        if(i > 0) dp[i][j] += dp[i-1][j];
        if(j > 0) dp[i][j] += dp[i][j-1];
        if(i>0 && j>0) dp[i][j] -= dp[i-1][j-1];
      }
    int q = in.nextInt();
    for(int i=0; i<q; i++) {
      int a = in.nextInt()-1;
      int b = in.nextInt()-1;
      int ans = dp[b][b];
      if(a > 0) ans -= dp[a-1][b]+dp[b][a-1]-dp[a-1][a-1];
      out.println(ans);
    }
    out.close();
  }
  static class FastIO extends PrintWriter {
    BufferedReader br;
    StringTokenizer st;
    
    public FastIO() {
      this(System.in,System.out);
    }
    public FastIO(InputStream in, OutputStream out) {
      super(new BufferedWriter(new OutputStreamWriter(out)));
      br = new BufferedReader(new InputStreamReader(in));
      scanLine();
    }
    public void scanLine() {
      try {
        st = new StringTokenizer(br.readLine().trim());
      } catch(Exception e) {
        throw new RuntimeException(e.getMessage());
      }
    }
    public int numTokens() {
      if(!st.hasMoreTokens()) {
        scanLine();
        return numTokens();
      }
      return st.countTokens();
    }
    public String next() {
      if(!st.hasMoreTokens()) {
        scanLine();
        return next();
      }
      return st.nextToken();
    }
    public double nextDouble() {
      return Double.parseDouble(next());
    }
    public long nextLong() {
      return Long.parseLong(next());
    }
    public int nextInt() {
      return Integer.parseInt(next());
    }
  }
}
