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.util.*;
import java.math.*;
import java.io.*;

public class CF245H {
	int[][] dp;
	boolean[][] isPalin;
	void findPalindromes(char[] s) {
		int n = s.length;
		dp = new int[n][n];
		isPalin = new boolean[n][n];
		for(int i = 0 ; i < n ; i++) {
			isPalin[i][i] = true;
			dp[i][i] = 1;
		}
		for(int i = 0 ; i < n - 1 ; i++) {
			isPalin[i][i + 1] = s[i] == s[i + 1];
			dp[i][i + 1] = isPalin[i][i + 1] ? 3 : 2;
		}
		for(int len = 2 ; len < n ; len++) {
			for(int i = 0 ; i < n - len ; i++) {
				int j = i + len;
				if(s[i] == s[j] && isPalin[i + 1][j - 1])
					isPalin[i][j] = true;
				dp[i][j] = dp[i][j - 1] + dp[i + 1][j] - dp[i + 1][j - 1] + (isPalin[i][j] ? 1 : 0);
			}
		}
	}
	public CF245H() {
		FS scan = new FS();
		PrintWriter out = new PrintWriter(System.out);
		char[] s = scan.next().toCharArray();
		findPalindromes(s);
		int q = scan.nextInt();
		for(int qq = 0 ; qq < q ; qq++) {
			int l = scan.nextInt() - 1, r = scan.nextInt() - 1;
			out.println(dp[l][r]);
		}
		out.close();
	}
	class FS {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		public String next() {
			while(!st.hasMoreTokens()) {
				try { st = new StringTokenizer(br.readLine());  }
				catch(Exception e) { e.printStackTrace(); }
			}
			return st.nextToken();
		}
		public int nextInt() { return Integer.parseInt(next()); }
	}
	public static void main(String[] args) { new CF245H(); }
}
