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.io.*;

public class h {

	public static void main(String[] args) throws Exception {

		BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
		String s = stdin.readLine();
		int n = s.length();
		boolean[][] isPal = new boolean[n][n];
		for (int i=0; i<n; i++)
			isPal[i][i] = true;
		for (int i=0; i<n-1; i++)
			if (s.charAt(i) == s.charAt(i+1))
				isPal[i][i+1] = true;

		for (int i=0; i<n; i++) {
			boolean res = true;
			for (int diff=1;; diff++) {
				if (i-diff < 0 || i+diff >= n) break;
				if (s.charAt(i-diff) != s.charAt(i+diff)) break;
				isPal[i-diff][i+diff] = true;
			}
		}

		for (int i=0; i<n-1; i++) {
			if (isPal[i][i+1]) {
				for (int diff=1;; diff++) {
					if (i-diff < 0 || i+1+diff >= n) break;
					if (s.charAt(i-diff) != s.charAt(i+1+diff)) break;
					isPal[i-diff][i+1+diff] = true;
				}
			}
		}

		int[][] res = new int[n][n];
		for (int i=0; i<n; i++)
			res[i][i] = 1;

		for (int i=n-2; i>=0; i--) {
			for (int j=i+1; j<n; j++) {
				res[i][j] = res[i][j-1];
				if (isPal[i][j]) res[i][j]++;
			}
		}

		for (int i=0; i<n; i++)
			for (int j=i-1; j>=0; j--)
				res[j][i] += res[j+1][i];



		int numQ = Integer.parseInt(stdin.readLine().trim());
		StringBuffer sb = new StringBuffer();
		for (int loop=0; loop<numQ; loop++) {
			StringTokenizer tok = new StringTokenizer(stdin.readLine());
			int sI = Integer.parseInt(tok.nextToken())-1;
			int eI = Integer.parseInt(tok.nextToken())-1;
			sb.append(res[sI][eI]+"\n");
		}
		System.out.print(sb);
	}
}