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.*;
public class PalindromeQuery {
	public static void main(String[] args) throws IOException {
//		BufferedReader br = new BufferedReader(new FileReader(".in"));
//		PrintWriter pw = new PrintWriter(new BufferedWriter(new FileWriter(".out")));
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		char[] a = br.readLine().toCharArray();
		StringTokenizer st = new StringTokenizer(br.readLine());
		int q = Integer.parseInt(st.nextToken());
		
		int n = a.length;
		long[][] dp = new long[n+2][n+2]; //# ways with start i, end j
		
		for (int l = n; l > 0; l--)
			for (int r = l; r <= n; r++) {
				if (l+1 >= r && a[l-1] == a[r-1]) //base case, b works, bb works
					dp[l][r]++;
				
				else if (dp[l+1][r-1] > 0 && a[l-1] == a[r-1]) 
					dp[l][r]++;
			}
		
		for (int l = n; l > 0; l--) {
			for (int r = l; r <= n; r++) {
				dp[l][r] += dp[l+1][r] + dp[l][r-1] - dp[l+1][r-1];
			}
		}
		StringBuilder sb = new StringBuilder();
		while(q-- > 0) {
			st = new StringTokenizer(br.readLine());
			int x = Integer.parseInt(st.nextToken());
			int y = Integer.parseInt(st.nextToken());
			sb.append(dp[x][y]+"\n");
			}
		System.out.println(sb);
		System.out.close();
	}
}