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 b {
	
	public static void main(String[] args) throws IOException {
		Scanner zizo = new Scanner(System.in);
		PrintWriter wr = new PrintWriter(System.out);
		
		char[]c = zizo.next().toCharArray();
		int n = c.length;
		int[][]pal = new int[n][n];
		int[][]dp = new int[n][n];
		for(int i = 0;i < n; i++)
			dp[i][i] = pal[i][i] = 1;
		for(int i = 0;i < n-1; i++) {
			pal[i][i+1] = c[i] == c[i+1]? 1 : 0;
			dp[i][i+1] = 2 + pal[i][i+1];
		}
		
		for(int l=2;l<n;l++) {
			for(int i=0;i<n-l;i++) {
				if(c[i+l]==c[i]&&pal[i+1][i+l-1]>0) {
				pal[i][i+l]=1;
				}
				dp[i][i+l]=dp[i][i+l-1]+dp[i+1][i+l]-dp[i+1][i+l-1]+pal[i][i+l];
			}
		}
		int q = zizo.nextInt();
		while(q-->0) {
			wr.println(dp[zizo.nextInt()-1][zizo.nextInt()-1]);
		}
		
		wr.close();
	}
}
class DSU {
	int n,sets;
	int[]rank,parent,size;
	DSU(int n){
		sets = n;
		rank = new int[n];
		parent = new int[n];
		size = new int[n];
		for(int i = 0;i < n; i++) {
			size[i] = 1;
			parent[i] = i;
		}
	}
	
	int findSet(int i) {
		return parent[i] == i? i : (parent[i] = findSet(parent[i]));
	}
	
	boolean union(int u,int v) {
		int x = findSet(u);
		int y = findSet(v);
		if(x == y)
			return false;
		if(rank[x] < rank[y]) {
			size[y] += size[x];
			parent[x] = y;
		}
		else {
			size[x] += size[y];
			if(rank[x] == rank[y])
				rank[x]++;
			parent[y] = x;
		}
		sets--;
		return true;
	}
}

class Scanner 
{
	StringTokenizer st;
	BufferedReader br;

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

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

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

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

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

	public double nextDouble() throws IOException
	{
		String x = next();
		StringBuilder sb = new StringBuilder("0");
		double res = 0, f = 1;
		boolean dec = false, neg = false;
		int start = 0;
		if(x.charAt(0) == '-')
		{
			neg = true;
			start++;
		}
		for(int i = start; i < x.length(); i++)
			if(x.charAt(i) == '.')
			{
				res = Long.parseLong(sb.toString());
				sb = new StringBuilder("0");
				dec = true;
			}
			else
			{
				sb.append(x.charAt(i));
				if(dec)
					f *= 10;
			}
		res += Long.parseLong(sb.toString()) / f;
		return res * (neg?-1:1);
	}

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


}