Problem: Two soldiers are playing a game. At the beginning first of them chooses a positive integer n and gives it to the second soldier. Then the second one tries to make maximum possible number of rounds. Each round consists of choosing a positive integer x > 1, such that n is divisible by x and replacing n with n / x. When n becomes equal to 1 and there is no more possible valid moves the game is over and the score of the second soldier is equal to the number of rounds he performed.

To make the game more interesting, first soldier chooses n of form a! / b! for some positive integer a and b (a ≥ b). Here by k! we denote the factorial of k that is defined as a product of all positive integers not large than k.

What is the maximum possible score of the second soldier?

Input

First line of input consists of single integer t (1 ≤ t ≤ 1 000 000) denoting number of games soldiers play.

Then follow t lines, each contains pair of integers a and b (1 ≤ b ≤ a ≤ 5 000 000) defining the value of n for a game.

Output

For each game output a maximum score that the second soldier can get.

Examples

Input

2
3 1
6 3


Output

2
5

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Main {
	
	static ArrayList<Integer> primes;
	static int[] isComposite , expSum;
	static long[] prefix;
	static int max = 6*(int) 1e6;

	static void sieve(int N)	
	{
		isComposite = new int[N+1];					
		isComposite[0] = isComposite[1] = 1;			
		primes = new ArrayList<Integer>();

		for (int i = 2; i <= N; ++i) 					
			if (isComposite[i] == 0) 					
			{
				primes.add(i);
				if(1l * i * i <= N)
					for (int j = i * i; j <= N; j += i)	
						isComposite[j] = 1;
			}   
	}
	
	static void fillExponents()
	{
		int[] lastExp = new int[max];
		expSum = new int[max];
		for(int p : primes)
		{
			int pow = 0;
			int e = 1;
			for(;1l*e*p < max;++pow)
				e *= p;
			for(;e>1;e/=p,--pow)
			{
				for(int i = e;i<max;i+=e)
				{
					if(lastExp[i]!=p)
					{
						lastExp[i]=p;
						expSum[i] += pow;
					}
				}
			}
		}
	}
	
	static long sumRange(int i,int j){return i==0?prefix[j]:prefix[j]-prefix[i-1];}
	
	public static void main(String[] args) throws Throwable {
		Scanner sc = new Scanner(System.in);
		sieve(max);
		fillExponents();
		
		prefix = new long[max];
		
		prefix[0] = expSum[0];
		for(int i = 1;i<prefix.length;i++)
			prefix[i] = 1l*expSum[i] + prefix[i-1];
		
		int t = sc.nextInt();
		StringBuilder sb = new StringBuilder();
		while(t-->0)
		{
			int a = sc.nextInt() , b = sc.nextInt();
			sb.append(sumRange(b+1,a)+"\n");
		}
		System.out.println(sb);
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;
		public Scanner(InputStream s) {br = new BufferedReader(new InputStreamReader(s));}
		public Scanner(String file) throws FileNotFoundException {br = new BufferedReader(new FileReader(file));}
		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 int[] nexIntArray() throws Throwable {
			st = new StringTokenizer(br.readLine());
			int[] a = new int[st.countTokens()];
			for (int i = 0; i < a.length; i++)a[i] = nextInt();
			return a;
		}
		public boolean ready() throws IOException {return br.ready();}
	}
}