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.util.*;
import java.io.*;
import java.math.*;
public class Main {
	public static long mod= (long) (1e9 +7);
	public static void main(String args[])
	{
		InputReader s= new InputReader(System.in);
		OutputStream outputStream= System.out;
		PrintWriter out= new PrintWriter(outputStream);
		
		int max = 5000000 + 1;
	    int fact[] = new int[max];
	    for(int i=2;i<max;i++){
	    	int t = i/2;
	    	if(t*2 == i){
	    		fact[i] = fact[t] + 1;
	    		continue;
	    	}
	    	for(int j=3;j*j<=i;j+=2){
	    		t = i/j;
	    		if(t*j == i){
	    			fact[i] = fact[t] + 1;
	    			break;
	    		}
	    	}
	    	if(fact[i] == 0)
	    		fact[i] = 1;
	    }
	    
		long sum[]= new long[max];
		for(int i=1;i<max;i++){
			sum[i]= sum[i-1] + fact[i];
		}
		
		int t= s.nextInt();
		while(t-->0){
			int a= s.nextInt();
			int b= s.nextInt();
			out.println(sum[a] - sum[b]);
		}
		out.close();
	}
	
	static long combinations(long n,long r){   // O(r)
		if(r==0 || r==n) return 1;
		r= Math.min(r, n-r);
		long ans=n;  // nC1=n;
		for(int i=1;i<r;i++){
			ans= ans*(n-i);
			ans= ans/(i+1);
		}
		return ans;
		
	}
	public static void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}
	static long modulo(long a,long b,long c) {
		long x=1;
		long y=a;
		while(b > 0){
			if(b%2 == 1){
				x=(x*y)%c;
			}
			y = (y*y)%c; // squaring the base
			b /= 2;
		}
		return  x%c;
	}
	static void catalan_numbers(int n) {
		long catalan[]= new long[n+1];
	    catalan[1] = 1;
	    for (int i = 2; i <= n; i++) {
	        for (int j = 1; j <= i - 1; j++) {
	            catalan[i] = catalan[i] + ((catalan[j]) * catalan[i - j]);
	        }
	    }
	}
	
	static ArrayList<Integer> primeFactors(int n)   // O(sqrt(n))
	{
	    // Print the number of 2s that divide n
		ArrayList<Integer> arr= new ArrayList<>();
	    while (n%2 == 0)
	    {
	        arr.add(2);
	        n = n/2;
	    }
	 
	    // n must be odd at this point.  So we can skip one element (Note i = i +2)
	    for (int i = 3; i <= Math.sqrt(n); i = i+2)
	    {
	        // While i divides n, print i and divide n
	        while (n%i == 0)
	        {
	            arr.add(i);
	            n = n/i;
	        }
	    }
	    // This condition is to handle the case when n is a prime number
	    // greater than 2
	    if (n > 2)
	        arr.add(n);
	    
	    return arr;
	}

	public static int expo(int a, int b){
		if (b==0)
	        return 1;
	    if (b==1)
	        return a;
	    if (b==2)
	        return a*a;

	    if (b%2==0){
	            return expo(expo(a,b/2),2);
	    }
	    else{
	        return a*expo(expo(a,(b-1)/2),2);
	    }
	}
	static class Pair implements Comparable<Pair>
	{
		long f;
		String s;
		Pair(long ii, String cc)
		{
			f=ii;
			s=cc;
		}
		
		public int compareTo(Pair o) 
		{
			return Long.compare(this.f, o.f);
		}
		
	}
	
	public static int[] sieve(int N){    // O(n*log(logn))
		int arr[]= new int[N+1];
		for(int i=2;i<=Math.sqrt(N);i++){
			if(arr[i]==0){
				for(int j= i*i;j<= N;j= j+i){
					arr[j]=1;
				}
			}
		}
		return arr;
		// All the i for which arr[i]==0 are prime numbers.
	}
	static long gcd(long a,long b){       // O(logn)
		if(b==0) return a;
		return gcd(b,a%b);
	}
	static class InputReader {

	    public BufferedReader reader;
	    public StringTokenizer tokenizer;
 
	    public InputReader(InputStream inputstream) {
	      reader = new BufferedReader(new InputStreamReader(inputstream));
	      tokenizer = null;
	    }
	    
	    public String nextLine(){
	    	String fullLine=null;
	    	while (tokenizer == null || !tokenizer.hasMoreTokens()) {
	            try {
	              fullLine=reader.readLine();
	            } catch (IOException e) {
	              throw new RuntimeException(e);
	            }
	            return fullLine;
	          }
	          return fullLine;
	    }
		public String next() {
	      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
	        try {
	          tokenizer = new StringTokenizer(reader.readLine());
	        } catch (IOException e) {
	          throw new RuntimeException(e);
	        }
	      }
	      return tokenizer.nextToken();
	    }
		public long nextLong() {
		      return Long.parseLong(next());
		    }
	    public int nextInt() {
	      return Integer.parseInt(next());
	    }
	  }
}