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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Map;
import java.util.NavigableMap;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

public class d304 {

	static class Task {		
		
		public void Solve(InputReader in, PrintWriter out)
		{
			long count=0;
			int dp[]=new int[5000001];
			boolean sieve[]=new boolean[5000001];
			int num=SieveOfErathostenes(5000000, sieve);
			for(int i=2;i<=5000000;i++)
			{
				if(sieve[i]==false)
				{
				for(int j=i;j<=5000000;j+=i)
				{
					dp[j]=dp[j/i]+1;
				}
				}
			}
			for(int i=2;i<=5000000;i++)
			{
				dp[i]+=dp[i-1];
			}
			int t=in.nextInt();
			while(t-->0)
			{
				int a=in.nextInt();
				int b=in.nextInt();
				out.println(dp[a]-dp[b]);
			}
	    }
     }
	
	   public static int SieveOfErathostenes(int n,boolean sieve[]){
	  		int cnt = 0;
	  		for(int i = 2 ; i <= n ; i++)
	  			if(sieve[i] == false){
	  			    cnt++;
	  				for(int j = i + i ; j <= n ; j += i)
	  					sieve[j] = true;
	  			}
	  		return cnt;	
	  	}


	
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.Solve(in,out);
        out.close();
    }
  
    static int[][] sort2D(int arr[][]){
        Arrays.sort(arr,new java.util.Comparator<int[]>(){
        public int compare(int[] a, int[] b) {
            return Integer.compare(a[0], b[0]);
        }});
        return arr;
    }
    
	static int[] di={1,0,-1,0,1,-1,-1,1};
	static int[] dj={0,1,0,-1,1,1,-1,-1};
    
	static class point{
		int x;int y;
		public point(int x,int y){
			this.x=x;
			this.y=y;
		}
	}

    static void sort(int arr[]){
		int cnt[]=new int[(1<<16)+1];
		int ys[]=new int[arr.length];	
		for(int j=0;j<=16;j+=16){
			Arrays.fill(cnt,0);
			for(int x:arr){cnt[(x>>j&0xFFFF)+1]++;}
			for(int i=1;i<cnt.length;i++){cnt[i]+=cnt[i-1];}
			for(int x:arr){ys[cnt[x>>j&0xFFFF]++]=x;}
			{ final int t[]=arr;arr=ys;ys=t;}
		}
		if(arr[0]<0||arr[arr.length-1]>=0)return;
		int i,j,c;
		for(i=arr.length-1,c=0;arr[i]<0;i--,c++){ys[c]=arr[i];}
		for(j=arr.length-1;i>=0;i--,j--){arr[j]=arr[i];}
		for(i=c-1;i>=0;i--){arr[i]=ys[c-1-i];}
	}
    
    static int lcm(int a,int b){return a*b/gcd(a,b);}
    static int abs(int x){if(x>=0)return x;else return -x;}
    static int gcd(int a,int b){return b==0?a:gcd(b,a%b);} 
    static int min(int x,int y){return x<y?x:y;}
    static int min(int x,int y,int z){return x<y?(x<z?x:z):(y<z?y:z);}
    static int max(int x,int y){return x>y?x:y;}
    static int max(int x,int y,int z){return x>y?(x>z?x:z):(y>z?y:z);}
    
    static long lcm(long a,long b){return a*b/gcd(a,b);}
    static long abs(long x){if(x>=0)return x;else return -x;}
    static long gcd(long a,long b){return b==0?a:gcd(b,a%b);}
    static long min(long x,long y){return x<y?x:y;}
    static long min(long x,long y,long z){return x<y?(x<z?x:z):(y<z?y:z);}
    static long max(long x,long y){return x>y?x:y;}
    static long max(long x,long y,long z){return x>y?(x>z?x:z):(y>z?y:z);}
    
    static void joutArray(int arr[]){
    	for(int i=0;i<arr.length;i++){
    		System.out.print(arr[i]+" ");
    	}
    	System.out.println();
    }
    
    static void joutArray(int arr[][],int n,int m){
    	for(int i=0;i<n;i++){
    		for(int j=0;j<m;j++)
    		System.out.print(arr[i][j]+" ");
    		System.out.println();
    	}
    	System.out.println();
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        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 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 int nextInt() {
            return Integer.parseInt(next());
        }
        
        public long nextLong() {
        	return Long.parseLong(next());
        }
        
        public double nextDouble() {
        	return Double.parseDouble(next());
        }
        
        public int[] nextIntArray(int n) {
        	int arr[]=new int[n];
        	for(int i=0;i<n;i++)
        		arr[i]=nextInt();
        	return arr;
        }
        
        public char[] nextCharArray(){
        	char arr[]=next().toCharArray();
        	return arr;
        }
        
        public HashMap<Integer,Integer> inHashMap(int n){
        	HashMap<Integer,Integer> hm=new HashMap<>();
        	for(int i=0;i<n;i++){
    			int num=nextInt();
    			hm.put(num,hm.get(num)==null?1:hm.get(num)+1);
    		}
        	return hm;
        }
     }
    
   }