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.*;
     
    /**
     *
     * @author umang
     */
     
    public class ProblemD {
        
        public static int mod = (int) (1e9+7);
        public static int[] p = new int[5000001];
        public static int[] sp = new int[5000001];
        
        public static void isPrime(){
            p[0]=-1;
            p[1]=-1;
            for(int i=2;i<p.length;i++){
                if(p[i]!=-1){
                    sp[i]=i;
                    p[i]=1;
                    for(int j=2*i;j<p.length;j+=i){
                        p[j]=-1;
                        if(sp[j]==0) sp[j]=i;
                    }
                }
            }
        }
        public static long lognPrimeFactorisation(int n){
            long c=0;
     
            for(int i=sp[n];i<=Math.sqrt(n) && i!=0;i=sp[n]){
                if(n%i==0){
                    while(n%i==0) {
                        n/=i;
                        c++;
                    }
                }
            }
            if(n>=2) c++;
            return c;
        }
        
        public static void main(String[] args) {
            new Thread(null ,new Runnable(){
                public void run(){
                    try{
                        solve();
                    } catch(Exception e){
                        e.printStackTrace();
                    }
                }
            },"1",1<<26).start();
        }
        
        public static void solve() {
     
            InputReader in = new InputReader(System.in);
            PrintWriter out = new PrintWriter(System.out);
            
            isPrime();
            long[] arr=new long[5000001];
            for(int i=2;i<arr.length;i++){
                arr[i]=lognPrimeFactorisation(i);
                arr[i]+=arr[i-1];
            }
            int t=in.nextInt();
            
            while(t-->0){
                int a=in.nextInt();
                int b=in.nextInt();
                out.println((arr[a]-arr[b]));
            }
            
            out.close();
        }
        
        static class Pair implements Comparable<Pair>{
     
            int x,y,i;
            
    	Pair (int x,int y,int i){
    		this.x=x;
    		this.y=y;
    		this.i=i;
    	}
     
    	Pair (int x,int y){
    		this.x=x;
    		this.y=y;
    	}
            
    	public int compareTo(Pair o) {
    		if(this.x!=o.x)
                        return Integer.compare(this.x,o.x);
    		else
                        return Integer.compare(this.y,o.y);
    		//return 0;
    	}
     
                public boolean equals(Object o) {
                if (o instanceof Pair) {
                    Pair p = (Pair)o;
                    return p.x == x && p.y == y && p.i==i;
                }
                return false;
            }
            public int hashCode() {
                return new Integer(x).hashCode() * 31 + new Integer(y).hashCode()+new Integer(i).hashCode()*37;
            }
        
        } 
     
        
        public static boolean isPal(String s){
            for(int i=0, j=s.length()-1;i<=j;i++,j--){
                    if(s.charAt(i)!=s.charAt(j)) return false;
            }
            return true;
        }
        public static String rev(String s){
    		StringBuilder sb=new StringBuilder(s);
    		sb.reverse();
    		return sb.toString();
        }
        
        public static long gcd(long x,long y){
    	if(x%y==0)
    		return y;
    	else
    		return gcd(y,x%y);
        }
        
        public static int gcd(int x,int y){
    	if(x%y==0)
    		return y;
    	else 
    		return gcd(y,x%y);
        }
        
        public static long gcdExtended(long a,long b,long[] x){
            
            if(a==0){
                x[0]=0;
                x[1]=1;
                return b;
            }
            long[] y=new long[2];
            long gcd=gcdExtended(b%a, a, y);
            
            x[0]=y[1]-(b/a)*y[0];
            x[1]=y[0];
            
            return gcd;
        }
        
        public static int abs(int a,int b){
    	return (int)Math.abs(a-b);
        }
     
        public static long abs(long a,long b){
    	return (long)Math.abs(a-b);
        }
        
        public static int max(int a,int b){
    	if(a>b)
    		return a;
    	else
    		return b;
        }
     
        public static int min(int a,int b){
    	if(a>b)
    		return b;
    	else 
    		return a;
        }
        
        public static long max(long a,long b){
    	if(a>b)
    		return a;
    	else
    		return b;
        }
     
        public static long min(long a,long b){
    	if(a>b)
    		return b;
    	else 
    		return a;
        }
     
        public static long pow(long n,long p,long m){
    	 long  result = 1;
    	  if(p==0)
    	    return 1;
    	if (p==1)
    	    return n;
    	while(p!=0)
    	{
    	    if(p%2==1)
    	        result *= n;
    	    if(result>=m)
    	    result%=m;
    	    p >>=1;
    	    n*=n;
    	    if(n>=m)
    	    n%=m;
    	}
    	return result;
        }
        
        public static long pow(long n,long p){
    	long  result = 1;
    	  if(p==0)
    	    return 1;
    	if (p==1)
    	    return n;
    	while(p!=0)
    	{
    	    if(p%2==1)
    	        result *= n;	    
    	    p >>=1;
    	    n*=n;	    
    	}
    	return result;
        }
        
    	static class InputReader {
     
    		private final InputStream stream;
    		private final byte[] buf = new byte[8192];
    		private int curChar, snumChars;
    		private SpaceCharFilter filter;
     
    		public InputReader(InputStream stream) {
    			this.stream = stream;
    		}
     
    		public int snext() {
    			if (snumChars == -1)
    				throw new InputMismatchException();
    			if (curChar >= snumChars) {
    				curChar = 0;
    				try {
    					snumChars = stream.read(buf);
    				} catch (IOException e) {
    					throw new InputMismatchException();
    				}
    				if (snumChars <= 0)
    					return -1;
    			}
    			return buf[curChar++];
    		}
     
    		public int nextInt() {
    			int c = snext();
    			while (isSpaceChar(c)) {
    				c = snext();
    			}
    			int sgn = 1;
    			if (c == '-') {
    				sgn = -1;
    				c = snext();
    			}
    			int res = 0;
    			do {
    				if (c < '0' || c > '9')
    					throw new InputMismatchException();
    				res *= 10;
    				res += c - '0';
    				c = snext();
    			} while (!isSpaceChar(c));
    			return res * sgn;
    		}
     
    		public long nextLong() {
    			int c = snext();
    			while (isSpaceChar(c)) {
    				c = snext();
    			}
    			int sgn = 1;
    			if (c == '-') {
    				sgn = -1;
    				c = snext();
    			}
    			long res = 0;
    			do {
    				if (c < '0' || c > '9')
    					throw new InputMismatchException();
    				res *= 10;
    				res += c - '0';
    				c = snext();
    			} while (!isSpaceChar(c));
    			return res * sgn;
    		}
     
    		public int[] nextIntArray(int n) {
    			int a[] = new int[n];
    			for (int i = 0; i < n; i++) {
    				a[i] = nextInt();
    			}
    			return a;
    		}
     
    		public long[] nextLongArray(int n) {
    			long a[] = new long[n];
    			for (int i = 0; i < n; i++) {
    				a[i] = nextLong();
    			}
    			return a;
    		}
                    
    		public String readString() {
    			int c = snext();
    			while (isSpaceChar(c)) {
    				c = snext();
    			}
    			StringBuilder res = new StringBuilder();
    			do {
    				res.appendCodePoint(c);
    				c = snext();
    			} while (!isSpaceChar(c));
    			return res.toString();
    		}
     
    		public String nextLine() {
    			int c = snext();
    			while (isSpaceChar(c))
    				c = snext();
    			StringBuilder res = new StringBuilder();
    			do {
    				res.appendCodePoint(c);
    				c = snext();
    			} while (!isEndOfLine(c));
    			return res.toString();
    		}
     
    		public boolean isSpaceChar(int c) {
    			if (filter != null)
    				return filter.isSpaceChar(c);
    			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    		}
     
    		private boolean isEndOfLine(int c) {
    			return c == '\n' || c == '\r' || c == -1;
    		}
     
    		public interface SpaceCharFilter {
    			public boolean isSpaceChar(int ch);
    		}
    	}
    }