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 javax.swing.*;
import javax.swing.plaf.basic.BasicInternalFrameTitlePane;
import java.beans.IntrospectionException;
import java.io.*;
import java.util.*;
import java.lang.*;
import java.math.*;
import java.text.DecimalFormat;
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
public class Main {
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
    //static long MOD = (long) (1e9 + 7);
    static int MOD = 998244353;
    static long MOD2 = MOD * MOD;
    static FastReader sc = new FastReader();
    static int pInf = Integer.MAX_VALUE;
    static int nInf = Integer.MIN_VALUE;
    static long ded = Long.MAX_VALUE;
    static long[] dp;
    public static void main(String[] args) {
        int test = 1;
        test = sc.nextInt();
        int n = 5000001;
        dp = new long[n+1];
        dp[1]= 0;
        int[] z = enumLowestPrimeFactors(5000001);
        for(int i = 2; i <= n; i++){
            dp[i] = dp[i/z[i]]+1;
        }
        for(int i = 2; i <= n; i++){
            dp[i] += dp[i-1];
        }
        while (test-- > 0) solve();
        out.flush();
        out.close();
    }
    public static int[] enumLowestPrimeFactors(int n)
    {
        int tot = 0;
        int[] lpf = new int[n+1];
        int u = n+32;
        double lu = Math.log(u);
        int[] primes = new int[(int)(u/lu+u/lu/lu*1.5)];
        for(int i = 2;i <= n;i++)lpf[i] = i;
        for(int p = 2;p <= n;p++){
            if(lpf[p] == p)primes[tot++] = p;
            int tmp;
            for(int i = 0;i < tot && primes[i] <= lpf[p] && (tmp = primes[i]*p) <= n;i++){
                lpf[tmp] = primes[i];
            }
        }
        return lpf;
    }
    static void  solve(){
        int x = sc.nextInt();
        int y = sc.nextInt();
        out.println(dp[x]-dp[y]);
    }
    static long sq(long a, long b){
        return Math.abs(a-b)*Math.abs(a-b);
    }
    public static long mul(long a, long b) {
        return ((a % MOD) * (b % MOD)) % MOD;
    }
    public static long add(long a, long b) {
        return ((a % MOD) + (b % MOD)) % MOD;
    }
    public static long sub(long a, long b) {
        return ((a % MOD) - (b % MOD)) % MOD;
    }
    //Pair Class
    static class Pair implements Comparable<Pair> {
        int x;
        int y;
        int idx;
        public Pair(int x, int y,int idx) {
            this.x = x;
            this.y = y;
            this.idx = idx;
        }
        @Override
        public int compareTo(Pair o) {
            if ((this.x == o.x)) {
                return (this.y - o.y);
            }
            return (this.x-o.x);
        }
    }
    static class TPair{
        String s;
        int x;
        int y;

        public TPair(String s,int x, int y) {
            this.s = s;
            this.x = x;
            this.y = y;
        }
    }
    //Shuffle Sort
    static final Random random = new Random();
    static void ruffleSort(int[] a) {
        int n = a.length;//shuffle, then sort
        for (int i = 0; i < n; i++) {
            int oi = random.nextInt(n), temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }
    //Brian Kernighans Algorithm
    static long countSetBits(long n) {
        if (n == 0) return 0;
        return 1 + countSetBits(n & (n - 1));
    }
    //Euclidean Algorithm
    static long gcd(long A, long B) {
        if (B == 0) return A;
        return gcd(B, A % B);
    }
    //Modular Exponentiation
    static long fastExpo(long x, long n) {
        if (n == 0) return 1;
        if ((n & 1) == 0) return fastExpo((x * x) % MOD, n / 2) % MOD;
        return ((x % MOD) * fastExpo((x * x) % MOD, (n - 1) / 2)) % MOD;
    }
    //AKS Algorithm
    static boolean isPrime(long n) {
        if (n <= 1) return false;
        if (n <= 3) return true;
        if (n % 2 == 0 || n % 3 == 0) return false;
        for (int i = 5; i <= Math.sqrt(n); i += 6)
            if (n % i == 0 || n % (i + 2) == 0) return false;
        return true;
    }
    public static long modinv(long x) {
        return modpow(x, MOD - 2);
    }
    public static long modpow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        long x = modpow(a, b / 2);
        x = (x * x) % MOD;
        if (b % 2 == 1) {
            return (x * a) % MOD;
        }
        return x;
    }

    public static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        //it reads the data about the specified point and divide the data about it ,it is quite fast
        //than using direct

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception r) {
                    r.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());//converts string to integer
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (Exception r) {
                r.printStackTrace();
            }
            return str;
        }
    }
}