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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;
import java.util.concurrent.ArrayBlockingQueue;

/**
 * Created by dhamada on 15/05/30.
 */
public class D {

    static int[] generatePrimes(int upto) {
        boolean[] isp = new boolean[upto];
        Arrays.fill(isp, true);

        int pi = 0;
        for (int i = 2; i < upto ; i++) {
            if (isp[i]) {
                pi++;
                for (int j = i * 2; j < upto; j += i) {
                    isp[j] = false;
                }
            }
        }

        int[] ret = new int[pi];
        int ri = 0;
        for (int i = 2 ; i < upto ; i++) {
            if (isp[i]) {
                ret[ri++] = i;
            }
        }
        return ret;
    }



    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int[] p = generatePrimes(5000010);

        // prec
        int[] v = new int[5000010];
        for (int pi : p) {
            for (int f = pi ; f < v.length ; f += pi) {
                v[f] = v[f/pi] + 1;
            }
        }

        int[] imos = new int[v.length];
        for (int i = 1; i < imos.length ; i++) {
             imos[i] += imos[i-1] + v[i];
        }

        int t = in.nextInt();
        for (int i = 0; i < t ; i++) {
            int a = in.nextInt();
            int b = in.nextInt();
            out.println(imos[a] - imos[b]);
        }
        out.flush();
    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int next() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public char nextChar() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            if ('a' <= c && c <= 'z') {
                return (char)c;
            }
            if ('A' <= c && c <= 'Z') {
                return (char)c;
            }
            throw new InputMismatchException();
        }

        public String nextToken() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char)c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }
}