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.ArrayList;
import java.util.InputMismatchException;

public class TaskF {

	public FasterScanner mFScanner;
	public PrintWriter mOut;
	private boolean[] prime;
	private long[] mDiv;
	private ArrayList<Integer> mPrimeList;

	public TaskF() {
		mFScanner = new FasterScanner();
		mOut = new PrintWriter(System.out);
	}

	public void solve() {
		int t;
		int a, b;
		long res;
		int maxNum = 5000001;

		t = mFScanner.nextInt();
		prime = new boolean[maxNum + 1];
		mDiv = new long[maxNum + 1];
		mPrimeList = new ArrayList<>();

		sieveOfEratosThenes(prime, maxNum);
		storeDiv(maxNum);

		// System.out.println("Done");

		for (int i = 0; i < t; i++) {
			a = mFScanner.nextInt();
			b = mFScanner.nextInt();
			res = mDiv[a] - mDiv[b];
			mOut.println(res);
		}

	}

	public void storeDiv(int N) {

		for (int num = 2; num <= N; num++) {

			long count = 0;
			int number = num;

			for (int pr : mPrimeList) {
				
				if (prime[number]) {
					count++;
					break;
				}

				if (number % pr != 0) {
					continue;
				}

				while (number % pr == 0) {
					number /= pr;
					count++;
				}

				if (number == 1)
					break;

			}

			mDiv[num] += mDiv[num - 1] + count;

		}

	}

	public void sieveOfEratosThenes(boolean[] prime, int N) {

		int i;
		long j;

		for (i = 2; i <= N; i++) {
			prime[i] = true;
		}

		for (i = 2; i <= N; i++) {
			if (!prime[i])
				continue;

			mPrimeList.add(i);
			j = 1L * i * i;

			while (j <= N) {
				prime[(int) j] = false;
				j += i;
			}
		}

	}

	public void flush() {
		mOut.flush();
	}

	public void close() {
		mOut.close();
	}

	public static void main(String[] args) {
		TaskF mSol = new TaskF();
		mSol.solve();
		mSol.flush();
		mSol.close();
	}

	class FasterScanner {
		private InputStream mIs;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public FasterScanner() {
			this(System.in);
		}

		public FasterScanner(InputStream is) {
			mIs = is;
		}

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

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

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

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

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

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

		public boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		public char[] nextCharArray(int N) {
			int i;
			char[] array;
			String str;

			array = new char[N];

			i = 0;

			str = nextLine();

			for (i = 0; i < N && i < str.length(); i++) {
				array[i] = str.charAt(i);
			}

			return array;
		}

		public char[][] nextChar2DArray(int M, int N) {
			int i;
			char[][] array;

			array = new char[M][N];

			i = 0;

			for (i = 0; i < M; i++) {
				array[i] = nextCharArray(N);
			}

			return array;
		}

		public int[] nextIntArray(int N) {
			int i;
			int[] array;

			array = new int[N];

			i = 0;

			for (i = 0; i < N; i++) {
				array[i] = nextInt();
			}

			return array;
		}

		public int[][] nextInt2DArray(int M, int N) {
			int i;
			int[][] array;

			array = new int[M][N];

			i = 0;

			for (i = 0; i < M; i++) {
				array[i] = nextIntArray(N);
			}

			return array;
		}

		public long[] nextLongArray(int N) {
			int i;
			long[] array;

			array = new long[N];

			i = 0;

			for (i = 0; i < N; i++) {
				array[i] = nextLong();
			}

			return array;
		}

		public long[][] nextLong2DArray(int M, int N) {
			int i;
			long[][] array;

			array = new long[M][N];

			i = 0;

			for (i = 0; i < M; i++) {
				array[i] = nextLongArray(N);
			}

			return array;
		}

		public double[] nextDoubleArray(int N) {
			int i;
			double[] array;

			array = new double[N];

			for (i = 0; i < N; i++) {
				array[i] = nextDouble();
			}

			return array;
		}

		public double[][] nextDouble2DArray(int M, int N) {
			int i;
			double[][] array;

			array = new double[M][N];

			for (i = 0; i < M; i++) {
				array[i] = nextDoubleArray(N);
			}

			return array;
		}

	}
}