Problem:
Score : 400 points

Problem Statement

We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.

You are given Q queries.

In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.

Constraints

1≤Q≤10^5

1≤l_i≤r_i≤10^5

l_i and r_i are odd.

All input values are integers.

Input

Input is given from Standard Input in the following format:

Q
l_1 r_1
:
l_Q r_Q

Output

Print Q lines. The i-th line (1≤i≤Q) should contain the response to the i-th query.

Sample Input 1

1
3 7

Sample Output 1

2

3 is similar to 2017, since both 3 and (3+1)/2=2 are prime.

5 is similar to 2017, since both 5 and (5+1)/2=3 are prime.

7 is not similar to 2017, since (7+1)/2=4 is not prime, although 7 is prime.

Thus, the response to the first query should be 2.

Sample Input 2

4
13 13
7 11
7 11
2017 2017

Sample Output 2

1
0
0
1

Note that 2017 is also similar to 2017.

Sample Input 3

6
1 53
13 91
37 55
19 51
73 91
13 49

Sample Output 3

4
4
1
1
1
2

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

MAX = 10 ** 5

def get_primes
  [].tap do |y|
    y << 2
    memos = [*3.step(Math.sqrt(MAX), 2)].map(&:to_i)
    until memos.empty?
      num = memos.shift
      memos.select! { |x| x == num or x % num != 0 }
      y << num
    end
  end
end

lr = Array.new(gets.chomp.to_i) { gets.chomp.split.map(&:to_i) }
primes = get_primes

lr.each do |l, r|
  count = 0
  l.step(r, 2).each do |num|
    if num <= primes[-1]
      exist1, exist2 = false, false
      primes.each do |prime|
        exist1 = true if num == prime
        exist2 = true if (num + 1) / 2 == prime
        break if exist1 and exist2
      end
    else
      exist1, exist2 = true, true
      primes.each do |prime|
        exist1 = false if num % prime == 0
        exist2 = false if (num + 1) / 2 % prime == 0
        break unless exist1 and exist2
      end
    end
    count += 1 if exist1 and exist2
  end
  puts count
end