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)

_ = gets.to_i
lr = []
rmax = 0
readlines.each do |line|
  l, r = line.split(" ").map(&:to_i)
  lr.push([l, r])
  rmax = [rmax, r].max
end

def is_prime(n)
  return false if n < 2
  return true if n == 2
  return false if n.even?

  num = n
  (3..Math.sqrt(n)).each do |i|
    num /= i if num % i == 0
  end

  [1, n].include?(num)
end

p = Array.new(rmax + 1, 0)
(0..(p.size + 1)).each do |i|
  p[i] = is_prime(i)
end

a = Array.new(rmax + 1, 0)
(0..a.size).each do |i|
  a[i + 1] = a[i]
  a[i + 1] += 1 if is_prime(i + 1) && is_prime((i + 2) / 2)
end

lr.each do |_lr|
  l, r = _lr
  puts a[r] - a[l - 1]
end