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 (2.7.1) (judge verdict: Accepted)

require "prime"

class Problem
  attr_accessor :a, :b, :n, :s, :ans
  N = 100000

  def initialize
    @n = gets.to_s.to_i
    @a = Array.new(N+1,0)
    @b = Array.new(N+1,0)
    Prime.each(N+1) do |i|
      a[i] = 1
      b[i] = 1 if a[(i+1)/2] == 1
    end
    @c = @b.each_with_object([0]) { |v, h| h << h[-1] + v }
  end

  def solve
    n.times do
      lo,hi = gets.to_s.split.map{ |v| v.to_i }
      puts @c[hi+1] - @c[lo]
    end
  end

end

pr = Problem.new
pr.solve