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: Accepted)

require 'prime'

is_prime = Array.new( 10 ** 5 + 1, false )
primes = Prime.each(10**5).to_a

primes.each{ |p| is_prime[p] = true }

nums_like_2017 = []
primes.each{ |p| nums_like_2017 << p if is_prime[(p+1)/2] }
m = nums_like_2017.size

Q = gets.to_i
Q.times do |i|
  
  l, r = gets.split.map(&:to_i)
  
  rn = nums_like_2017.bsearch_index{ |x| x > r }
  rn = m if rn.nil?
  ln = nums_like_2017.bsearch_index{ |x| x >= l }
  ln = m if ln.nil?
  
  puts rn - ln
end