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)

lines = $stdin.read
$pn = []

def is_prime?(n)
  if n == 1
    false
  elsif $pn.include?(n)
    true
  else
    ans = true
    max = Math.sqrt(n).round
    for t in 2..max
      ans = false if n % t == 0
    end
    $pn << n if ans
    ans
  end
end

def like_2017?(n)
  is_prime?(n) and is_prime?((n+1)/2)
end

array = lines.split("\n")
Q = array[0].to_i
array[1..Q].each do |str|
  l,r = str.split(" ").map(&:to_i)
  arr = l.step(r, 2).to_a
  puts arr.count{|p| like_2017?(p)}
end