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)

tmp = [*(2..10**5)]
$primes = []
while n = tmp.shift
  $primes << n
  tmp.delete_if {|m| m % n == 0 }
end
$eseprimes = $primes.clone
$eseprimes.delete_if {|m| !$primes.include?((m+1)/2) }

$count = Array.new(10**5,0)
c = 0
s = 0
[*$eseprimes, $count.size+1].each do |e|
  $count.fill(c, s..e)
  c += 1
  s = e
end

gets.to_i.times do
  l,r = gets.split.map(&:to_i)
  puts $count[r] - $count[l-1]
end