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)

Q = gets.to_i
plist = []
2.upto(100000) do |n|
  isprime = true
  2.upto(n - 2) do |k|
    break if k ** 2 > n
    if n % k == 0 
      isprime = false
      break
    end
  end
  plist.push(n) if isprime
end

llist = plist.select{|n| plist.include?((n + 1) / 2)}
llist.unshift(-1)
llist.push(10 ** 6)

Q.times do
  l, r = gets.split(' ').map(&:to_i)
  l = llist.bsearch_index{|n| n >= l}
  r = llist.bsearch_index{|n| n > r}
  puts r - l
end