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: Runtime Error)

require "prime"

q = gets.to_i
l_min, r_max = 100000000000, 0
queries = []
q.times do
  l, r = gets.split.map &:to_i
  queries << [l, r]
  l_min = l if l_min > l
  r_max = r if r_max < r
end

sum = 0
prev = 0
is_prime = []
sums = []
Prime.each(r_max) do |p|
  (prev...p).each do |i| sums[i] = sum end
  is_prime[p] = true
  prev = p+1
  sum += 1 if is_prime[(p+1)/2]
  sums[p] = sum
end

queries.each do |(l, r)|
  p sums[r] - sums[l-1]
end