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: Wrong Answer)


def get_prime_list(max)
  prime_table = Array.new(max + 1){true}
  prime_list = []
  (2..max).each do |n|
    if prime_table[n] == true
      prime_list << n
      k = n * n
      while k <= max
        prime_table[k] = false
        k += n
      end
    end
  end
  return prime_table, prime_list
end

max = 10 ** 5
pt, pl = get_prime_list(max)

sub_prime = Array.new(max){0}
pl.each { |p| sub_prime[p] = 1 if pt[(p + 1) / 2] }

sum = Array.new(max + 1){0}
max.times { |i| sum[i + 1] = sum[i] + sub_prime[i] }

q = gets.strip.to_i
d = q.times.map { gets.strip.split.map(&:to_i) }
d.each do |l, r| 
  puts sum[r + 1] - sum[l]
end