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
array = []
q.times do
  array << gets.split(" ").map(&:to_i)
end

## エラトステネスのふるいを使い、MAXである10**5までの素数を求める
MAX = 100000
is_prime = Array.new(MAX, 1)
is_prime[0] = 0
is_prime[1] = 0
(2...MAX).each do |i|
  if is_prime[i] == 1
    (2...MAX).each do |j|
      break if i * j > MAX
      is_prime[i * j] = 0
    end
  end
end

a = Array.new(MAX, 0)
MAX.times do |i|
  if i % 2 == 1
    a[i] = 1 if is_prime[i] == 1 && is_prime[(i + 1) / 2] == 1
  end
end


## 累積和
s = Array.new(MAX + 1, 0)
MAX.times do |i|
  s[i + 1] = s[i] + a[i]
end

result = []
array.each do |e|
  result << s[e[1] + 1] - s[e[0]]
end

puts result