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)

def prime?(n)
  return n >= 2 if n <= 3
  return true if n == 5
  return false unless 30.gcd(n) == 1
  (7..n**(0.5)).step(30) do |p|
    return false if
      n % (p) == 0 || n % (p + 4) == 0 || n % (p + 6) == 0 || n % (p + 10) == 0 ||
      n % (p + 12) == 0 || n % (p + 16) == 0 || n % (p + 22) == 0 || n % (p + 24) == 0
  end
  true
end

Q = gets.to_i
max = 10**5+10

a = Array.new(max, 0)
max.times do |i|
  if prime?(i) && prime?((i+1)/2)
    a[i] = 1
  end
end

s = Array.new(max+1, 0)
max.times do |i|
  s[i+1] = s[i] + a[i]
end

ans = []
Q.times do
  l, r = gets.split.map(&:to_i)
  ans << s[r+1] - s[l]
end
puts ans