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)

Q = gets.to_i

def is_prime(x)
  if x < 2
    return false
  end

  if x == 2
    return true
  end

  if x % 2 == 0
    return false
  end

  i = 3
  while i <= x**(1/2.0)
    if x % i == 0
      return false
    end
    i += 2
  end

  return true
end

MAX = 10**5 + 1
like_numbers = Array.new(MAX) { 0 }
1.upto(MAX) do |i|
  if i % 2 == 0
    next
  else
    if is_prime(i) && is_prime((i+1)/2)
      like_numbers[i] = 1
    end
  end
end

# p like_numbers

sum = Array.new(MAX+1) {0}
0.upto(MAX-1) do |i|
  sum[i+1] = sum[i] + like_numbers[i]
end

# p sum

Q.times do
  l, r = gets.split.map(&:to_i)
  puts sum[r] - sum[l]
end