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.chomp.to_i
p_length = 100001


# 1~10^5までの素数をbooleanで持つ
# 累積和でそれぞれ何個か調べる
# あとは順番に処理


prime = Array.new(p_length, false)

def fetch_prime_list(max)
  table = Array.new(max + 1,true)
  prime_list = []

  (2..max).each do |num|
    if table[num] == true
      prime_list << num
      k = num * num
      while k <= max
        table[k] = false
        k += num
      end
    end
  end
  return prime_list
end

#配列を返すメソッド
p_arr =  fetch_prime_list(p_length)

p_arr.each do |num|
  prime[num] = true
end

ruiseki = [0]

1.upto(p_length) do |i|
  if i.odd? && prime[i] && prime[(i + 1)/2]
    tmp = 1
  else
    tmp = 0
  end

  ruiseki[i] = ruiseki[i-1] + tmp
end


ans = []

Q.times do |i|
  l, r = gets.chomp.split.map(&:to_i)
  ans << ruiseki[r] - ruiseki[l-1]
end

ans.each do |r|
  puts r
end