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_list(n)
  return [] if n < 2

  # seve 篩（ふるい）
  seve = Array.new(n + 1){true}
  primes = {}

  (2..n).each do |i|
    if seve[i] == true
      primes[i] = 1
      k = i * i
      while k <= n
        seve[k] = false
        k += i
      end
    end
  end
  primes
end

MAX = 10 ** 5

pl = prime_list(MAX)

Q = gets.strip.to_i
lr = Q.times.map { gets.strip.split.map(&:to_i) }

a = Array.new(MAX + 1) {0}

c = 0
(1..MAX).each do |i|
  unless pl[i].nil?
    c += 1 unless pl[(i + 1) / 2].nil?
  end
  a[i] = c
end

lr.each do |l, r|
  puts a[r] - a[l - 1] 
end