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)

# coding: utf-8

def era(n)
    $primes = Array.new(n, true)
    $primes[0], $primes[1] = false, false
    (2..Math.sqrt(n)).each do |i|
        if $primes[i]
            (i * i).step(n, i).each do |j|
                $primes[j] = false
            end
        end
    end
end

max = 1000001
era(max)

$niteru2017 = Array.new(1000001, 0)

tmp = 0
1.step(100001) {|i|
    if i % 2 == 0
        $niteru2017[i] = $niteru2017[i-1]
    elsif $primes[i] && $primes[(i+1)/2]
        tmp += 1
        $niteru2017[i] = tmp
    else
        $niteru2017[i] = $niteru2017[i-1]
    end
}

q = gets.to_i

for i in 1..q do
    l, r = gets.chomp.split(" ").map(&:to_i);
    puts $niteru2017[r] - $niteru2017[l-1]
end