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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

main::IO()
main = do
    q <- readLn::IO Int

    queries <- sequence $ replicate q (map read . words <$> getLine)
    mapM_ print $ map (\[a,b] -> solve a b) queries


solve::Int -> Int -> Int
solve a b = (length . filter (\x -> factor ((x+1)`div`2) == [] && a <= x && x /= 2) . sieveOfEratosthenes) b

sieveOfEratosthenes :: Int -> [Int]
sieveOfEratosthenes n
    | n < 2 = []
    | n == 2 = [2]
    | otherwise = sieve [x | x <- [2..n]] n
    where
        sieve :: [Int] -> Int -> [Int]
        sieve [] _ = []
        sieve (x:xs) n
            | x^2 > n = x:xs
            | otherwise = x : (sieve [a | a <- xs, a `mod` x > 0] n)

factor ::Int -> [Int]
factor n = filter (\x -> n `mod` x ==0)[2..n-1]