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)

--import Data.IntMap.Strict (IntMap)
import Data.Ix
import Data.Function

main :: IO()
main = do
    _ <- getLine
    lrs <- getContents
    mapM_ (print . countRange . map read . words) (lines lrs)
        where
            countRange [l,r] = count r - count (l - 1)
            count :: Int -> Int
            count 0 = 0
            count 1 = 0
            count n = (if is2017Like n then 1 else 0) + count (n - 1)
            is2017Like 2 = False
            is2017Like 3 = True
            is2017Like n = mod n 4 == 1 && isPrime n && isPrime ((n + 1) `div` 2)
            isPrime n = null [i | i <- takeWhile (\x -> x * x <= n) primes, mod n i == 0]
            primes = 2 : 3 : primes'
                where
                    primes' = 5 : f 1 7 primes'
                    f m s (p : ps) = [n | n <- ns, gcd m n == 1] ++ f (m * p) (p * p) ps
                        where ns = [x + y | x <- [s, s + 6 .. p * p - 2], y <- [0, 4]]