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 Control.Monad
import Data.Set as S hiding (foldl)

count l r =
  length $ takeWhile (<=r) $ dropWhile (<l) like2017s

like2017s =
  [ x |x<-p, elem (div (x+1) 2) p  ]
  where p = primes [2..10^5]

primes :: [Int] -> [Int]  
primes = S.toList . (seive 2) . S.fromList  

seive :: Int -> Set Int-> Set Int
seive p xs  
     | p*p > S.findMax xs = xs  
     | otherwise        = seive (p+1) $ foldl (\acc x -> S.delete x acc) xs [2*p,3*p..q]  
                         where q = S.findMax xs
                               
solve :: [(Int,Int)] -> [Int]
solve [] = []
solve ((l,r):lrs) =
  count l r : solve lrs
  
main = do
  q <- read <$> getLine
  lrs <- replicateM q $ (\(x:y:[]) -> (read x,read y)) . words <$> getLine
  forM_ (solve lrs) $ (\e -> print e)