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 Control.Applicative
import System.IO

isPrime :: Int -> Bool
isPrime num
    | num == 1 = False
    | otherwise = null(filter (\x -> num `mod` x == 0) [2..floor(sqrt(fromIntegral num))])

solve :: [Int] -> Int
solve [l,r] = length[x | x<-[l..r], isPrime x, isPrime $ (x+1) `div` 2, odd x]

rl :: IO ()
rl=do
  e<-isEOF
  if e
    then return ()
    else do
      ss <- (map read . words) <$> getLine -- input: 123 456 789
-- ss = [123, 456, 789]
      putStrLn $ show $ solve ss
      rl

main = do
  q <- readLn :: IO Int
  rl