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: Accepted)

import Control.Monad
import Data.Maybe
import Control.Monad.ST
import Data.List
import Data.Array
import Data.Array.ST
import qualified Data.ByteString.Char8 as B

main = do
  let a = buildSum (sieve 100000)
  q <- readLn
  forM_ [1..q] $ \_ -> do
    [l, r] <- map (fst . fromJust . B.readInt) . B.words <$> B.getLine
    print $ a!(r+1) - a!l

sieve :: Int -> Array Int Bool
sieve n = runST $ do
  a <- newArray (0, n) True :: ST s (STUArray s Int Bool)
  writeArray a 0 False
  writeArray a 1 False
  forM_ [2..n] $ \i -> do
    x <- readArray a i
    when x $ do
      forM_ [i*2, i*3 .. n] $ \j -> writeArray a j False
  freeze a

buildSum :: Array Int Bool -> Array Int Int
buildSum s = let n = length s - 1
             in listArray (0, n+1) . scanl (+) 0 . map (\i -> if s!i && s!((i+1)`div`2) then 1 else 0) $ [0..n]