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: Wrong Answer)

import Control.Monad
import Control.Monad.ST
import Data.List
import Control.Monad.Trans.State.Strict
import Data.Char (isSpace)
import Data.Maybe (fromJust)
import qualified Data.Vector.Unboxed as UV
import qualified Data.Vector.Unboxed.Mutable as MV

import qualified Data.ByteString.Char8 as B

type Parser a = StateT B.ByteString Maybe a

parseInt :: Parser Int
parseInt = StateT (B.readInt . B.dropWhile isSpace)

parseInt2 :: Parser (Int,Int)
parseInt2 = liftM2 (,) parseInt parseInt

parse :: Parser [(Int,Int)]
parse = do
    q<-parseInt
    replicateM q parseInt2

pr=2:q
q=3:5:7:3#q
m#(a:b:x)=[n|n<-[a^2,a^2+2..b^2-2],gcd n m<2]++(m*b)#(b:x)

prs = takeWhile (<=100000) pr

csum = UV.create $ do
    pv <- MV.replicate 100001 0:: ST s (MV.STVector s Int)
    sv <- MV.replicate 100001 0:: ST s (MV.STVector s Int)
    forM_ prs $ \p -> MV.write pv p 1
    forM_ prs $ \p -> do
        a <- MV.read pv ((p+1)`div`2)
        when (a == 1) $ MV.write sv p 1
    forM_ [1..100000] $ \i ->
        MV.write sv i =<< (+) <$> MV.read sv (i-1) <*> MV.read sv i
    return sv

main = do
    lrs<- fromJust.evalStateT parse <$> B.getContents::IO[(Int,Int)]
    putStr $ unlines $ map (show.(\(l,r)-> (csum UV.! r) - (csum UV.! (l-1)))) lrs