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 qualified Data.Map as M

isP::Int->Bool
isP n 
   |n<2 =False
   |n==2 =True
   |n `mod` 2==0 =False
   |otherwise = try n 3
   where
        try :: Int->Int->Bool
        try m i
           |i*i > m=True
           |m `mod` i==0 =False
           |otherwise=try m (i+2)

f3::Maybe Int->Int
f3 (Just x)=x
f3 Nothing=0

f2::M.Map Int Int->[String]->[Int]
f2 _ [] = []
f2 ms (x:xs) =let (a:b:[])=map read (words x)::[Int]
                  c1=f3 (M.lookup (a-1) ms)
                  c2=f3 (M.lookup (b) ms)
              in c2-c1:f2 ms xs

main =do
      e <- getLine
      es <- getContents 
      let ms=tail $ scanl (\acc x-> acc + if isP x && isP ((x+1) `div` 2) then 1 else 0) 0 [0..100000]
          ms2=zip [0..] ms
          ms3=M.fromList ms2
      mapM_ putStrLn $ map show $ f2 ms3 (lines es)