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 Julia (0.5.0) (judge verdict: Accepted)

function parseInt(x) parse(Int, x) end
parseMap(x::Array{SubString{String}, 1}) = map(parseInt, x)

function isPrime(x)
	if x <= 1
		return(0)
	elseif x == 2
		return(1)
	elseif x%2 == 0
		return(0)
	else
		i = 3
		flg = 0
		while i <= floor(sqrt(x))
			if x%i == 0
				return(0)
				flg = 1
				break
			else
				i += 2
			end
		end
		if flg == 0
			return(1)
		end
	end
end

function isBPrime(x)
  if isPrime(x) == 1 && isPrime(div(x+1,2)) == 1
    return(1)
  else
    return(0)
  end
end

function main()
  x = Array{Int}(100000)
  x[1] = 0
  for i in 2:100000
  	x[i] = x[i-1]+isBPrime(i)
  end
  q = parseInt(readline())
  for i in 1:q
    l, r = parseMap(split(readline()))
    if l == 1
    	println(x[r])
    else
	    println(x[r]-x[l-1])
	end
  end
end

main()