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 Lua (5.3.2) (judge verdict: Wrong Answer)

Q=io.read("n")
l={}
r={}
for i=1,Q do
  l[i]=io.read("n")
  r[i]=io.read("n")
end
function prime(o)
  local res=true
  if o==1 or o==2 then
    return res
  elseif o>2 then
    for i=2,o-1 do
      if o%i==0 then
        res=false
      end
    end
    return res
  end
end
for i=1,Q do
  local count=0
  for j=l[i],r[i] do
    if prime(j) and prime((j+1)//2) then
      count=count+1
    end
  end
  print(count)
end