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 (Lua 5.3.5) (judge verdict: Accepted)

local t={}
t[0],t[1],t[2]=0,0,0
for i=3,10^5,2 do
    local check=true
    for j=2,math.sqrt(i) do
        if i%j==0 then
            check=false
            break
        end
    end
    if check then
        for j=2,math.sqrt((i+1)//2) do
            if ((i+1)//2)%j==0 then
                check=false
                break
            end
        end
    end
    t[i]=t[i-1]+(check and 1 or 0)
    t[i+1]=t[i]
end

local q=io.read("n")
for i=1,q do
    local l,r=io.read("n","n")
    print(t[r]-t[l-1])
end