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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
  n,i,j,x,y:longint;
  a:array[0..100000]of boolean;
  b:array[0..100000]of longint;
begin
  readln(n);
  a[1]:=true;
  for i:=2 to trunc(sqrt(100000)) do
    if a[i]=false then
      for j:=2 to 100000 div i do
        a[i*j]:=true;
  b[1]:=0;
  for i:=2 to 100000 do
    if (a[i]=false)and(a[(i+1) div 2]=false) then b[i]:=b[i-1]+1
                                             else b[i]:=b[i-1];
  for i:=1 to n do
  begin
    readln(x,y);
    writeln(b[y]-b[x-1]);
  end;
end.