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 Python (3.8.2) (judge verdict: Accepted)

q=int(input())
lr=[list(map(int,input().split())) for _ in range(q)]
mr=0
for l,r in lr:
  mr=max(mr,r)
l=[1 for _ in range(mr+1)]
l[0],l[1]=0,0
s=[0 for _ in range(mr+1)]
for i in range(2,int(mr**(1/2))+1):
  x=i*2
  while x<=mr:
    l[x]=0
    x+=i
for i in range(2,mr+1):
  if l[i]==1 and l[(i+1)//2]==1:
    s[i]=s[i-1]+1
  else:
    s[i]=s[i-1]
for l,r in lr:
  print(s[r]-s[l-1])