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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import math
Q = int(input())

l = []
r = []
while True:
  try:
    lr=list(map(int,input().split()))
    l.append(lr[0])
    r.append(lr[1])
  except:
    break

def is_prime(num):
  if(type(num) != type(0)):
    print('error at '+str(num)+' type = '+str(type(num)))
    print(type(int))
    return 0
  if(num<2):
    return 0
  elif(num == 2):
    return 1
  n = math.ceil(math.sqrt(num))
  for i in range(2,n+1):
    if((num%i) == 0):
      return 0
  return 1

def create_list():
  MAXI = max(r)+1
  sn = [0]
  for i in range(1,MAXI+1,2):
    sn.append(is_prime(i) * is_prime(int((i+1)/2))) #odd
    sn.append(0) #even
  return sn

base = create_list()

for i in range(Q):
  if(l[i]==r[i]):
    print(base[l[i]])
  else:
    lnum = base[0:l[i]]
    rnum = base[0:r[i]]
    print( sum(rnum)-sum(lnum) )