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 (3.4.3) (judge verdict: Time Limit Exceeded)

import math

# def primes(x):
#     if x < 2: return []

#     primes = [i for i in range(x)]
#     primes[1] = 0 # 1は素数ではない
#     x_sqrt = math.sqrt(x) # 記憶させていちいち計算しない

#     # エラトステネスのふるい
#     for prime in primes:
#         if prime == 0:
#             continue # 先に処理
#         if prime > x_sqrt: 
#             break
#         for non_prime in range(2 * prime, x, prime):
#             primes[non_prime] = 0

#     return [prime for prime in primes if prime != 0]
def primes_sieve2(limit):
    a = [True] * limit                          # Initialize the primality list
    a[0] = a[1] = False

    for (i, isprime) in enumerate(a):
        if isprime:
            yield i
            for n in range(i*i, limit, i):     # Mark factors non-prime
                a[n] = False
                
q = int(input())
l_list = []
r_list = []
for _ in range(q):
    l, r = list(map(int,input().split()))
    l_list.append(l)
    r_list.append(r)
    
maxr = max(r_list)
p_list = list(primes_sieve2(maxr+1))

sim_list = []
for p in p_list:
    if (p+1)/2 in p_list:
        sim_list.append(p)
        
cumulation = [0 for _ in range(maxr+1)]
for s in sim_list:
    cumulation[s] = 1

for i in range(1,len(cumulation)):
    cumulation[i] += cumulation[i-1]

for i in range(q):
    print(cumulation[r_list[i]]-cumulation[l_list[i]-1])