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 sieve_of_erastosthenes(num):
    input_list = [0 if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else 1 for i in range(num)]
    input_list[0] = input_list[1] = 0
    input_list[2] = input_list[3] = input_list[5] = 1
    sqrt = math.sqrt(num)
    for serial in range(3, num, 2):
        if serial >= sqrt:
            return input_list
        for s in range(serial ** 2, num, serial): 
            input_list[s] = 0

q = int(input())
l_list = []
r_list = []
for i in range(q):
    l, r = map(int, input().split())
    l_list.append(l)
    r_list.append(r)
minval = min(l_list)
maxval = max(r_list)
sieve = sieve_of_erastosthenes(maxval+1)
def is_prime(x):
    # print(x)
    return sieve[x]
def is_like2017(x):
    return is_prime(x) * is_prime(int((x+1)/2))
like2017 = list(range(maxval+1))
for i in like2017:
    like2017[i] = is_like2017(i)
for l, r in zip(l_list, r_list):
    print(sum(like2017[l:r+1]))