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: Accepted)

from sys import stdin, setrecursionlimit
from itertools import accumulate

setrecursionlimit(10 ** 9)
INF = 1 << 60


def input():
    return stdin.readline().strip()


def prime_numbers(n):
    if n < 2:
        return []

    m = (n + 1) // 2
    p = [True] * m
    for i in range(1, int((n ** 0.5 - 1) / 2) + 1):
        if p[i]:
            for j in range(2 * i * (i + 1), m, 2 * i + 1):
                p[j] = False

    a = [2 * i + 1 for i in range(m) if p[i]]
    a[0] = 2
    return a


N = 10 ** 5
P = set(prime_numbers(N))
P = [n for n in P if (n + 1) // 2 in P]
a = [0] * (N + 1)
for n in P:
    a[n] = 1
a = list(accumulate(a))

Q = int(input())
for _ in range(Q):
    l, r = map(int, input().split())
    print(a[r] - a[l - 1])