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)

# import re
# from scipy.sparse.csgraph import connected_components  # Pythonのみ！
# ↑cf.  https://note.nkmk.me/python-scipy-connected-components/
# from scipy.sparse import csr_matrix
# import string
import sys
sys.setrecursionlimit(10 ** 5 + 10)
def input(): return sys.stdin.readline().strip()

def resolve():

    # n以下の素数のリストprimes
    n = 10**5
    primes = set(range(2, n + 1))

    # 合成数 x は p<=x**0.5を満たす素因子 p をもつという性質を利用
    for i in range(2, int(n ** 0.5 + 1)):
        primes.difference_update(range(i * 2, n + 1, i))
    primes = list(primes)

    L=[0]*10**5
    for i in primes:
        if (i+1)//2 in primes:
            L[i]=1

    from itertools import accumulate


    B = [0] + L
    B = list(accumulate(B))  # 累積和を格納したリスト作成

    # この問題は長さが1-Nの連続部分の和の最大値を出せというものなので以下の通り

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


resolve()