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: Wrong Answer)

q=int(input())
x=[list(map(int, input().split())) for i in range(q)]
s=[0 for i in range(672)]
#素数のリスト
n = 10**5
primes = set(range(2, n+1))
for i in range(2, int(n**0.5+1)):
    primes.difference_update(range(i*2, n+1, i))
primes=list(primes)

primes.sort()
for i in range(len(primes)):
    if primes[i]>5*10**4:
        break
    primes.append(2*primes[i])

primes.sort()
count=0
for i in range(len(primes)-1):
    if primes[i+1]-primes[i]==1 and primes[i+1]%2==0:
        count+=1
        s[count-1]=[primes[i],count]
a=0
b=0

for i in range(q):
    for j in range(len(s)):
        if s[j][0]>=x[i][0]:
            a=s[j][1]
            break
    for j in range(len(s)):
        if s[j][0]>x[i][1]:
            b=s[j][1]-1
            break
    if a==0:
        a=672
    if b==0:
        b=672
    print(b-a+1)
    a=b=0