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: Wrong Answer)

def is_prime_trial_division(n):
    if n < 2:
        return False
    else:
        for i in range(2, n):
            if i * i > n:
                break
            elif n % i == 0:
                return False
        return True
 

q = int(input())

plist = set()
for i in range(1,100000,2):
    if is_prime_trial_division(i):
        if  int((i+1)/2) in plist or is_prime_trial_division(int((i+1)/2)):
            plist.add(i)

#print(plist)

pcnt=[]
cnt=1
for i in range(100000):
    if i in plist:
        print("cnt", i)
        cnt+=1
    pcnt.append(cnt)

for i in range(q):
    tl, tr = map(int,input().split(' '))
#    cnt=0
#    subs = set()
#    for j in range(tl,tr+1,2):
#        subs.add(j)
#    cnt = len(plist.intersection(subs))
#    print(cnt)
#        if j in plist:
#            cnt +=1
    ans=pcnt[tr-1]-pcnt[tl-1]
#    print(tr, pcnt[tr])
#    print(tl, pcnt[tl])
    print(ans)