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



Sample input:
1
3 7


Sample output:
2

Submission status: Wrong Answer

Solution code:
def eratosthenes(N):
    prime=[]
    a=list(range(2,N+1))
    end=N**0.5
    while len(a) and a[0]<=end:
        nn=a.pop(0)
        prime.append(nn)
        a=[i for i in a if i%nn!=0]
    prime+=a
    return prime
def binsearch_lb(lst,lb):
    """lb以上の最小のインデックス
    """
    li=0
    ri=len(lst)-1
    if lst[li]>=lb:
        return 0
    if lst[ri]<lb:
        return -1
    while li+1<ri:
        tgt=(li+ri)//2
        if lst[tgt]<lb:
            li=tgt
        else:
            ri=tgt
    return ri
def binsearch_ub(lst,ub):
    """ub以下の最大のインデックス
    """
    li=0
    ri=len(lst)-1
    if lst[li]>ub:
        return -1
    if lst[ri]<=ub:
        return ri
    while li+1<ri:
        tgt=(li+ri)//2
        if lst[tgt]>ub:
            ri=tgt
        else:
            li=tgt
    return li
N=int(input().strip())
primes=sorted(eratosthenes(int(1e5)))
p_set=set(primes)
primes2=[]
for p in primes:#MlogM
    if (p+1)//2 in p_set:
        primes2.append(p)
for i in range(N):#N
    l,r=map(int,input().split())
    li=binsearch_lb(primes2,l)#l以上のインデックス logM
    ri=binsearch_ub(primes2,r)#r以下のインデックス
    print(ri-li+1)