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 (7.3.0) (judge verdict: Accepted)

ii = lambda : int(input())
mi = lambda : map(int,input().split())
li = lambda : list(map(int,input().split()))

q = ii()
rmax = 0
qer = []
for i in range(q):
    l,r = mi()
    qer.append([l,r])
    if rmax < r:
        rmax = r

# rmaxまで計算
# 奇数かつ4n-1ではない
# 4n+1

# 素数表
import math
primeList = [2,3,5,7,11,13]
for i in range(17,rmax+1,2):
    for j in primeList:
        if j > math.sqrt(i):
            primeList.append(i)
            break
        if i % j == 0:
            break

# print(primeList)
        
def checksim(x,pl):
    if x in pl and (x+1)//2 in pl:
        return 1
    return 0

tans = [0] * (rmax+1)
tans[3] = 1
for i in range(5,rmax+1,4):
    if checksim(i, primeList):
        tans[i] = 1

# cumsum
ans = [0]*(rmax+1)
tcumsum = 0
for i in range(rmax+1):
    if tans[i] == 1:
        tcumsum += 1
    ans[i] = tcumsum

for i in qer:
    print(ans[i[1]] - ans[i[0]-1])