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)

# /usr/bin/python
# -*- coding: utf-8 -*-
#
import math


N_MAX = 10**5

## fact[i] := iが素数なら1,でなければ0
fact = [1] * (N_MAX+1)
for i in range(2,N_MAX+1):
  if fact[i] == 0:
    continue
  
  for j in range(i*2, N_MAX+1, i):
    fact[j] = 0

## csum[i] := 3からiまでの素数の総数
## fact[i] と fact[(i+1)//2] の両方が素数なら1足す
csum = [0] * (N_MAX+1)
for i in range(3, N_MAX+1):
  if i%2 == 0:
    csum[i] = csum[i-1]
  else:
    csum[i] = csum[i-1] + (fact[i] & fact[(i+1)//2])

q = int(input())
ans = [0] * q
for i in range(q):
  l,r = map(int, input().split())
  ans[i] = csum[r] - csum[l-1]

for a in ans:
  print(a)