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 (3.8.2) (judge verdict: Accepted)

q = int(input())

# エラストネスの篩
n = 10**5+1
flag = [True]*n
flag[1] = False
for i in range(4, n, 2): flag[i] = False
for i in range(3, int(n**0.5)+1, 2):
  if flag[i]:
    for j in range(i+i, n, i): flag[j] = False

# 2017に似た数の累積和
nums = [0]*n
for i in range(1,n):
  if i%2 == 1:
    if flag[i] and flag[(i+1)//2]: nums[i] = nums[i-1]+1
    else: nums[i] = nums[i-1]
  else: nums[i] = nums[i-1]

for _ in range(q):
  l,r = map(int, input().split())
  print(nums[r]-nums[l-1])