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: Accepted)

class imosOneDimension:
    def __init__(self, size):
        self.table = [0 for i in range(size)]

    def setTable(self):
        for i in range(len(self.table)-1):
            if is_prime(i) and is_prime(int((i + 1) / 2)):
                self.table[i] = 1
                # self.table[i] += self.table[i - 1]

    def cumulativeSum(self):
        for i in range(1, len(self.table)):
            self.table[i] += self.table[i - 1]


def is_prime(n):
    if (n == 1):
        return False
    if (n == 2):
        return True
    if (n % 2 == 0):
        return False
    i = 3
    while (i ** 2 <= n):
        if (n % i == 0):
            return False
        i += 2
    return True

imos = imosOneDimension(size=10 ** 5 + 1)
imos.setTable()
tableOneHot = []
for i in range(len(imos.table)):
    if imos.table[i] == 1:
        tableOneHot.append(i)
#print(tableOneHot)
#print(imos.table)

imos.cumulativeSum()
#print(imos.table)
q = int(input())
for i in range(q):
    l, r = [int(i) for i in input().split()]
    print(imos.table[r] - imos.table[l - 1])