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)

def d_2017LikeNumber(Q, I):  # Q:クエリの数、I:探索区間の左端と右端
    def prime_list(M):
        # 0以上M以下の素数のリスト
        s = [True] * (M + 1)  # i番目の要素はiが素数ならTrue、非素数ならFalse
        s[0] = s[1] = False
        for x in range(2, int(M**0.5) + 1):
            if s[x]:
                for i in range(x + x, len(s), x):
                    # 素数xの倍数は素数ではない
                    s[i] = False
        return s

    def calc_like2017(M, p):
        # i番目の要素が、1以上i以下の"2017に似た数"の個数となるようなリスト
        # 0番目は0と定義する
        # M以下の素数のリストpを予め作っておく必要がある
        c = [0] * (M + 1)
        for i in range(3, M + 1, 2):  # 0,1,2は定義上2017に似た数にならない
            if p[i] and p[(i + 1) // 2]:
                c[i] += 1
        for i in range(3, M + 1):
            c[i] += c[i - 1]
        return c

    c = calc_like2017(10**5, prime_list(10**5))
    ans = ''
    for query in I:
        l, r = query[0], query[1]
        ans += '{}\n'.format(c[r] - c[l - 1])
    return ans[:-1]

Q = int(input())
I = [[int(i) for i in input().split()] for j in range(Q)]
print(d_2017LikeNumber(Q, I))