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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

function Main(input) {
    input = input.trim().split("\n").map(function(x) { return x.split(" ")});    
    var Q = parseInt(input[0][0], 10);
    var arr_lr = [];
    var min = 1e+5;
    var max = 1;
    var line;
    for (var i = 0; i < Q; i++){
        line = input[i + 1].map(e => parseInt(e, 10));
        min = Math.min(min, line[0], line[1]);
        max = Math.max(max, line[0], line[1]);
        arr_lr.push(line);
    }
    var bin = Array.from({length: max}, () => 1);
    bin[0] = 0;
    for (var i = 2; i <= Math.sqrt(max); i++){
        for (var j = 2; j <= max / i; j++){
            bin[i * j - 1] = 0;
        }
    }
    var bin2 = Array.from({length: max}, () => 0);
    for (var i = 0; i < Math.floor((max + 1)/2); i++){
        if (bin[i] >= 1) bin2[i * 2] = 1;
    }
    var ruisekiwa = Array.from({length: max}, () => 0);
    for (var i = 1; i < ruisekiwa.length; i++){
        ruisekiwa[i] = ruisekiwa[i - 1] + bin[i] * bin2[i];
    }

    var v_ans = [];
    for (var x of arr_lr){
        if (x[0] === 1) v_ans.push(ruisekiwa[x[1] - 1]);
        else v_ans.push(ruisekiwa[x[1] - 1] - ruisekiwa[x[0] - 2]);
    }
    console.log(v_ans.join("\n"));
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));