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 v5.12) (judge verdict: Wrong Answer)

"use strict";
    
const main = arg => {
    arg = arg.trim().split("\n");
    const Q  = parseInt(arg[0]);
    const lr = arg.slice(1, Q + 1);
    
    let primeMap = [];
    
    // 100000までの素数表を作る
    for(let i=1; i<=100000; i++) {
        if(i === 1) {
            primeMap[i] = false;
            continue;
        }
        
        let flag = true;
        
        for(let j=2; j<i; j++) {
            if(i % j === 0) {
                flag = false;
                break;
            }
            
            if(j > Math.sqrt(i)) {
                break;
            }
        }
        
        if(flag) primeMap[i] = true;
    }
    
    let totalSum = [...Array(100000)].fill(0);
    
    // 奇数のうち2017-likeかどうかを判定する
    for(let i=1; i<=100000; i += 2) {
        // NもN+1も素数かどうか
        if(primeMap[i] && primeMap[((parseInt(i) + 1) / 2)]) {
            totalSum[i]++;
        }
    }

    // 累積和に上書きする
    for(let i=1; i<=100; i++) {
        totalSum[i] += totalSum[i - 1];
    }
    
    let answer = [];
    
    // 累積和からlrの範囲をとる
    for(let i in lr) {
        let l = parseInt(lr[i].split(" ")[0]);
        let r = parseInt(lr[i].split(" ")[1]);
        
        answer.push(totalSum[r] - totalSum[l - 1]);
    }
    
    console.log(answer.join("\n"));
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));