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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc *bufio.Scanner

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

const LIM = 100000

func eratosthenes(prime []bool, n int) {
	for i := 2; i <= n; i++ {
		if !prime[i] {
			continue
		}
		for j := i * i; j <= n; j += i {
			prime[j] = false
		}
	}
}

func main() {
	sc = bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)

	prime := make([]bool, LIM+1)
	for i := 2; i <= LIM; i++ {
		prime[i] = true
	}
	eratosthenes(prime, LIM)

	acc := make([]int, LIM+1)
	for i := 3; i < LIM; i += 2 {
		switch {
		case prime[i] && prime[(i+1)/2]:
			acc[i] = acc[i-2] + 1
		default:
			acc[i] = acc[i-2]
		}
	}

	q := nextInt()
	for i := 0; i < q; i++ {
		l, r := nextInt(), nextInt()
		switch {
		case l == 1:
			fmt.Println(acc[r])
		default:
			fmt.Println(acc[r] - acc[l-2])
		}
	}
}