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"
)

type pair struct {
	l, r int
}

func main() {
	q := getInt()
	ps := make([]pair, q)
	for i := range ps {
		ps[i].l = getInt() - 1
		ps[i].r = getInt()
	}

	ln := 100000
	primes := furui(ln)
	like2017s := make(map[int]bool)
	for i, p := range primes {
		f := (p + 1) / 2
		match := false
		for j := 0; j < i; j++ {
			if f == primes[j] {
				match = true
			}
		}

		if match {
			like2017s[p] = true
		}
	}

	s := make([]int, ln+1)
	for i := 1; i < len(s); i++ {
		s[i] = s[i-1]
		if _, ok := like2017s[i]; ok {
			s[i]++
		}
	}

	for _, p := range ps {
		res := s[p.r] - s[p.l]
		fmt.Println(res)
	}
}

func furui(n int) []int {
	ns := make([]int, n-1)
	for i := range ns {
		ns[i] = i + 2
	}

	for i := 0; ; i++ {
		p := ns[i]
		if p*p > n {
			break
		}
		for j := i + 1; j < len(ns); j++ {
			if ns[j]%p == 0 {
				ns = remove(ns, j)
				j--
			}
		}
	}

	return ns
}

func remove(s []int, i int) []int {
	return append(s[:i], s[i+1:]...)
}

// -----------------------------------------

var sc = bufio.NewScanner(os.Stdin)

func init() {
	// buf := 200001
	// sc.Buffer(make([]byte, buf), buf)
	sc.Split(bufio.ScanWords)
}

func getInt() int {
	i, err := strconv.Atoi(getString())
	if err != nil {
		panic(err)
	}
	return i
}

func getString() string {
	sc.Scan()
	s := sc.Text()
	return s
}