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 (1.14.1) (judge verdict: Accepted)

package main

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

const (
	maxBufSize = 1024 * 1024
)

var (
	sc = func() *bufio.Scanner {
		sc := bufio.NewScanner(os.Stdin)
		buf := make([]byte, 1)
		sc.Buffer(buf, maxBufSize)
		sc.Split(bufio.ScanWords)
		return sc
	}()
	out = bufio.NewWriter(os.Stdout)
)

func prime(maximum int) [] bool {
	sieve := make([]bool, maximum)
	for i := range sieve {
		sieve[i] = true
	}

	sieved := func(prime int) {
		for i := prime + prime; i < maximum; i += prime {
			sieve[i] = false
		}
	}

	sieve[0] = false; sieve[1] = false
	sieved(2)
	end := int(math.Pow(float64(maximum), 0.5) + 1)
	for i := 3; i < end; i += 2 {
		if sieve[i] {
			sieved(i)
		}
	}
	return sieve
}

func solve(q int64, ls []int64, rs []int64) []int64 {
	ps := prime(100001)
	lls := make([]int64,  100001)
	c := int64(0)
	for i, _ := range lls {
		if (i % 2) != 0 && ps[i] && ps[(i + 1) / 2] {
			c ++
		}
		lls[i] = c
	}
	res := make([]int64, q)
	for i, _ := range res {
		res[i] = lls[rs[i]] - lls[ls[i] -1]
	}
	return res
}

func main() {
	defer out.Flush()

	q := nextInt()
	ls := make([]int64, q)
	rs := make([]int64, q)
	for i, _ := range ls {
		ls[i] = nextInt()
		rs[i] = nextInt()
	}
	res := solve(q, ls, rs)
	for _, r := range res {
		fmt.Fprintln(out, r)
	}
}

func next() string {
	sc.Scan()
	return sc.Text()
}

func nextStringAsBytes() []byte {
	sc.Scan()
	return []byte(sc.Text())
}

func nextInt() int64 {
	a, _ := strconv.ParseInt(next(), 10, 64)
	return a
}

func nextFloat() float64 {
	a, _ := strconv.ParseFloat(next(), 64)
	return a
}

func nextInts(n int64) []int64 {
	ret := make([]int64, n)
	for i := int64(0); i < n; i++ {
		ret[i] = nextInt()
	}
	return ret
}

func nextFloats(n int64) []float64 {
	ret := make([]float64, n)
	for i := int64(0); i < n; i++ {
		ret[i] = nextFloat()
	}
	return ret
}
func nextStrings(n int64) []string {
	ret := make([]string, n)
	for i := int64(0); i < n; i++ {
		ret[i] = next()
	}
	return ret
}

func containStr(arr []string, target string) bool {
	for _, v := range arr {
		if v == target {
			return true
		}
	}
	return false
}

func PrintOut(src interface{}, joinner string) {
	switch reflect.TypeOf(src).Kind() {
	case reflect.Slice:
		s := reflect.ValueOf(src)
		for idx := 0; idx < s.Len(); idx++ {
			fmt.Fprintf(out, "%v", s.Index(idx))
			if idx < s.Len()-1 {
				fmt.Fprintf(out, "%s", joinner)
			} else {
				fmt.Fprintln(out)
			}
		}
	default:
		fmt.Fprintln(out, "orz")
	}
}

// mapからkeysとvaluesを返す
func splitKeyValue(m map[interface{}]interface{}) (keys, values []interface{}) {
	switch reflect.TypeOf(m).Kind() {
	case reflect.Map:
		s := reflect.ValueOf(m)
		for _, v := range s.MapKeys() {
			keys = append(keys, v)
			values = append(values, s.MapIndex(v))
		}
	default:
		fmt.Fprintln(out, "orz")
	}
	return
}