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: Time Limit Exceeded)

package main
import (
  "fmt"
  "math"
)
func isPrime(a int) bool {
  if a == 2 {
    return true
  }
  if a == 1 || a%2 == 0 {
    return false
  }
  rootA := int(math.Sqrt(float64(a)))
  for i := 3; i <= rootA; i += 2 {
    if a%i == 0 {
      return false
    }
  }
  return true
}

func main() {
  var q int
  fmt.Scan(&q)
  ls := make([]int, q)
  rs := make([]int, q)
  for i := 0; i < q; i++ {
    fmt.Scan(&ls[i], &rs[i])
  }
  primeMap := make(map[int]bool)
  for i := 0; i < q; i++ {
    r := rs[i]
    l := ls[i]
    result := 0
    for j := l; j <= r; j += 2 {
      if primeMap[j] {
        result++
        continue
      }
      if isPrime(j) && isPrime((j+1)/2) {
        result++
        primeMap[j] = true
      }
    }
    fmt.Println(result)
  }
}