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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define MAX 100000
int main(){
  int prime_num[MAX] = {};
  int S[MAX] = {};
  int a[MAX] = {};
  int ans[MAX] = {};
  int l, r, i, j;
  int Q; scanf("%d", &Q);

  // hurui
  prime_num[0] = 1;
  prime_num[1] = 1;
  for(i = 2; i < MAX; i++){
    if(prime_num[i] == 1) continue;
    else{
      for(j = i * 2; j < MAX / j; j += i){
	prime_num[j] = 1;
      }
    }
  }

  // like 2017
  for(i = 0; i < MAX; i++){
    if(prime_num[i] == 1) continue;
    else{
      if(prime_num[i] == 0 && prime_num[(i + 1)/ 2] == 0) a[i] = 1;
    }
  }

  // ruiseki wa
  S[0] = 0;
  /* for(i = 0; i < MAX; i++){ */
  /*   for(j = 0; j < i; j++){ */
  /*     if(i != 0) S[i] += a[j]; */
  /*   } */
  /* } */
  for(i = 0; i < MAX; i++) S[i + 1] = S[i] + a[i];
    
  for(i = 0; i < Q; i++){
    scanf("%d", &l);
    scanf("%d", &r);
    r++;
    ans[i] = S[r] - S[l];
  }
  for(i = 0; i < Q; i++){
    printf("%d\n", ans[i]);
  }
  return 0;
}