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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#ifdef HIRO
#define d(f_, ...) printf((f_), ##__VA_ARGS__)
#else
#define d(f_, ...)
#endif

using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<long long, long long> pllll;
typedef vector<int> vi;
typedef vector<long long> vll;
typedef vector< pair<int, int> > vii;
typedef vector< pair<long long, long long> > vllll;
typedef map<int, int> mii;
typedef map<long long, long long> mllll;
typedef queue<int> qi;
typedef queue< pair<int, int> > qp;
#define mp make_pair
#define pi 3.14159265358979323846
#define MAX max_element
#define MIN min_element
#define all(v) v.begin(), v.end()
#define gt(T) greater<T>()
#define sum(v) accumulate(v.begin(), v.end(), 0ll)
#define uni(v) do{ \
  sort(v.begin(), v.end()); \
  decltype(v)::iterator result = unique(v.begin(), v.end()); \
  v.erase(result, v.end()); \
}while(0)
#define fi(init, n) for(int i = init; i < n; ++i)
#define fj(init, n) for(int j = init; j < n; ++j)
#define fk(init, n) for(int k = init; k < n; ++k)
#define zero(x) memset(x, 0, sizeof(x))
#define negative(x) memset(x, ~0, sizeof(x))
#define bitsum(x) __builtin_popcount(x)
const ll MOD = 1e9 + 7;
const int INF = 1e9;
const int di[] = { 0, 1, 0, -1 };
const int dj[] = { 1, 0, -1, 0 };

template<typename T>
T gcd(T a, T b) {
	return b ? gcd(b, a % b) : a;
}
template<typename T>
T lcm(T a, T b) {
	return a / gcd(a, b) * b;
}
template<typename T>
int finder(vector<T> vec, T number) {
	auto itr = find(vec.begin(), vec.end(), number);
	size_t index = distance(vec.begin(), itr);
	if (index != vec.size()) return 1;
	else return 0;
}
ll frac(ll n){
	if (n == 0) return 1;
	return (n * frac(n - 1)) % MOD;
}
template<class T> inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template<class T> inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
int prime[100010];
int res[100010];
int main(int argc, char** argv) {
#ifdef HIRO
  string quiz(argv[1]);
  string id(argv[2]);
  string filename("input/" + quiz + "/" + id + ".txt");
  ifstream fin(filename);
  if (fin.peek() == ifstream::traits_type::eof()) {
    cout << "No input.";
    return 0;
  }
  ifstream cin(filename);
  std::cin.rdbuf(cin.rdbuf());
#endif
  ll ans = 0;
  ll q;
  cin >> q;
  // ll n, m;
  // cin >> n >> m;
  // ll n, m, k;
  // cin >> n >> m >> k;
  negative(prime);
  prime[1] = 0;
  prime[2] = 1;
  fi(3, 100001) {
    if(i % 2 == 0) {
      prime[i] = 0;
      continue;
    }
    prime[i] = 1;
    for(int j = 3; j <= sqrt(i); j += 2)
      if(i % j == 0) {
        prime[i] = 0;
        break;
      }
    // printf("%d: %d\n", i, prime[i]);
  }
  fi(1, 100001) {
    res[i] = res[i - 1];
    if(i % 2 == 0) continue;
    if(prime[i] && prime[(i + 1) / 2])
      res[i]++;
  }
  int l, r;
  fk(0, q) {
    cin >> l >> r;
    // printf("%d: %d, %d: %d\n", r, res[r], l - 1, res[l - 1]);
    cout << res[r] - res[l - 1] << endl;
  }
  // cout << ans << endl;
  return 0;
}