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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
 
#define MOD 1000000007
#define INF  2000000000
//#define int ll
#define ll long long
#define ld long double
#define vi vector<int>
#define pa pair<int, int>
#define pb push_back
#define mp make_pair
 
#define INIT ios::sync_with_stdio(false);cin.tie(0);
#define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T& t) { cin >> t; }
template<typename First, typename...Rest>void MACRO_VAR_Scan(First& first, Rest&...rest) { cin >> first; MACRO_VAR_Scan(rest...); }
#define VEC(type, c, n) vector<type> c(n);for(auto& i:c)cin>>i;
#define MAT(type, c, m, n) vector<vector<type>> c(m, vector<type>(n));for(auto& r:c)for(auto& i:r)cin>>i;
 
#define BR cout << "\n";
#define SP cout << " ";
#define ENDL cout<<endl;
#define OUT(d) cout<<(d);
#define OUTL(d) cout<<(d)<<endl;
#define YES OUTL("YES")
#define Yes OUTL("Yes")
#define NO OUTL("NO")
#define No OUTL("No")
#define RET return 0;
#define SUM(a, n) accumulate(a, a+n, 0)
#define VSUM(v) accumulate(ALL(v), 0);
 
#define REP(i, n) for(int i=0;i<(n);i++)
#define RREP(i, n) for(int i=n-1;i>=0;--i)
#define FOR(i, m, n) for(int i = m;i < n; i++)
#define RFOR(i, a, b) for(int i=(a)-1;i>=(b);--i)
#define AREP(a, n) for(auto (a):(n))
#define ALL(a) (a).begin(),(a).end()
#define IN(n, a, b) ((a)<=(n)&&(n)<(b))

signed main(){ INIT;
    VAR(int, q);
    int rmax = 0, l[q], r[q];
    REP(i, q){
        cin >> l[i] >> r[i];
        rmax = max(rmax, r[i]);
    }
    int a[100001];
    REP(i, rmax) a[i] = 1;
    a[0] = a[1] = 0;
    int t = 2;
    while(t <= rmax){
        for(int x = t*2; x <= rmax; x += t) a[x] = 0;
        t++;
        while(!a[t])t++;
    }
    int b[10001];
    b[0] = 0;
    FOR(i, 1, rmax + 1){
        if(i == 2017) b[i] = b[i-1] + 1;
        else{
            b[i] = b[i-1] + (a[i] && a[(i+1)/2]);
        }
    }
    REP(i, q){
        OUTL(b[r[i]] - b[l[i]-1]);
    }
RET;}