#include <bits/stdc++.h>
#define GET_MACRO(_1,_2,_3,_4,_5,_6,_7,_8,NAME,...) NAME
#define pr(...) cerr<< GET_MACRO(__VA_ARGS__,pr8,pr7,pr6,pr5,pr4,pr3,pr2,pr1)(__VA_ARGS__) <<endl
#define pr1(a) (#a)<<"="<<(a)<<" "
#define pr2(a,b) pr1(a)<<pr1(b)
#define pr3(a,b,c) pr1(a)<<pr2(b,c)
#define pr4(a,b,c,d) pr1(a)<<pr3(b,c,d)
#define pr5(a,b,c,d,e) pr1(a)<<pr4(b,c,d,e)
#define pr6(a,b,c,d,e,f) pr1(a)<<pr5(b,c,d,e,f)
#define pr7(a,b,c,d,e,f,g) pr1(a)<<pr6(b,c,d,e,f,g)
#define pr8(a,b,c,d,e,f,g,h) pr1(a)<<pr7(b,c,d,e,f,g,h)
#define prArr(a) {cerr<<(#a)<<"={";int i=0;for(auto t:(a))cerr<<(i++?", ":"")<<t;cerr<<"}"<<endl;}
using namespace std;
using Int = long long;
using _int = int;
using ll = long long;
using Double = long double;
const Int INF = (1LL<<60)+1e9; // ~ 1.15 * 1e18
const Int mod = (1e9)+7;
const Double EPS = 1e-8;
const Double PI = 6.0 * asin((Double)0.5);
using P = pair<Int,Int>;
template<class T> T Max(T &a,T b){return a=max(a,b);}
template<class T> T Min(T &a,T b){return a=min(a,b);}
template<class T1, class T2> ostream& operator<<(ostream& o,pair<T1,T2> p){return o<<"("<<p.first<<","<<p.second<<")";}
template<class T1, class T2, class T3> ostream& operator<<(ostream& o,tuple<T1,T2,T3> t){
  return o<<"("<<get<0>(t)<<","<<get<1>(t)<<","<<get<2>(t)<<")";}
template<class T1, class T2> istream& operator>>(istream& i,pair<T1,T2> &p){return i>>p.first>>p.second;}
template<class T> ostream& operator<<(ostream& o,vector<T> a){Int i=0;for(T t:a)o<<(i++?" ":"")<<t;return o;}
template<class T> istream& operator>>(istream& i,vector<T> &a){for(T &t:a)i>>t;return i;}


vector<Int>getPrime(Int n){
  vector<bool>used(n+1,0);
  
  for(ll i=2;i*i<=n;i++)
    if(!used[i])for(Int j=2;j<=n/i;j++)used[i*j]=1;
  
  vector<Int> res;
  for(Int i=2;i<=n;i++)if(!used[i])res.push_back(i);

  return res;
}

bool isPrime(ll n){
  if(n < 2) return 0;
  for(ll i=2;i*i<=n;i++)if(n%i==0) return 0;
  return 1;
}

signed main(){
  srand((unsigned)time(NULL));
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(12);
  
  Int l, r;
  cin>>l>>r;

  vector<Int> prime = getPrime(1e5);

  vector<Int> cnt(r - l + 1);
  vector<Int> val(r - l + 1);
  for(int i=0;i<=r-l;i++) val[i] = l + i;
  
  for(Int p:prime){
    Int num = ((l-1)/p) * p + p;
    while(num <= r){
      Int score = 0, tmp = num, pp = 1;
      while(tmp%p == 0) tmp/=p, score++, pp *= p;
      cnt[num - l] += score;
      val[num - l] /= pp;

      num += p;
    }
  }
  Int ans = 0;
  for(Int i=0;i<=r - l;i++) ans += isPrime(cnt[i] + (val[i] != 1));
  cout<<ans<<endl;
  return 0;
}


### Prompt

Please formulate a CPP solution to the following problem:

A positive integer is called a "prime-factor prime" when the number of its prime factors is prime. For example, $12$ is a prime-factor prime because the number of prime factors of $12 = 2 \times 2 \times 3$ is $3$, which is prime. On the other hand, $210$ is not a prime-factor prime because the number of prime factors of $210 = 2 \times 3 \times 5 \times 7$ is $4$, which is a composite number.

In this problem, you are given an integer interval $[l, r]$. Your task is to write a program which counts the number of prime-factor prime numbers in the interval, i.e. the number of prime-factor prime numbers between $l$ and $r$, inclusive.



Input

The input consists of a single test case formatted as follows.


$l$ $r$


A line contains two integers $l$ and $r$ ($1 \leq l \leq r \leq 10^9$), which presents an integer interval $[l, r]$. You can assume that $0 \leq r-l < 1,000,000$.

Output

Print the number of prime-factor prime numbers in $[l,r]$.

Examples

Input

1 9


Output

4


Input

10 20


Output

6


Input

575 57577


Output

36172


Input

180 180


Output

1


Input

9900001 10000000


Output

60997


Input

999000001 1000000000


Output

592955

### Response

```cpp
#include <bits/stdc++.h>
#define GET_MACRO(_1,_2,_3,_4,_5,_6,_7,_8,NAME,...) NAME
#define pr(...) cerr<< GET_MACRO(__VA_ARGS__,pr8,pr7,pr6,pr5,pr4,pr3,pr2,pr1)(__VA_ARGS__) <<endl
#define pr1(a) (#a)<<"="<<(a)<<" "
#define pr2(a,b) pr1(a)<<pr1(b)
#define pr3(a,b,c) pr1(a)<<pr2(b,c)
#define pr4(a,b,c,d) pr1(a)<<pr3(b,c,d)
#define pr5(a,b,c,d,e) pr1(a)<<pr4(b,c,d,e)
#define pr6(a,b,c,d,e,f) pr1(a)<<pr5(b,c,d,e,f)
#define pr7(a,b,c,d,e,f,g) pr1(a)<<pr6(b,c,d,e,f,g)
#define pr8(a,b,c,d,e,f,g,h) pr1(a)<<pr7(b,c,d,e,f,g,h)
#define prArr(a) {cerr<<(#a)<<"={";int i=0;for(auto t:(a))cerr<<(i++?", ":"")<<t;cerr<<"}"<<endl;}
using namespace std;
using Int = long long;
using _int = int;
using ll = long long;
using Double = long double;
const Int INF = (1LL<<60)+1e9; // ~ 1.15 * 1e18
const Int mod = (1e9)+7;
const Double EPS = 1e-8;
const Double PI = 6.0 * asin((Double)0.5);
using P = pair<Int,Int>;
template<class T> T Max(T &a,T b){return a=max(a,b);}
template<class T> T Min(T &a,T b){return a=min(a,b);}
template<class T1, class T2> ostream& operator<<(ostream& o,pair<T1,T2> p){return o<<"("<<p.first<<","<<p.second<<")";}
template<class T1, class T2, class T3> ostream& operator<<(ostream& o,tuple<T1,T2,T3> t){
  return o<<"("<<get<0>(t)<<","<<get<1>(t)<<","<<get<2>(t)<<")";}
template<class T1, class T2> istream& operator>>(istream& i,pair<T1,T2> &p){return i>>p.first>>p.second;}
template<class T> ostream& operator<<(ostream& o,vector<T> a){Int i=0;for(T t:a)o<<(i++?" ":"")<<t;return o;}
template<class T> istream& operator>>(istream& i,vector<T> &a){for(T &t:a)i>>t;return i;}


vector<Int>getPrime(Int n){
  vector<bool>used(n+1,0);
  
  for(ll i=2;i*i<=n;i++)
    if(!used[i])for(Int j=2;j<=n/i;j++)used[i*j]=1;
  
  vector<Int> res;
  for(Int i=2;i<=n;i++)if(!used[i])res.push_back(i);

  return res;
}

bool isPrime(ll n){
  if(n < 2) return 0;
  for(ll i=2;i*i<=n;i++)if(n%i==0) return 0;
  return 1;
}

signed main(){
  srand((unsigned)time(NULL));
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(12);
  
  Int l, r;
  cin>>l>>r;

  vector<Int> prime = getPrime(1e5);

  vector<Int> cnt(r - l + 1);
  vector<Int> val(r - l + 1);
  for(int i=0;i<=r-l;i++) val[i] = l + i;
  
  for(Int p:prime){
    Int num = ((l-1)/p) * p + p;
    while(num <= r){
      Int score = 0, tmp = num, pp = 1;
      while(tmp%p == 0) tmp/=p, score++, pp *= p;
      cnt[num - l] += score;
      val[num - l] /= pp;

      num += p;
    }
  }
  Int ans = 0;
  for(Int i=0;i<=r - l;i++) ans += isPrime(cnt[i] + (val[i] != 1));
  cout<<ans<<endl;
  return 0;
}


```