Problem:
B: 自身の 2 倍
問題
クエリが
Q
個与えられます。1 個のクエリにつき、 1 つの正の整数
N
が与えられるので、次の 2 つの条件を満たす正の整数
M
の個数を求めてください。
2 \leq M \leq N
を満たす
M
の約数のうち、
M
を除いたものの総積が
M
の
2
倍以上になる
入力形式
入力は以下の形式で与えられます。
Q
N_1
N_2
:
N_Q
1
行目では、クエリ数
Q
が与えられます。
2
行目から
N+1
行目では、各クエリについて与えられる 1 つの正の整数
N
が与えられます。
制約
1 \leq Q \leq 10^5
2 \leq N_i \leq 10^5
(1 \leq i \leq Q)
出力形式
上記の 2 つの条件を満たす正の整数の個数を、各
N_i
に対して、改行区切りで出力してください。
入力例
3
43
9
24
出力例
11
0
5
N=24
の時、
M
として考えられるのは
12
,
16
,
18
,
20
,
24
の
5
種類である。

Submitted solutions:

code_snippet: #include <bits/stdc++.h>


using namespace std;
//make -f ../makefile SRC=
/*
TODO
solve inverse problem:
if v == p^1 or p^2 or p^3
or v == p1*p2

*/


//------------------------------------------------------------------------------
bool DEBUG = false;
const int INF = 1000000000;

const int MAX_V = 100000;
static bool prime[MAX_V+1];
static int SPF[MAX_V+1];

static bool S[MAX_V+1];
static int P[MAX_V+1];
//------------------------------------------------------------------------------
void sieve()
{
    prime[0] = false;
    prime[1] = false;

    for (int i=2; i<=MAX_V; i++) prime[i] = true;

    for (int i=2; i*i<=MAX_V; i++)
    {
        if (prime[i])
        {
            for (int j=2*i; j<=MAX_V; j+=i) prime[j] = false;
        }
    }

    SPF[1] = 1;
    for (int i=2; i<=MAX_V; i++) SPF[i] = i;

    for (int i=4; i<=MAX_V; i+=2) SPF[i] = 2;

    for (int i=3; i*i<=MAX_V; i++)
    {
        if (SPF[i] != i) continue;
        for (int j=i*i; j<=MAX_V; j+=i)
            if (SPF[j] == j)
                SPF[j] = i;
    }

}

void setup()
{
    for (int i=0; i<=MAX_V; i++) S[i] = true;
    S[0] = false;
    S[1] = false;

    for (int i=2; i<=MAX_V; i++)
        if (prime[i])
            S[i] = false;

    for (int i=2; i<=316; i++)
        if (prime[i])
            S[i*i] = false;

    for (int i=2; i<=46; i++)
        if (prime[i])
            S[i*i*i] = false;

    for (int i=2; i<=MAX_V; i++)
        if (S[i] && prime[ i/SPF[i] ])
            S[i] = false;
    P[0] = 0;
    P[1] = 0;
    for (int i=2; i<=MAX_V; i++)
    {
        if (S[i]) P[i] = 1 + P[i-1];
        else P[i] = P[i-1];
    }
}

//------------------------------------------------------------------------------
int main()
{
    //test(); return 0;
    //DEBUG = true;
    sieve();
    setup();
    //return 0;
    //--------------------------------------------------------------------------
    int N, v, num;
    num = scanf("%d ", &N);
    for (int i=0; i<N; ++i)
    {
        num = scanf("%d ", &v);
        printf("%d\n", P[v]);
    }
    //--------------------------------------------------------------------------
    return 0;
}
//------------------------------------------------------------------------------
accuracy: 1
time_ms: 10
memory_kb: 4580
final_rank: 3

code_snippet: #include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
using namespace std;
using std::cout;
using std::cin;
using std::endl;
using ll=long long;
using ld=long double;
ll ILL=9167167167167167167;
const int INF=100000000;

#define rep(i,a) for (int i=0;i<a;i++)
#define all(p) p.begin(),p.end()
template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
template<class T> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> ll UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;}
template<class T> bool chmax(T &a,const T &b){if(a<b){a=b;return 1;}else return 0;}
template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
void yneos(bool a){if(a) cout<<"Yes\n"; else cout<<"No\n";}
template<class T> void vec_out(vector<T> &p){for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}




void solve();
// oddloop
int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	
	int t=1;
	//cin>>t;
	rep(i,t) solve();
}

void solve(){
	int Q;
	cin>>Q;
	int L=1e5+10;
	vector<vector<int>> table(L);
	vector<int> p(L);
	for(int i=2;i<L;i++){
		for(int j=i*2;j<L;j+=i) table[j].push_back(i);
		int tmp=i*2-1;
		for(auto x:table[i]) tmp/=x;
		if(tmp==0) p[i]++;
		p[i]+=p[i-1];
	}
	rep(i,Q){
		int a;
		cin>>a;
		cout<<p[a]<<"\n";
	}
}
accuracy: 1
time_ms: 30
memory_kb: 13272
final_rank: 8

code_snippet: #include<bits/stdc++.h>
using ll = long long;
#define var auto
const char newl = '\n';

using namespace std;

template<typename T1, typename T2> inline void chmin(T1& a, T2 b) { if (a > b) a = b; }
template<typename T1, typename T2> inline void chmax(T1& a, T2 b) { if (a < b) a = b; }

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  vector<int> accum(1e5 + 1);
  for (ll i = 2; i < accum.size(); i++) {
    accum[i] = accum[i - 1];
    ll prod = 1;
    for (int j = 1; j * j <= i; j++) {
      if (i * i * 2 <= prod) continue;
      if (i % j != 0) continue;

      prod *= j;
      var k = i / j;
      if (j < k) prod *= k;

    }
    prod /= i;
    if (i * 2 <= prod) accum[i]++;
  }
  int q;
  cin >> q;
  for (int i = 0; i < q; i++) {
    int n;
    cin >> n;
    cout << accum[n] << endl;
  }
}
accuracy: 1
time_ms: 120
memory_kb: 3500
final_rank: 11

code_snippet: #include<bits/stdc++.h>

#define int ll
#define rep(i, N) for(int i = 0; i < N; i++)
#define per(i, N) for(int i = N-1; i >= 0; i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define TakAo(ans) ans ? cout << "Takahashi\n" : cout << "Aoki\n"
#define YesNo(ans) ans ? cout << "Yes\n" : cout << "No\n"
#define yesno(ans) ans ? cout << "yes\n" : cout << "no\n"
#define equal(f1, f2) (abs(f1 - f2) <= EPS)
#define endl '\n'
#define fi first
#define se second
#define pb push_back
#define mkpr make_pair
#define mktpl make_tuple

using namespace std;
using ll = int64_t;
using ld = long double;
using P = pair<int, int>;
using Tpl = tuple<int, int, int>;
using vvec = vector<vector<int>>;
using vvvec = vector<vector<vector<int>>>;

const ld EPS = 1e-8;
const ld Pi = acos(-1);
const ll INF = 1e9+10;
const int MOD = 998244353;
//const int MOD = 1e9+7;
const int NIL = -1;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, -1, 0, 1};

ll cel(ll a, ll b){ return (a + b - 1) / b; }
ll Gcd(ll a, ll b){ return b ? Gcd(b, a % b) : a; }
ll Lcm(ll a, ll b){ return a / Gcd(a, b) * b; }
ll sq(ll a){ return a * a; }
ll cube(ll a){ return a * a * a; }
ll powi(ll a, ll b){ ll res = 1; rep(i, b) res *= a; return res; }
template<class T> bool chmin(T &a, T b){ if(a > b){ a = b; return 1;} return 0; }
template<class T> bool chmax(T &a, T b){ if(a < b){ a = b; return 1;} return 0; }

void Main(){
	int Q; cin >> Q;
	const int maxn = 1e5;

	vector<ll> table(maxn+1, 1);
	vector<int> ans(maxn+1, 0);

	for(int i = 2; i <= maxn; i++){
		for(ll j = i * 2; j <= maxn; j += i){
			table[j] *= i;
			if(table[j] >= j * 2){
				ans[j] = 1;
				table[j] = 0;
			}
		}
	}
	
	rep(i, maxn) ans[i+1] += ans[i];

	while(Q--){
		int N; cin >> N;
		cout << ans[N] << endl;
	}
}

signed main(){
    cin.tie(nullptr);
	ios_base::sync_with_stdio(false);
	cout << fixed << setprecision(15);
	Main();
    return 0;
}
accuracy: 1
time_ms: 10
memory_kb: 4676
final_rank: 4

code_snippet: #pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

#define _overload(_1, _2, _3, _4, name, ...) name
#define _rep1(Itr, N) _rep3(Itr, 0, N, 1)
#define _rep2(Itr, a, b) _rep3(Itr, a, b, 1)
#define _rep3(Itr, a, b, step) for (i64 Itr = a; Itr < b; Itr += step)
#define repeat(...) _overload(__VA_ARGS__, _rep3, _rep2, _rep1)(__VA_ARGS__)
#define rep(...) repeat(__VA_ARGS__)

#define ALL(X) begin(X), end(X)

using namespace std;
using i64 = long long;
using u64 = unsigned long long;

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    const i64 MAXN = 100000;

    i64 q;
    cin >> q;

    auto div = [](i64 n) {
        i64 ret = 0;
        for (i64 i = 1; i * i <= n; i++) {
            if (n % i == 0) {
                ret++;
                if (n / i != i) ret++;
            }
        }
        return ret;
    };
    vector<i64> ans(MAXN + 1);
    rep(i, 1, MAXN + 1) {
        ans[i] = ans[i - 1];
        if (div(i) >= 5) ans[i]++;
    }

    rep(i, q) {
        i64 n;
        cin >> n;
        cout << ans[n] << endl;
    }

    return 0;
}
accuracy: 1
time_ms: 200
memory_kb: 3876
final_rank: 18

code_snippet: #include<bits/stdc++.h>
using ll = long long;
#define var auto
const char newl = '\n';

using namespace std;

template<typename T1, typename T2> inline void chmin(T1& a, T2 b) { if (a > b) a = b; }
template<typename T1, typename T2> inline void chmax(T1& a, T2 b) { if (a < b) a = b; }

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  vector<int> accum(1e5 + 1);
  for (ll i = 2; i < accum.size(); i++) {
    accum[i] = accum[i - 1];
    ll prod = 1;
    for (int j = 1; j * j <= i; j++) {
      if (i * i * 2 <= prod) continue;
      if (i % j != 0) continue;

      prod *= j;
      var k = i / j;
      if (j < k) prod *= k;

    }
    prod /= i;
    if (i * 2 <= prod) accum[i]++;
  }
  int q;
  cin >> q;
  for (int i = 0; i < q; i++) {
    int n;
    cin >> n;
    cout << accum[n] << endl;
  }
}
accuracy: 1
time_ms: 120
memory_kb: 3612
final_rank: 13

code_snippet: #line 2 "/home/yuruhiya/programming/library/template/template.cpp"
#include <bits/stdc++.h>
#line 4 "/home/yuruhiya/programming/library/template/constants.cpp"
#include <string_view>
#line 7 "/home/yuruhiya/programming/library/template/constants.cpp"

#define rep(i, n) for (int i = 0; i < (n); ++i)
#define FOR(i, m, n) for (int i = (m); i < (n); ++i)
#define rrep(i, n) for (int i = (n)-1; i >= 0; --i)
#define rfor(i, m, n) for (int i = (m); i >= (n); --i)
#define unless(c) if (!(c))
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define range_it(a, l, r) (a).begin() + (l), (a).begin() + (r)

using namespace std;
using ll = long long;
using LD = long double;
using VB = vector<bool>;
using VVB = vector<VB>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;
using VS = vector<string>;
using VD = vector<LD>;
using PII = pair<int, int>;
using VP = vector<PII>;
using PLL = pair<ll, ll>;
using VPL = vector<PLL>;
template <class T> using PQ = priority_queue<T>;
template <class T> using PQS = priority_queue<T, vector<T>, greater<T>>;
constexpr int inf = 1000000000;
constexpr long long inf_ll = 1000000000000000000ll, MOD = 1000000007;
constexpr long double PI = 3.14159265358979323846, EPS = 1e-12;
namespace CharacterClass {
	constexpr string_view
	    digit = "0123456789",
	    xdigit = "0123456789ABCDEFabcdef", lower = "abcdefghijklmnopqrstuvwxyz",
	    upper = "ABCDEFGHIJKLMNOPQRSTUVWXYZ",
	    alpha = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz",
	    alnum = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz",
	    word = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ_abcdefghijklmnopqrstuvwxyz",
	    punct = R"(!"#$%&'()*+,-./:;<=>?@[\]^_`{|}~)",
	    graph =
	        R"(!"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~)",
	    print =
	        R"( !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~)",
	    blank = " \t", space = " \t\n\r\f\v";
}  // namespace CharacterClass
#line 7 "/home/yuruhiya/programming/library/template/Input.cpp"
using namespace std;

#ifdef _WIN32
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#define fwrite_unlocked fwrite
#define fflush_unlocked fflush
#endif
class Scanner {
	static int gc() {
		return getchar_unlocked();
	}
	static char next_char() {
		char c;
		read(c);
		return c;
	}
	template <class T> static void read(T& v) {
		cin >> v;
	}
	static void read(char& v) {
		while (isspace(v = gc()))
			;
	}
	static void read(bool& v) {
		v = next_char() != '0';
	}
	static void read(string& v) {
		v.clear();
		for (char c = next_char(); !isspace(c); c = gc()) v += c;
	}
	static void read(int& v) {
		v = 0;
		bool neg = false;
		char c = next_char();
		if (c == '-') {
			neg = true;
			c = gc();
		}
		for (; isdigit(c); c = gc()) v = v * 10 + (c - '0');
		if (neg) v = -v;
	}
	static void read(long long& v) {
		v = 0;
		bool neg = false;
		char c = next_char();
		if (c == '-') {
			neg = true;
			c = gc();
		}
		for (; isdigit(c); c = gc()) v = v * 10 + (c - '0');
		if (neg) v = -v;
	}
	static void read(double& v) {
		v = 0;
		double dp = 1;
		bool neg = false, after_dp = false;
		char c = next_char();
		if (c == '-') {
			neg = true;
			c = gc();
		}
		for (; isdigit(c) || c == '.'; c = gc()) {
			if (c == '.') {
				after_dp = true;
			} else if (after_dp) {
				v += (c - '0') * (dp *= 0.1);
			} else {
				v = v * 10 + (c - '0');
			}
		}
		if (neg) v = -v;
	}
	static void read(long double& v) {
		v = 0;
		long double dp = 1;
		bool neg = false, after_dp = false;
		char c = next_char();
		if (c == '-') {
			neg = true;
			c = gc();
		}
		for (; isdigit(c) || c == '.'; c = gc()) {
			if (c == '.') {
				after_dp = true;
			} else if (after_dp) {
				v += (c - '0') * (dp *= 0.1);
			} else {
				v = v * 10 + (c - '0');
			}
		}
		if (neg) v = -v;
	}
	template <class T, class U> static void read(pair<T, U>& v) {
		read(v.first);
		read(v.second);
	}
	template <class T> static void read(vector<T>& v) {
		for (auto& e : v) read(e);
	}
	template <size_t N = 0, class T> static void read_tuple_impl(T& v) {
		if constexpr (N < tuple_size_v<T>) {
			read(get<N>(v));
			read_tuple_impl<N + 1>(v);
		}
	}
	template <class... T> static void read(tuple<T...>& v) {
		read_tuple_impl(v);
	}
	struct ReadVectorHelper {
		size_t n;
		ReadVectorHelper(size_t _n) : n(_n) {}
		template <class T> operator vector<T>() {
			vector<T> v(n);
			read(v);
			return v;
		}
	};
	struct Read2DVectorHelper {
		size_t n, m;
		Read2DVectorHelper(const pair<size_t, size_t>& nm) : n(nm.first), m(nm.second) {}
		template <class T> operator vector<vector<T>>() {
			vector<vector<T>> v(n, vector<T>(m));
			read(v);
			return v;
		}
	};

public:
	string read_line() const {
		string v;
		for (char c = gc(); c != '\n' && c != '\0'; c = gc()) v += c;
		return v;
	}
	template <class T> T read() const {
		T v;
		read(v);
		return v;
	}
	template <class T> vector<T> read_vector(size_t n) const {
		vector<T> a(n);
		read(a);
		return a;
	}
	template <class T> operator T() const {
		return read<T>();
	}
	int operator--(int) const {
		return read<int>() - 1;
	}
	ReadVectorHelper operator[](size_t n) const {
		return ReadVectorHelper(n);
	}
	Read2DVectorHelper operator[](const pair<size_t, size_t>& nm) const {
		return Read2DVectorHelper(nm);
	}
	void operator()() const {}
	template <class H, class... T> void operator()(H&& h, T&&... t) const {
		read(h);
		operator()(forward<T>(t)...);
	}

private:
	template <template <class...> class, class...> struct Multiple;
	template <template <class...> class V, class Head, class... Tail>
	struct Multiple<V, Head, Tail...> {
		template <class... Args> using vec = V<vector<Head>, Args...>;
		using type = typename Multiple<vec, Tail...>::type;
	};
	template <template <class...> class V> struct Multiple<V> { using type = V<>; };
	template <class... T> using multiple_t = typename Multiple<tuple, T...>::type;
	template <size_t N = 0, class T> void multiple_impl(T& t) const {
		if constexpr (N < tuple_size_v<T>) {
			auto& vec = get<N>(t);
			using V = typename remove_reference_t<decltype(vec)>::value_type;
			vec.push_back(read<V>());
			multiple_impl<N + 1>(t);
		}
	}

public:
	template <class... T> auto multiple(size_t h) const {
		multiple_t<T...> result;
		while (h--) multiple_impl(result);
		return result;
	}
} in;
#define inputs(T, ...) \
	T __VA_ARGS__;     \
	in(__VA_ARGS__)
#define ini(...) inputs(int, __VA_ARGS__)
#define inl(...) inputs(long long, __VA_ARGS__)
#define ins(...) inputs(string, __VA_ARGS__)
#line 7 "/home/yuruhiya/programming/library/template/Output.cpp"
#include <charconv>
#line 10 "/home/yuruhiya/programming/library/template/Output.cpp"
using namespace std;

struct BoolStr {
	const char *t, *f;
	BoolStr(const char* _t, const char* _f) : t(_t), f(_f) {}
} Yes("Yes", "No"), yes("yes", "no"), YES("YES", "NO"), Int("1", "0");
struct DivStr {
	const char *d, *l;
	DivStr(const char* _d, const char* _l) : d(_d), l(_l) {}
} spc(" ", "\n"), no_spc("", "\n"), end_line("\n", "\n"), comma(",", "\n"),
    no_endl(" ", "");
class Printer {
	BoolStr B{Yes};
	DivStr D{spc};

public:
	void print(int v) const {
		char buf[12]{};
		if (auto [ptr, e] = to_chars(begin(buf), end(buf), v); e == errc{}) {
			fwrite(buf, sizeof(char), ptr - buf, stdout);
		} else {
			assert(false);
		}
	}
	void print(long long v) const {
		char buf[21]{};
		if (auto [ptr, e] = to_chars(begin(buf), end(buf), v); e == errc{}) {
			fwrite(buf, sizeof(char), ptr - buf, stdout);
		} else {
			assert(false);
		}
	}
	void print(bool v) const {
		print(v ? B.t : B.f);
	}
	void print(vector<bool>::reference v) const {
		print(v ? B.t : B.f);
	}
	void print(char v) const {
		putchar_unlocked(v);
	}
	void print(const char* v) const {
		fwrite_unlocked(v, 1, strlen(v), stdout);
	}
	void print(double v) const {
		printf("%.20f", v);
	}
	void print(long double v) const {
		printf("%.20Lf", v);
	}
	template <class T> void print(const T& v) const {
		cout << v;
	}
	template <class T, class U> void print(const pair<T, U>& v) const {
		print(v.first);
		print(D.d);
		print(v.second);
	}
	template <class InputIterater>
	void print_range(const InputIterater& begin, const InputIterater& end) const {
		for (InputIterater i = begin; i != end; ++i) {
			if (i != begin) print(D.d);
			print(*i);
		}
	}
	template <class T> void print(const vector<T>& v) const {
		print_range(v.begin(), v.end());
	}
	template <class T, size_t N> void print(const array<T, N>& v) const {
		print_range(v.begin(), v.end());
	}
	template <class T> void print(const vector<vector<T>>& v) const {
		for (size_t i = 0; i < v.size(); ++i) {
			if (i) print(D.l);
			print(v[i]);
		}
	}

	Printer() = default;
	Printer(const BoolStr& _boolstr, const DivStr& _divstr) : B(_boolstr), D(_divstr) {}
	Printer& operator()() {
		print(D.l);
		return *this;
	}
	template <class H> Printer& operator()(H&& h) {
		print(h);
		print(D.l);
		return *this;
	}
	template <class H, class... T> Printer& operator()(H&& h, T&&... t) {
		print(h);
		print(D.d);
		return operator()(forward<T>(t)...);
	}
	template <class InputIterator>
	Printer& range(const InputIterator& begin, const InputIterator& end) {
		print_range(begin, end);
		print(D.l);
		return *this;
	}
	template <class T> Printer& range(const T& a) {
		range(a.begin(), a.end());
		return *this;
	}
	template <class... T> void exit(T&&... t) {
		operator()(forward<T>(t)...);
		std::exit(EXIT_SUCCESS);
	}
	Printer& flush() {
		fflush_unlocked(stdout);
		return *this;
	}
	Printer& set(const BoolStr& b) {
		B = b;
		return *this;
	}
	Printer& set(const DivStr& d) {
		D = d;
		return *this;
	}
	Printer& set(const char* t, const char* f) {
		B = BoolStr(t, f);
		return *this;
	}
} out;
#line 3 "/home/yuruhiya/programming/library/template/Step.cpp"
using namespace std;

template <class T> struct Step {
	using value_type = T;

	class iterator {
		value_type a, b, c;

	public:
		constexpr iterator() : a(value_type()), b(value_type()), c(value_type()) {}
		constexpr iterator(value_type _b, value_type _c, value_type _s)
		    : a(_b), b(_c), c(_s) {}
		constexpr iterator& operator++() {
			--b;
			a += c;
			return *this;
		}
		constexpr iterator operator++(int) {
			iterator tmp = *this;
			--b;
			a += c;
			return tmp;
		}
		constexpr const value_type& operator*() const {
			return a;
		}
		constexpr const value_type* operator->() const {
			return &a;
		}
		constexpr bool operator==(const iterator& i) const {
			return b == i.b;
		}
		constexpr bool operator!=(const iterator& i) const {
			return !(b == i.b);
		}
		constexpr value_type start() const {
			return a;
		}
		constexpr value_type size() const {
			return b;
		}
		constexpr value_type step() const {
			return c;
		}
	};
	constexpr Step(value_type b, value_type c, value_type s) : be(b, c, s) {}
	constexpr iterator begin() const {
		return be;
	}
	constexpr iterator end() const {
		return en;
	}
	constexpr value_type start() const {
		return be.start();
	}
	constexpr value_type size() const {
		return be.size();
	}
	constexpr value_type step() const {
		return be.step();
	}
	constexpr value_type sum() const {
		return start() * size() + step() * (size() * (size() - 1) / 2);
	}
	operator vector<value_type>() const {
		return to_a();
	}
	auto to_a() const {
		vector<value_type> result;
		result.reserve(size());
		for (auto i : *this) {
			result.push_back(i);
		}
		return result;
	}

private:
	iterator be, en;
};
template <class T> constexpr auto step(T a) {
	return Step<T>(0, a, 1);
}
template <class T> constexpr auto step(T a, T b) {
	return Step<T>(a, b - a, 1);
}
template <class T> constexpr auto step(T a, T b, T c) {
	return Step<T>(a, a < b ? (b - a - 1) / c + 1 : 0, c);
}
#line 8 "/home/yuruhiya/programming/library/template/Ruby.cpp"
using namespace std;

template <class F> struct Callable {
	F func;
	Callable(const F& f) : func(f) {}
};
template <class T, class F> auto operator|(const T& v, const Callable<F>& c) {
	return c.func(v);
}

struct Sort_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			sort(begin(v), end(v), f);
			return v;
		});
	}
	template <class T> friend auto operator|(T v, [[maybe_unused]] const Sort_impl& c) {
		sort(begin(v), end(v));
		return v;
	}
} Sort;
struct SortBy_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			sort(begin(v), end(v),
			     [&](const auto& i, const auto& j) { return f(i) < f(j); });
			return v;
		});
	}
} SortBy;
struct RSort_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			sort(rbegin(v), rend(v), f);
			return v;
		});
	}
	template <class T> friend auto operator|(T v, [[maybe_unused]] const RSort_impl& c) {
		sort(rbegin(v), rend(v));
		return v;
	}
} RSort;
struct RSortBy_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			sort(begin(v), end(v),
			     [&](const auto& i, const auto& j) { return f(i) > f(j); });
			return v;
		});
	}
} RSortBy;
struct Reverse_impl {
	template <class T> friend auto operator|(T v, const Reverse_impl& c) {
		reverse(begin(v), end(v));
		return v;
	}
} Reverse;
struct Unique_impl {
	template <class T> friend auto operator|(T v, const Unique_impl& c) {
		v.erase(unique(begin(v), end(v), end(v)));
		return v;
	}
} Unique;
struct Uniq_impl {
	template <class T> friend auto operator|(T v, const Uniq_impl& c) {
		sort(begin(v), end(v));
		v.erase(unique(begin(v), end(v)), end(v));
		return v;
	}
} Uniq;
struct Rotate_impl {
	auto operator()(int&& left) {
		return Callable([&](auto v) {
			int s = static_cast<int>(size(v));
			assert(-s <= left && left <= s);
			if (0 <= left) {
				rotate(begin(v), begin(v) + left, end(v));
			} else {
				rotate(begin(v), end(v) + left, end(v));
			}
			return v;
		});
	}
} Rotate;
struct Max_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) { return *max_element(begin(v), end(v), f); });
	}
	template <class T> friend auto operator|(T v, const Max_impl& c) {
		return *max_element(begin(v), end(v));
	}
} Max;
struct Min_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) { return *min_element(begin(v), end(v), f); });
	}
	template <class T> friend auto operator|(T v, const Min_impl& c) {
		return *min_element(begin(v), end(v));
	}
} Min;
struct MaxPos_impl {
	template <class T> friend auto operator|(T v, const MaxPos_impl& c) {
		return max_element(begin(v), end(v)) - begin(v);
	}
} MaxPos;
struct MinPos_impl {
	template <class T> friend auto operator|(T v, const MinPos_impl& c) {
		return min_element(begin(v), end(v)) - begin(v);
	}
} MinPos;
struct MaxBy_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			auto max_it = begin(v);
			auto max_val = f(*max_it);
			for (auto it = next(begin(v)); it != end(v); ++it) {
				if (auto val = f(*it); max_val < val) {
					max_it = it;
					max_val = val;
				}
			}
			return *max_it;
		});
	}
} MaxBy;
struct MinBy_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			auto min_it = begin(v);
			auto min_val = f(*min_it);
			for (auto it = next(begin(v)); it != end(v); ++it) {
				if (auto val = f(*it); min_val > val) {
					min_it = it;
					min_val = val;
				}
			}
			return *min_it;
		});
	}
} MinBy;
struct MaxOf_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			auto max_val = f(*begin(v));
			for (auto it = next(begin(v)); it != end(v); ++it) {
				if (auto val = f(*it); max_val < val) {
					max_val = val;
				}
			}
			return max_val;
		});
	}
} MaxOf;
struct MinOf_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			auto min_val = f(*begin(v));
			for (auto it = next(begin(v)); it != end(v); ++it) {
				if (auto val = f(*it); min_val > val) {
					min_val = val;
				}
			}
			return min_val;
		});
	}
} MinOf;
struct Count_impl {
	template <class V> auto operator()(const V& val) {
		return Callable([&](auto v) { return count(begin(v), end(v), val); });
	}
} Count;
struct CountIf_impl {
	template <class F> auto operator()(const F& f) {
		return Callable([&](auto v) { return count_if(begin(v), end(v), f); });
	}
} CountIf;
struct Index_impl {
	template <class V> auto operator()(const V& val) {
		return Callable([&](auto v) -> optional<int> {
			auto result = find(begin(v), end(v), val);
			return result != end(v) ? optional(result - begin(v)) : nullopt;
		});
	}
} Index;
struct IndexIf_impl {
	template <class F> auto operator()(const F& f) {
		return Callable([&](auto v) -> optional<int> {
			auto result = find_if(begin(v), end(v), f);
			return result != end(v) ? optional(result - begin(v)) : nullopt;
		});
	}
} IndexIf;
struct FindIf_impl {
	template <class F> auto operator()(const F& f) {
		return Callable([&](auto v) -> optional<typename decltype(v)::value_type> {
			auto result = find_if(begin(v), end(v), f);
			return result != end(v) ? optional(*result) : nullopt;
		});
	}
} FindIf;
struct Sum_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			return accumulate(next(begin(v)), end(v), f(*begin(v)),
			                  [&](const auto& a, const auto& b) { return a + f(b); });
		});
	}
	template <class T> friend auto operator|(T v, const Sum_impl& c) {
		return accumulate(begin(v), end(v), typename T::value_type{});
	}
} Sum;
struct Includes {
	template <class V> auto operator()(const V& val) {
		return Callable([&](auto v) { return find(begin(v), end(v), val) != end(v); });
	}
} Includes;
struct IncludesIf_impl {
	template <class F> auto operator()(const F& f) {
		return Callable([&](auto v) { return find_if(begin(v), end(v), f) != end(v); });
	}
} IncludesIf;
struct RemoveIf_impl {
	template <class F> auto operator()(const F& f) {
		return Callable([&](auto v) {
			v.erase(remove_if(begin(v), end(v), f), end(v));
			return v;
		});
	}
} RemoveIf;
struct Each_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			for (const auto& i : v) {
				f(i);
			}
		});
	}
} Each;
struct Select_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			using value_type = typename decltype(v)::value_type;
			vector<value_type> result;
			for (const auto& i : v) {
				if (f(i)) result.push_back(i);
			}
			return result;
		});
	}
} Select;
struct Map_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			using result_type = invoke_result_t<F, typename decltype(v)::value_type>;
			vector<result_type> result;
			result.reserve(size(v));
			for (const auto& i : v) {
				result.push_back(f(i));
			}
			return result;
		});
	}
} Map;
struct Indexed_impl {
	template <class T> friend auto operator|(const T& v, Indexed_impl& c) {
		using value_type = typename T::value_type;
		vector<pair<value_type, int>> result;
		result.reserve(size(v));
		int index = 0;
		for (const auto& i : v) {
			result.emplace_back(i, index++);
		}
		return result;
	}
} Indexed;
struct AllOf_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			for (const auto& i : v) {
				if (!f(i)) return false;
			}
			return true;
		});
	}
} AllOf;
struct AnyOf_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			for (const auto& i : v) {
				if (f(i)) return true;
			}
			return false;
		});
	}
} AnyOf;
struct NoneOf_impl {
	template <class F> auto operator()(F&& f) {
		return Callable([&](auto v) {
			for (const auto& i : v) {
				if (f(i)) return false;
			}
			return true;
		});
	}
} NoneOf;

struct Tally_impl {
	template <class F> auto operator()(size_t max_val) {
		return Callable([&](auto v) {
			vector<size_t> result(max_val);
			for (const auto& i : v) {
				result[static_cast<size_t>(i)]++;
			}
			return result;
		});
	}
	template <class T, class value_type = typename T::value_type>
	friend auto operator|(const T& v, Tally_impl& c) {
		map<value_type, size_t> result;
		for (const auto& i : v) {
			result[i]++;
		}
		return result;
	}
} Tally;

template <class T> auto operator*(const vector<T>& a, size_t n) {
	T result;
	for (size_t i = 0; i < n; ++i) {
		result.insert(result.end(), a.begin(), a.end());
	}
	return result;
}
auto operator*(string a, size_t n) {
	string result;
	for (size_t i = 0; i < n; ++i) {
		result += a;
	}
	return result;
}
template <class T, class U> auto& operator<<(vector<T>& a, const U& b) {
	a.insert(a.end(), all(b));
	return a;
}
template <class T> auto& operator<<(string& a, const T& b) {
	a.insert(a.end(), all(b));
	return a;
}
template <class T, class U> auto operator+(vector<T> a, const U& b) {
	a << b;
	return a;
}
template <class T> auto operator+(string a, const T& b) {
	a << b;
	return a;
}
#line 7 "/home/yuruhiya/programming/library/template/functions.cpp"
using namespace std;

template <class T = long long> constexpr T TEN(size_t n) {
	T result = 1;
	for (size_t i = 0; i < n; ++i) result *= 10;
	return result;
}
template <class T, class U,
          enable_if_t<is_integral_v<T> && is_integral_v<U>, nullptr_t> = nullptr>
constexpr auto div_ceil(T n, U m) {
	return (n + m - 1) / m;
}
template <class T, class U> constexpr auto div_ceil2(T n, U m) {
	return div_ceil(n, m) * m;
}
template <class T> constexpr T triangle(T n) {
	return (n & 1) ? (n + 1) / 2 * n : n / 2 * (n + 1);
}
template <class T> constexpr T nC2(T n) {
	return (n & 1) ? (n - 1) / 2 * n : n / 2 * (n - 1);
}
template <class T, class U> constexpr auto middle(const T& l, const U& r) {
	return l + (r - l) / 2;
}
template <class T, class U, class V>
constexpr bool in_range(const T& v, const U& lower, const V& upper) {
	return lower <= v && v < upper;
}
template <class T, enable_if_t<is_integral_v<T>, nullptr_t> = nullptr>
constexpr bool is_square(T n) {
	T s = sqrt(n);
	return s * s == n || (s + 1) * (s + 1) == n;
}
template <class T = long long> constexpr T BIT(int b) {
	return T(1) << b;
}
template <class T> constexpr int BIT(T x, int i) {
	return (x & (1 << i)) ? 1 : 0;
}
template <class T, class U, enable_if_t<is_integral_v<U>, nullptr_t> = nullptr>
constexpr T Pow(T a, U n) {
	assert(n >= 0);
	T result = 1;
	while (n > 0) {
		if (n & 1) {
			result *= a;
			n--;
		} else {
			a *= a;
			n >>= 1;
		}
	}
	return result;
}
template <class T, class U, enable_if_t<is_integral_v<U>, nullptr_t> = nullptr>
constexpr T Powmod(T a, U n, T mod) {
	assert(n >= 0);
	if (a > mod) a %= mod;
	T result = 1;
	while (n > 0) {
		if (n & 1) {
			result = result * a % mod;
			n--;
		} else {
			a = a * a % mod;
			n >>= 1;
		}
	}
	return result;
}
template <class T> bool chmax(T& a, const T& b) {
	if (a < b) {
		a = b;
		return true;
	}
	return false;
}
template <class T> bool chmin(T& a, const T& b) {
	if (a > b) {
		a = b;
		return true;
	}
	return false;
}
template <class T> int sz(const T& v) {
	return v.size();
}
template <class T, class U> int lower_index(const T& a, const U& v) {
	return lower_bound(all(a), v) - a.begin();
}
template <class T, class U> int upper_index(const T& a, const U& v) {
	return upper_bound(all(a), v) - a.begin();
}
template <class T> auto Slice(const T& v, size_t i, size_t len) {
	return i < v.size() ? T(v.begin() + i, v.begin() + min(i + len, v.size())) : T();
}
template <class T, class U = typename T::value_type> U Gcdv(const T& v) {
	return accumulate(next(v.begin()), v.end(), U(*v.begin()), gcd<U, U>);
}
template <class T, class U = typename T::value_type> U Lcmv(const T& v) {
	return accumulate(next(v.begin()), v.end(), U(*v.begin()), lcm<U, U>);
}
namespace internal {
	template <class T, size_t N> auto make_vector(vector<int>& sizes, const T& init) {
		if constexpr (N == 1) {
			return vector(sizes[0], init);
		} else {
			int size = sizes[N - 1];
			sizes.pop_back();
			return vector(size, make_vector<T, N - 1>(sizes, init));
		}
	}
}  // namespace internal
template <class T, size_t N>
auto make_vector(const int (&sizes)[N], const T& init = T()) {
	vector s(rbegin(sizes), rend(sizes));
	return internal::make_vector<T, N>(s, init);
}
#line 9 "/home/yuruhiya/programming/library/template/template.cpp"
#if __has_include(<library/dump.hpp>)
#include <library/dump.hpp>
#define LOCAL
#else
#define dump(...) ((void)0)
#endif

template <class T> constexpr T oj_local(const T& oj, const T& local) {
#ifndef LOCAL
	return oj;
#else
	return local;
#endif
}
#line 5 "/home/yuruhiya/programming/library/Math/Divisors.cpp"
using namespace std;

template <class T> vector<T> Divisors(T n) {
	assert(0 < n);
	vector<T> result;
	T i = 1;
	for (; i * i < n; ++i) {
		if (n % i == 0) result.push_back(i);
	}
	bool flag = i * i == n;
	if (flag) result.push_back(i);
	for (i = (int)result.size() - 1 - flag; i >= 0; --i) {
		result.push_back(n / result[i]);
	}
	return result;
}
template <class T> int DivisorsCount(T n) {
	assert(0 < n);
	int cnt = 0;
	T sq = sqrt(n);
	for (T i = 1; i <= sq; ++i) {
		cnt += n % i == 0;
	}
	return cnt * 2 - (sq * sq == n);
}
template <class T> T DivisorsSum(T n) {
	assert(0 < n);
	T i = 1, result = 0;
	for (; i * i < n; ++i) {
		if (n % i == 0) result += i + n / i;
	}
	return result + i * (i * i == n);
}
#line 3 "a.cpp"

int main() {
	const int MAX_N = 100005;
	VI ans(MAX_N);
	FOR(x, 2, MAX_N) {
		bool flag = [&] {
			ll mul = 1;
			for (ll d : Divisors(x)) {
				if (d == x) continue;
				mul *= d;
				if (mul >= x * 2) return true;
			}
			return false;
		}();
		ans[x] = ans[x - 1] + flag;
	}

	for (int q = in; q--;) {
		ini(n);
		out(ans[n]);
	}
}
accuracy: 1
time_ms: 50
memory_kb: 3576
final_rank: 6

code_snippet: #include <bits/stdc++.h>
//#include <atcoder/all>
//using namespace atcoder;
const double pi = 3.141592653589793238462643383279;
using namespace std;
//typedef
//------------------------------------------
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef pair<long long, long long> PLL;
typedef pair<int, PII> TIII;
typedef long long LL;
typedef unsigned long long ULL;
typedef vector<LL> VLL;
typedef vector<VLL> VVLL;

//container util
//------------------------------------------
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define SZ(a) int((a).size())
#define SQ(a) ((a) * (a))
#define EACH(i, c) for (typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define EXIST(s, e) ((s).find(e) != (s).end())
#define SORT(c) sort((c).begin(), (c).end())

//repetition
//------------------------------------------
#define FOR(i, s, n) for (int i = s; i < (int)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define MOD 1000000007

#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define trav(a, x) for (auto &a : x)
#define all(x) x.begin(), x.end()
#define sz(x) (int)(x).size()

typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;

#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
const double EPS = 1e-3, PI = acos(-1);
//ここから編集
ll arr[101010];
int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(6);
    REP(i,101010) arr[i] = 1;
    for(int i=2; i<=100000; i++){
        for(int j=i*2; j<=100000; j+=i){
            if(arr[j] > 2*j) continue;
            arr[j] *= i;
        }
    }
    vector<int> v;
    REP(i,100001){
        if(i >= 2 && arr[i] >= 2*i)v.push_back(i);
    }
    int Q; cin >> Q;
    REP(i,Q){
        int t; cin >> t;
        cout << upper_bound(all(v), t) - v.begin() << endl;
    }
    return 0;
}
accuracy: 1
time_ms: 100
memory_kb: 4236
final_rank: 10

code_snippet: #include <bits/stdc++.h>
using namespace std;

using ll = long long;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  
  vector<ll> x(1e5 + 1, 1);
  vector<int> acc(1e5 + 1);
  for (ll i = 2; i <= 1e5; i++) {
    for (ll j = 2; i * j <= 1e5; j++) {
      x[i * j] *= i;
      if (x[i * j] >= 2 * i * j) acc[i * j] = 1;
    }
  }
  
  for (int i = 0; i <= 1e5; i++) {
    if (x[i] >= 2 * i) acc[i] = 1;
    if (i) acc[i] += acc[i - 1];
  }
  
  int q;
  cin >> q;
  
  while (q--) {
    int n;
    cin >> n;
    cout << acc[n] - acc[1] << '\n';
  }
}
accuracy: 1
time_ms: 10
memory_kb: 4336
final_rank: 2

code_snippet: #include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int main(){
    int n;
    cin >> n;
    int lim = 1e5;
    vector<int> numfact(lim+1, 0);
    for(int i=2; i<lim; i++){
        for(int j=i*2; j<=lim; j+=i){
            numfact[j]++;
        }
    }
    vector<int> ans(lim+1);
    for(int i=0; i<=lim; i++){
        ans[i] = (numfact[i]>2)? 1: 0;
        if(i>0) ans[i] += ans[i-1];
    }
    for(int i=0; i<n; i++){
        int a;
        cin >> a;
        cout << ans[a] << endl;
    }
    return 0;
}
accuracy: 1
time_ms: 100
memory_kb: 3632
final_rank: 9

code_snippet: #include <stdio.h>

int main(void)
{
  int a;
  int l;
  int max=0;
  long Q[100000]={0};
  long sum[100000]={0};
  long mul[100000]={0};
  int i,j=0;
  
  scanf("%d",&a);
  for(l=0;l<a;l++){
    scanf("%d", &Q[l]);
    if(max<=Q[l])
      max=Q[l];
  }

  for(i=1;i<=max;i++)
    mul[i]=1;
  
  for(i=2;i<=max;i++){
    for(j=2*i;j<=max;j+=i){
      mul[j]*=i;
      if(mul[j]>2*j)
	mul[j]=2*j;
    }
  }
  
  for(i=2;i<=max;i++){
    sum[i]=sum[i-1];
    if(mul[i]>=2*i)
      sum[i]++;
  }
  
  for(l=0;l<a;l++)
    printf("%d\n",sum[Q[l]]);

  return 0;
}
accuracy: 1
time_ms: 10
memory_kb: 5068
final_rank: 5

code_snippet: #include<iostream>
#include<vector>

using namespace std;

int csum[100001];

int main() {
	csum[1] = 0;
	for (int i = 2; i <= 100000; i++) {
		int times = 1;
		for (int x = 2; x * x <= i; x++) {
			if (i % x == 0) {
				times *= x;
				if (times >= 2 * i) {
					csum[i] = 1;
					break;
				}
				times *= (i / x);
				if (times >= 2 * i) {
					csum[i] = 1;
					break;
				}
			}
		}
		
	}

	for (int i = 1; i <= 100000; i++) {
		csum[i] += csum[i - 1];
	}
	
	int q;
	cin >> q;
	for (int i = 0; i < q; i++) {
		int N;
		cin >> N;
		cout << csum[N] - csum[1] << endl;
	}
	return 0;
}
accuracy: 1
time_ms: 120
memory_kb: 3500
final_rank: 11

code_snippet: #include <cstdio>
#include <iostream>
#include <string>
#include <sstream>
#include <stack>
#include <algorithm>
#include <cmath>
#include <queue>
#include <map>
#include <set>
#include <cstdlib>
#include <bitset>
#include <tuple>
#include <assert.h>
#include <deque>
#include <bitset>
#include <iomanip>
#include <limits>
#include <chrono>
#include <random>
#include <array>
#include <unordered_map>
#include <functional>
#include <complex>
#include <numeric>
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

const long long MAX = 5100000;
const long long INF = 1LL << 60;
const long long mod = 1000000007LL;
//const long long mod = 998244353LL;

using namespace std;
typedef unsigned long long ull;
typedef long long ll;

bool IsPrime[MAX];
ll MinFactor[MAX]; vector<ll> preprocess(ll n = MAX) {
    vector<ll> res;
    for (ll i = 0; i < n; ++i) IsPrime[i] = true, MinFactor[i] = -1;
    IsPrime[0] = false; IsPrime[1] = false;
    MinFactor[0] = 0; MinFactor[1] = 1;
    for (ll i = 2; i < n; ++i) {
        if (IsPrime[i]) {
            MinFactor[i] = i;
            res.push_back(i);
            for (ll j = i * 2; j < n; j += i) {
                IsPrime[j] = false;
                if (MinFactor[j] == -1) MinFactor[j] = i;
            }
        }
    }
    return res;
}

vector<pair<ll, ll> > fast_prime_factor(ll n) {
    vector<pair<ll, ll> > res;
    while (n != 1) {
        ll prime = MinFactor[n];
        ll exp = 0;
        while (MinFactor[n] == prime) {
            ++exp;
            n /= prime;
        }
        res.push_back(make_pair(prime, exp));
    }
    return res;
}

ll power(ll x, ll n) {
    if (n == 0) {
        return 1;
    }
    if (n % 2 == 0) {
        return power(x * x, n / 2);
    }
    else {
        return x * power(x, n - 1);
    }
}

ll cnt[105000];
int main()
{
	/*
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	*/
    preprocess();
	vector<ll> pr;
    for (ll i = 2; i <= 100000; i++) {
        cnt[i] = cnt[i - 1];
        vector<pair<ll, ll>> p = fast_prime_factor(i);
        ll c = 1;
        for (auto e : p) {
            c *= (e.second + 1);
        }
        if (c >= 5) cnt[i]++;
    }
	ll Q; scanf("%lld", &Q);
	while (Q--) {
		ll n; scanf("%lld", &n);
        printf("%lld\n", cnt[n]);
	}
	return 0;
}
accuracy: 1
time_ms: 180
memory_kb: 51728
final_rank: 20

code_snippet: #include<bits/stdc++.h>
using namespace::std;
using ll =long long;
#define rep(i,a,n) for(ll i=a;i<n;i++)
#define INF (1LL<<60)
template<class T> using V=vector<T>;

vector<int> finddivisor(int x){
  vector<int> d;
  for(int i=1;i*i<=x;i++){
    if(x%i==0){
      d.push_back(i);
      if(i*i!=x)d.push_back(x/i);
    }
  }
  return d;
}


int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  V<int> cnt(100010,0),d;
  rep(i,2,100010){
    ll pro=1;
    d=finddivisor(i);
    rep(j,0,(int)d.size()){
      if(d[j]!=i)pro*=d[j];

      if(2*i<=pro){
        cnt[i]++;
        break;
      }
    }
  }

  rep(i,1,100010){
    cnt[i]+=cnt[i-1];
  }

  int qq;cin>>qq;
  while(qq--){
    int x;cin>>x;
    cout<<cnt[x]<<'\n';
  }
}
accuracy: 1
time_ms: 70
memory_kb: 3272
final_rank: 7

code_snippet: #include <bits/stdc++.h>
#define N (long long)(1e5)
using namespace std;

long long q;
vector<long long> sum;

void prepair();
void solve();

int main() {
  cin >> q;
  prepair();
  solve();
  return 0;
}

void prepair() {
  sum.assign(N + 1, 0);
  for(int i = 2; i <= N; ++i) {
    sum[i] = sum[i - 1];
    long long cnt = 0;
    for(long long j = 2; j * j <= i; ++j)
      if(i % j == 0) ++cnt;
    if(cnt >= 2) ++sum[i];
  }
}
void solve() {
  for(int i = 0; i < q; ++i) {
    int n;
    cin >> n;
    cout << sum[n] << endl;
  }
}
accuracy: 1
time_ms: 270
memory_kb: 3632
final_rank: 19

code_snippet: #include <bits/stdc++.h>
using namespace std;
using ll=long long;
using vec=vector<ll>;
#define For(i,a,b) for(i=a;i<(ll)b;i++)
#define rep(i,N) for(i=0;i<(ll)N;i++)
#define print(a) cout<<a<<endl
#define pb push_back
vec prime(ll N){
  ll i=2;
  vec res;
  while(i*i<=N){
    while(!(N%i)){
      res.pb(i);
      N/=i;
    }
    i++;
  }
  if(N!=1)res.pb(N);
  return res;
}
int main(){
  ll i,Q,N;
  cin>>Q;
  vec x(100001,0);
  For(i,12,100001){
    vec v=prime(i);
    if(v.size()<3)x[i]=x[i-1];
    else if(v.size()>3)x[i]=x[i-1]+1;
    else if(v[0]==v[2]){
      x[i]=x[i-1];
    }else{
      x[i]=x[i-1]+1;
    }
  }
  while(Q--){
    cin>>N;
    print(x[N]);
  }
}
accuracy: 1
time_ms: 170
memory_kb: 3624
final_rank: 16

code_snippet: #include <bits/stdc++.h>
//#include "bits/stdc++.h"

#define rep(i,n) for(ll (i)=0;(i)<(ll)(n);(i)++)
#define all(x) (x).begin(),(x).end()
#define MOD 1000000007LL
#define INF (1LL<<60LL)
#define int long long
typedef long long ll;

using namespace std;

#define MAX_N 100001

signed main() {
	vector<ll> ans(MAX_N, 0);
	for (int i = 2; i < MAX_N; i++) {
		ll k = 0;
		for (int j = 2; j <= sqrt(i); j++) {
			if (i % j == 0)k++;
			if (k >= 2)break;
		}
		ans[i] = ans[i - 1];
		if (k >= 2) ans[i]++;
	}
	ll q; cin >> q;
	rep(i, q) {
		ll n; cin >> n;
		cout << ans[n] << endl;
	}
}
accuracy: 1
time_ms: 170
memory_kb: 3464
final_rank: 15

code_snippet: #include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>

#include <iostream>
#include <complex>
#include <string>
#include <algorithm>
#include <numeric>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <bitset>

#include <functional>
#include <cassert>

typedef long long ll;
using namespace std;

#ifndef LOCAL
#define debug(x) ;
#else
#define debug(x) cerr << __LINE__ << " : " << #x << " = " << (x) << endl;

template <typename T1, typename T2>
ostream &operator<<(ostream &out, const pair<T1, T2> &p) {
  out << "{" << p.first << ", " << p.second << "}";
  return out;
}

template <typename T>
ostream &operator<<(ostream &out, const vector<T> &v) {
  out << '{';
  for (const T &item : v) out << item << ", ";
  out << "\b\b}";
  return out;
}
#endif

#define mod 1000000007 //1e9+7(prime number)
#define INF 1000000000 //1e9
#define LLINF 2000000000000000000LL //2e18
#define SIZE 200010

int ans[SIZE];

int main(){
  int Q;
  int MAXN = 100000;

  cin >> Q;

  for (int i=2; i<=MAXN; i++) {
    int counter = 0;
    for (int j=2; j*j<=i; j++) {
      counter += (i % j == 0) * ((j * j != i) + 1);
    }

    ans[i] = (counter >= 3) + ans[i-1];
  }

  for (int i=0; i<Q; i++) {
    int N;
    cin >> N;
    cout << ans[N] << '\n';
  }

  return 0;
}
accuracy: 1
time_ms: 160
memory_kb: 3512
final_rank: 14

code_snippet: #include<bits/stdc++.h>
using namespace std;
using Int = long long;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}


struct FastIO{
  FastIO(){
    cin.tie(0);
    ios::sync_with_stdio(0);
  }
}fastio_beet;

//INSERT ABOVE HERE
signed main(){
  const Int MAX = 2e5;
  vector<Int> ok(MAX,0);
  for(Int i=2;i<MAX;i++){
    Int res=1;
    for(Int j=2;j*j<=i;j++){
      if(i%j) continue;
      res*=j;
      if(j*j!=i) res*=i/j;
      if(res>=i*2) break;
    }
    ok[i]=res>=i*2;
  }

  vector<Int> ans(MAX,0);
  for(Int i=1;i<MAX;i++) ans[i]=ans[i-1]+ok[i];

  Int q;
  cin>>q;
  for(Int i=0;i<q;i++){
    Int x;
    cin>>x;
    cout<<ans[x]<<"\n";
  }
  cout<<flush;
  return 0;
}
accuracy: 1
time_ms: 160
memory_kb: 5876
final_rank: 17

code_snippet: #include<bits/stdc++.h>
using namespace std;
typedef long long ll;
 
 
signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(20);
 
    int q;
    cin>>q;
    int f[100010]={};
    for(int i=2;i<=100000;i++){
        for(int j=i+i;j<=100000;j+=i) f[j]++;
    }
    int ans[100010]={};
    int cnt = 0;
    for(int i=0;i<=100000;i++){
        if(f[i]>=3) cnt++;
        ans[i] = cnt;
    }
    while(q--){
        ll n;
        cin>>n;
        cout << ans[n] << "\n";

    }
}
accuracy: 1
time_ms: 10
memory_kb: 3968
final_rank: 1