#include using namespace std; /* #ifndef ONLINE_JUDGE #include #include using bll = boost::multiprecision::cpp_int; using bdouble = boost::multiprecision::cpp_dec_float_100; #endif */ #ifdef LOCAL_DEV void debug_impl() { std::cerr << '\n'; } template void debug_impl(Head head, Tail... tail) { std::cerr << " " << head << (sizeof...(tail) ? "," : ""); debug_impl(tail...); } #define debug(...) do { std::cerr << "(" << #__VA_ARGS__ << ") ="; debug_impl(__VA_ARGS__); } while (false) #else #define debug(...) do {} while (false) #endif #ifdef LOCAL_TEST #define BOOST_STACKTRACE_USE_ADDR2LINE #define BOOST_STACKTRACE_ADDR2LINE_LOCATION /usr/local/opt/binutils/bin/addr2line #define _GNU_SOURCE #include namespace std { template class dvector : public std::vector { public: dvector() : std::vector() {} explicit dvector(size_t n, const T& value = T()) : std::vector(n, value) {} dvector(const std::vector& v) : std::vector(v) {} dvector(const std::initializer_list il) : std::vector(il) {} dvector(const std::string::iterator first, const std::string::iterator last) : std::vector(first, last) {} dvector(const typename std::vector::iterator first, const typename std::vector::iterator last) : std::vector(first, last) {} dvector(const typename std::vector::reverse_iterator first, const typename std::vector::reverse_iterator last) : std::vector(first, last) {} dvector(const typename std::vector::const_iterator first, const typename std::vector::const_iterator last) : std::vector(first, last) {} dvector(const typename std::vector::const_reverse_iterator first, const typename std::vector::const_reverse_iterator last) : std::vector(first, last) {} T& operator[](size_t n) { try { return this->at(n); } catch (const std::exception& e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; return this->at(n); } } const T& operator[](size_t n) const { try { return this->at(n); } catch (const std::exception& e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; return this->at(n); } } }; } class dbool { private: bool boolvalue; public: dbool() : boolvalue(false) {} dbool(bool b) : boolvalue(b) {} dbool(const dbool& b) : boolvalue(b.boolvalue) {} operator bool&() { return boolvalue; } operator const bool&() const { return boolvalue; } }; template std::ostream& operator<<(std::ostream& s, const std::dvector& v) { for (size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; } template std::ostream& operator<<(std::ostream& s, const std::dvector>& vv) { s << "\\\n"; for (size_t i = 0; i < vv.size(); ++i){ s << vv[i] << "\n"; } return s; } template std::ostream& operator<<(std::ostream& s, const std::set& se) { s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; } template std::ostream& operator<<(std::ostream& s, const std::multiset& se) { s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; } template std::ostream& operator<<(std::ostream& s, const std::array& a) { s << "{ "; for (size_t i = 0; i < N; ++i){ s << a[i] << "\t"; } s << "}"; return s; } template std::ostream& operator<<(std::ostream& s, const std::map& m) { s << "{\n"; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << "\n"; } s << "}"; return s; } template std::ostream& operator<<(std::ostream& s, const std::pair& p) { return s << "(" << p.first << ", " << p.second << ")"; } #define vector dvector #define bool dbool class SIGFPE_exception : std::exception {}; class SIGSEGV_exception : std::exception {}; void catch_SIGFPE(int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGFPE_exception(); } void catch_SIGSEGV(int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGSEGV_exception(); } signed convertedmain(); signed main() { signal(SIGFPE, catch_SIGFPE); signal(SIGSEGV, catch_SIGSEGV); return convertedmain(); } #define main() convertedmain() #endif //#define int long long using ll = long long; //constexpr int INF = 1e9;//INT_MAX=(1<<31)-1=2147483647 constexpr ll INF = (ll)1e18;//(1LL<<63)-1=9223372036854775807 constexpr ll MOD = (ll)1e9 + 7; constexpr double EPS = 1e-9; constexpr ll dx[4] = {1LL, 0LL, -1LL, 0LL}; constexpr ll dy[4] = {0LL, 1LL, 0LL, -1LL}; constexpr ll dx8[8] = {1LL, 0LL, -1LL, 0LL, 1LL, 1LL, -1LL, -1LL}; constexpr ll dy8[8] = {0LL, 1LL, 0LL, -1LL, 1LL, -1LL, 1LL, -1LL}; #define rep(i, n) for(ll i=0, i##_length=(n); i< i##_length; ++i) #define repeq(i, n) for(ll i=1, i##_length=(n); i<=i##_length; ++i) #define rrep(i, n) for(ll i=(n)-1; i>=0; --i) #define rrepeq(i, n) for(ll i=(n) ; i>=1; --i) #define all(v) (v).begin(), (v).end() #define rall(v) (v).rbegin(), (v).rend() void p() { std::cout << '\n'; } template void p(Head head, Tail... tail) { std::cout << head << (sizeof...(tail) ? " " : ""); p(tail...); } template inline void pv(std::vector& v) { for(ll i=0, N=v.size(); i inline T gcd(T a, T b) { return b ? gcd(b,a%b) : a; } template inline T lcm(T a, T b) { return a / gcd(a, b) * b; } template inline bool chmax(T& a, T b) { return a < b && (a = b, true); } template inline bool chmin(T& a, T b) { return a > b && (a = b, true); } template inline void uniq(std::vector& v) { v.erase(std::unique(v.begin(), v.end()), v.end()); } /*-----8<-----template-----8<-----*/ //MAXVAL以下の素数を求める + MAXVAL以下の整数を素因数分解 //[1-1e7]くらいの範囲で素因数分解をまとめて行いたい場合にお得 class Eratosthenes { public: //primes[i] : i番目の素数 vector primes; //isprime[i] = true:素数, false:合成数 vector isprime; //min_factor[i] : iに含まれる最小の素因数 vector min_factor; private: inline void upflag(int *flags, int BITS, int i) { flags[i / BITS] |= 1 << (i % BITS); } inline int getflag(int *flags, int BITS, int i) { return (flags[i / BITS] >> (i % BITS)) & 1; } inline void setprime(int x) { primes.push_back(x); isprime[x] = true; min_factor[x] = x; } inline void setcomposite(int x, int factorval) { if(min_factor[x] == -1) min_factor[x] = factorval; } public: Eratosthenes(ll MAXVAL) : primes(), isprime(MAXVAL+1, false), min_factor(MAXVAL+1, -1) { int BITS = (sizeof(int) * 8); int FLAGS_NUM = (MAXVAL / BITS + 1); int flags[FLAGS_NUM] = {}; int i, j, f, s; int max = (int)sqrt(MAXVAL) + 1; setcomposite(0,0);if(MAXVAL==0)return; setcomposite(1,1);if(MAXVAL==1)return; setprime(2);if(MAXVAL==2)return; setprime(3);if(MAXVAL==3)return; for (i = 4; i<=MAXVAL; i+=2) setcomposite(i,2); for (i = 9; i<=MAXVAL; i+=6) setcomposite(i,3); for (i = 5, f = 4; i <= max; i += (f = 6 - f)) { if (!getflag(flags,BITS,i)) { setprime(i); s = MAXVAL / i; for (j = s - !(s & 1); j >= i; j -= 2) { if (!getflag(flags,BITS,i)){ upflag(flags,BITS,i*j); setcomposite(i*j,i); } } } } for (; i <= MAXVAL; i += (f = 6 - f)){ if (!getflag(flags,BITS,i)){ setprime(i); } } } // n を素因数分解する map prime_factorize(ll n) { map res; while (n != 1) { ll prime = min_factor[n]; ll exp = 0; while (min_factor[n] == prime) { ++exp; n /= prime; } res[prime]=exp; } return res; } // n の約数を返す vector divisor(ll n){ vector res; map m=prime_factorize(n); ll N=m.size(); vector bitlen(N+1); ll i=0; for(pair pr:m){ bitlen[i]=pr.second+1; i++; } vector bit(N+1, 0); while(!bit[N]){ ll t=1,i=0; for(pair pr:m){ t*=pow(pr.first,bit[i]); i++; } res.push_back(t); for(ll i=0; ++bit[i]==bitlen[i]; i++)bit[i]=0; } return res; } }; /*-----8<-----library-----8<-----*/ void solve() { ll N; cin>>N; Eratosthenes er(N); vector v(N+1,-1); repeq(i,N){ vector a=er.divisor(i); v[i]=a.size(); } ll minval=INF; repeq(i,N-1){ ll t=i-v[i]; ll s=(N-i)-v[N-i]; chmin(minval,abs(t-s)); } repeq(i,N-1){ ll t=i-v[i]; ll s=(N-i)-v[N-i]; if(minval==(ll)abs(t-s)){ p(i,N-i); } } } signed main() { solve(); return 0; }