#include using namespace std; #define rep(i,n) for(ll i=0;i=0;i--) #define perl(i,r,l) for(ll i=r-1;i>=l;i--) #define fi first #define se second #define pb push_back #define ins insert #define pqueue(x) priority_queue,greater> #define all(x) (x).begin(),(x).end() #define CST(x) cout<; using vvl=vector>; using pl=pair; using vpl=vector; using vvpl=vector; const ll MOD=1000000007; const ll MOD9=998244353; const int inf=1e9+10; const ll INF=4e18; const ll dy[8]={1,0,-1,0,1,1,-1,-1}; const ll dx[8]={0,1,0,-1,1,-1,1,-1}; template inline bool chmax(T &a, T b) { return ((a < b) ? (a = b, true) : (false)); } template inline bool chmin(T &a, T b) { return ((a > b) ? (a = b, true) : (false)); } class osak{ vector res; public: vector prime; osak(long long n){//sieve(n),O(N); res=vector(n); iota(res.begin(), res.end(), 0); for (int i = 2; i*i < n; ++i) { if (res[i] < i) continue; for (int j = i*i; j < n; j += i) if (res[j] == j) res[j] = i; } for(int i = 2; i < n; ++i){ if(res[i]==i)prime.emplace_back(i); } } map factor(int n) { map factor; while (n > 1) { factor[res[n]]++; n /= res[n]; } return factor; } vector divisor(int N){//O(div.size()) map facs=factor(N); vector ret={1}; for(auto p:facs){ ll range=ret.size(); ll now=1; for(int i=0;i= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;} mint operator+(const mint a) const { return mint(*this) += a;} mint operator-(const mint a) const { return mint(*this) -= a;} mint operator*(const mint a) const { return mint(*this) *= a;} mint pow(ll t) const { if (!t) return 1; mint a = pow(t>>1); a *= a; if (t&1) a *= *this; return a; } bool operator==(const mint &p) const { return x == p.x; } bool operator!=(const mint &p) const { return x != p.x; } // for prime mod mint inv() const { return pow(mod-2);} mint& operator/=(const mint a) { return *this *= a.inv();} mint operator/(const mint a) const { return mint(*this) /= a;} }; istream& operator>>(istream& is, mint& a) { return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) { return os << a.x;} using vm=vector; using vvm=vector; int main(){ ll n;cin >> n; osak os(n); map ans; for(int i=1;i