#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define X first #define Y second #define pb push_back #define rep(X,Y) for (int X = 0;X < (int)(Y);++X) #define reps(X,S,Y) for (int X = (int)(S);X < (int)(Y);++X) #define rrep(X,Y) for (int X = (int)(Y)-1;X >=0;--X) #define rreps(X,S,Y) for (int X = (int)(Y)-1;X >= (int)(S);--X) #define repe(X,Y) for (X = 0;X < (Y);++X) #define peat(X,Y) for (;X < (Y);++X) #define all(X) X.begin(),X.end() #define rall(X) X.rbegin(),X.rend() #define eb emplace_back #define UNIQUE(X) X.erase(unique(all(X)),X.end()) #define Endl endl #define NL <<"\n" #define cauto const auto using namespace std; using ll=long long; using pii=pair; using pll=pair; template using vv=vector>; template inline bool MX(T &l,const T &r){return l inline bool MN(T &l,const T &r){return l>r?l=r,1:0;} //#undef NUIP #ifdef NUIP #include "benri.h" #else #define out(args...) #endif void ouT(ll x,int d=3){auto re=to_string(x);if((int)re.size()>d) re=x>0?"oo":"-oo";cout<vector table(int n, T v){ return vector(n, v);} template auto table(int n, Args... args){auto val = table(args...); return vector(n, move(val));} #endif template pair operator+(const pair &p,const pair &q){ return {p.X+q.X,p.Y+q.Y};} template pair& operator+=(pair &p,const pair &q){ p.X+=q.X; p.Y+=q.Y; return p;} template pair operator-(const pair &p,const pair &q){ return {p.X-q.X,p.Y-q.Y};} template pair& operator-=(pair &p,const pair &q){ p.X-=q.X; p.Y-=q.Y; return p;} template istream& operator>>(istream &is, pair &p){ is>>p.X>>p.Y; return is;} template T read(){ T re; cin>>re; return re;} template T read(const T &dec){ T re; cin>>re; return re-dec;} template vector readV(const int sz){ vector re(sz); for(auto &x:re) x=read(); return re;} template vector readV(const int sz, const T &dec){ vector re(sz); for(auto &x:re) x=read(dec); return re;} vv readG(const int &n,const int &m){ vv g(n); rep(_,m){ cauto a=read(1),b=read(1); g[a].pb(b); g[b].pb(a);} return g;} vv readG(const int &n){ return readG(n,n-1);} vv readD(const int &n,const int &m){ vv g(n); rep(_,m){ cauto a=read(1),b=read(1); g[a].pb(b); } return g;} vv readD(const int &n){ return readD(n,n-1);} template vv> readG(const int &n,const int &m){ vv> g(n); rep(_,m){ cauto a=read(1),b=read(1); cauto c=read(); g[a].eb(b,c); g[b].eb(a,c);} return g;} template vv> readG(const int &n){ return readG(n,n-1);} template vv> readD(const int &n,const int &m){ vv> g(n); rep(_,m){ cauto a=read(1),b=read(1); cauto c=read(); g[a].eb(b,c); } return g;} template vv> readD(const int &n){ return readD(n,n-1);} #ifdef __cpp_deduction_guides template vector readT(int n, T v){ return readV(n,v);} template auto readT(int n, Args... args){ vector re(1,readT(args...));rep(_,n-1) re.eb(readT(args...)); return re;} template void read_tuple_impl(istream &is, Tuple& t, index_sequence){((is >> get(t)), ...);} template auto& operator>>(istream &is, tuple& t){ read_tuple_impl(is, t, index_sequence_for{}); return is;} template bool erase(multiset &st, const T &v){if(cauto it=st.find(v); it==st.end()) return false; else{ st.erase(it); return true;}} #endif #ifdef __cpp_init_captures template void addadd(T& t1, const T& t2, integer_sequence){ cauto l = { (get(t1) += get(t2), 0)... }; (void)l;} template tuple& operator += (tuple& lhs, const tuple& rhs){ addadd(lhs, rhs, index_sequence_for{}); return lhs;} template tuple operator +(tuple lhs, const tuple& rhs){ return lhs += rhs;} template void subsub(T& t1, const T& t2, integer_sequence){ cauto l = { (get(t1) -= get(t2), 0)... }; (void)l;} template tuple& operator -= (tuple& lhs, const tuple& rhs){ subsub(lhs, rhs, index_sequence_for{}); return lhs;} template tuple operator - (tuple lhs, const tuple& rhs){ return lhs -= rhs;} #endif #define TT cauto TTT=read();rep(_,TTT) struct sorted_impl{templatefriend vectoroperator-(vectora,sorted_impl){sort(all(a));return a;}friend string operator-(string a,sorted_impl){sort(all(a));return a;}}sorted;struct reversed_impl{templatefriend vectoroperator-(vector a,reversed_impl){reverse(all(a));return a;}friend string operator-(string a,reversed_impl){reverse(all(a));return a;}}reversed;struct distinct_impl{templatefriend vectoroperator-(vector a,distinct_impl){sort(all(a));UNIQUE(a);return a;}}distinct;templatestruct sortedWith{const S f;sortedWith(const S &f):f(f){}templatefriend vectoroperator-(vector a,const sortedWith&b){sort(all(a),[&](cauto&i,cauto&j){return b.f(i)int operator/(const T&v,const vector&vs){return lower_bound(all(vs),v)-vs.begin();} vector Inds(const int n){vector inds(n);iota(all(inds),0);return inds;} const ll MOD=1e9+7; //998244353; struct UF{ vector data; UF(const int &size):data(size,-1){} int unite(int x, int y){ x=root(x); y=root(y); if(x==y) return 0; if(-data[y]>-data[x]) swap(x,y); data[x]+=data[y]; data[y]=x; return y+1; } bool findSet(const int &x, const int &y){ return root(x)==root(y);} int root(const int &x){ return data[x]<0?x:data[x]=root(data[x]);} int size(const int &x){ return -data[root(x)];} int size(){ return count_if(all(data),[](const int &x){ return x<0;});}; //unverified int operator()(const int &x, const int &y){ return unite(x,y);} // int operator()(const pii &xy){ return unite(xy.X,xy.Y);} int operator[](const int &x){ return root(x);} bool operator[](const pii &xy){ return findSet(xy.X,xy.Y);} }; ll solve(const vector &vs){ const int n=vs.size(); vector> es; rep(i,n)rep(j,min(800,i)) es.eb(1ll*vs[i]/__gcd(vs[i],vs[j])*vs[j], i,j); sort(all(es)); out(es,1); ll re=0; UF uf(n); for(cauto &[d,x,y]:es)if(uf(x,y)) re+=d; return re; } int main(){ ios_base::sync_with_stdio(false); cin.tie(0); cout< vs(n); iota(all(vs),2); ll re=0; set st; for(cauto &v:vs-sorted-reversed){ if(st.emplace(v).Y){ for(int i=v+v;i<112345;i+=v)if(st.erase(i)) re+=i; }else{ re+=v; } } out(st.size(),1); re+=solve(vector(all(st))); cout<