#pragma GCC target("avx") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include // #include // #include // #include // using namespace __gnu_pbds; // #include // namespace multiprecisioninteger = boost::multiprecision; // using cint=multiprecisioninteger::cpp_int; using namespace std; using ll=long long; using datas=pair; using ddatas=pair; using tdata=pair; using vec=vector; using mat=vector; using pvec=vector; using pmat=vector; // using llset=tree,rb_tree_tag,tree_order_statistics_node_update>; #define For(i,a,b) for(i=a;i<(ll)b;++i) #define bFor(i,b,a) for(i=b,--i;i>=(ll)a;--i) #define rep(i,N) For(i,0,N) #define rep1(i,N) For(i,1,N) #define brep(i,N) bFor(i,N,0) #define brep1(i,N) bFor(i,N,1) #define all(v) (v).begin(),(v).end() #define allr(v) (v).rbegin(),(v).rend() #define vsort(v) sort(all(v)) #define vrsort(v) sort(allr(v)) #define uniq(v) vsort(v),(v).erase(unique(all(v)),(v).end()) #define endl "\n" #define popcount __builtin_popcountll #define eb emplace_back #define print(x) cout< ostream& operator<<(ostream& os,const pair& p){return os<<"("< ostream& operator<<(ostream& os,const vector& v){ os<<"{";bool f=false; for(auto& x:v){if(f)os<<",";os< ostream& operator<<(ostream& os,const set& v){ os<<"{";bool f=false; for(auto& x:v){if(f)os<<",";os< ostream& operator<<(ostream& os,const multiset& v){ os<<"{";bool f=false; for(auto& x:v){if(f)os<<",";os< ostream& operator<<(ostream& os,const map& v){ os<<"{";bool f=false; for(auto& x:v){if(f)os<<",";os< inline bool chmax(T& a,const T b){bool x=a inline bool chmin(T& a,const T b){bool x=a>b;if(x)a=b;return x;} #ifdef DEBUG void debugg(){cout<void debugg(const T& x,const Args&... args){cout<<" "<sync_with_stdio(0); cout<size;--i)modncrlistm[i-1]=modncrlistm[i]*i%mod; } return modncrlistp[n]*modncrlistm[r]%mod*modncrlistm[n-r]%mod; } ll modpow(ll a,ll n,const ll m=mod){ if(n<0)return 0; ll res=1; while(n>0){ if(n&1)res=res*a%m; a=a*a%m; n>>=1; } return res; } constexpr ll gcd(const ll a,const ll b) noexcept{return (!b)?abs(a):(a%b==0)?abs(b):gcd(b,a%b);} constexpr ll lcm(const ll a,const ll b) noexcept{return a/gcd(a,b)*b;} struct unionfind{ private: int maxN; vector par,treesize; public:unionfind(int N) :maxN(N),par(N),treesize(N,1){ for(int i=0;itreesize[y])swap(x,y); par[x]=y; treesize[y]+=treesize[x]; return true; } bool merge(pair v){ return merge(v.first,v.second); } bool parcheck(int x,int y){ return root(x)==root(y); } bool parcheck(pair v){ return parcheck(v.first,v.second); } int size(int x){ return treesize[root(x)]; } void clear(){ treesize.assign(maxN,1); for(int i=0;i> groups(){ vector> res(maxN); for(int i=0;i> res2; for(vector x:res){ if(x.size())res2.emplace_back(x); } return res2; } }; struct HLD{ private: //無向木であること! vector> g; int fdfs(int now,int p,int depth){ int d=0; dep[now]=depth; par[now]=p; for(size_t i=0;i+1 par,nxt,in,out,ETlist,dep; HLD(vector> G,int first=0):g(G),par(G.size()),nxt(G.size()),in(G.size()),out(G.size()){ ETlist.reserve(G.size()); init(first); }; HLD(int N):g(N),par(N),nxt(N),in(N),out(N),dep(N){ETlist.reserve(N);}; void add_edge(int a,int b){ g[a].emplace_back(b); g[b].emplace_back(a); } void init(int first=0){ { int d=0;par[first]=-1; for(auto& x:g[first])if(chmax(d,fdfs(x,first,1)))swap(x,g[first][0]); } nxt[first]=first; sdfs(first); } int la(int x,int k){ int y=nxt[x]; if(in[x]-in[y]>=k)return ETlist[in[x]-k]; if(y==0)return 0; return la(par[y],k-(in[x]-in[y])-1); } int lca(int a,int b){ if(in[a]>in[b])swap(a,b); if(nxt[a]==nxt[b])return a; return lca(a,par[nxt[b]]); } }; #include using mint=atcoder::modint998244353; ostream& operator<<(ostream& os,const mint& v){ return os< pair> diameter(const vector>>& g){ int N=g.size(); Edge *dist,LIM=numeric_limits::max(); dist=new Edge[N]; fill(dist,dist+N,LIM); queue que; que.emplace(dist[0]=0); while(!que.empty()){ auto now=que.front(); for(auto x:g[now]){ if(dist[x.second]==LIM){ dist[x.second]=dist[now]+x.first; que.emplace(x.second); } } que.pop(); } Ver f=max_element(dist,dist+N)-dist; fill(dist,dist+N,LIM); dist[f]=0; que.emplace(f); Ver *par=new Ver[N]; while(!que.empty()){ auto now=que.front(); for(auto x:g[now]){ if(dist[x.second]==LIM){ par[x.second]=now; dist[x.second]=dist[now]+x.first; que.emplace(x.second); } } que.pop(); } Ver s=max_element(dist,dist+N)-dist; Edge ans=dist[s]; vector res(1,s); while(s!=f)res.emplace_back(s=par[s]); delete[] par; delete[] dist; return pair>(ans,res); } vector linear_sieve(int N){ vector p,lpf(N+1,0); for(int i=2;i<=N;++i){ if(lpf[i]==0){ p.emplace_back(i); lpf[i]=i; } for(auto x:p){ if(x>lpf[i]||i*x>N)break; lpf[i*x]=x; } } return lpf; } ll N,M,K,H,W,A,B,C,D; string s,t; int main(){ // startupcpp(); auto lpf=linear_sieve(200000); pmat g(200001); ll i,j; cin>>N; vec a(N),b(N); mat bp(N); rep(i,N){ cin>>a[i]>>b[i]; map mp; j=b[i]; while(j>1){ bp[i].emplace_back(lpf[j]); mp[lpf[j]]++; j/=lpf[j]; } uniq(bp[i]); for(auto[p,cnt]:mp){ g[p].emplace_back(modpow(p,cnt),i); } } mint allprod=1; rep(i,200001){ if(g[i].size()){ vrsort(g[i]); allprod*=g[i][0].first; } } debug(allprod); mint ans; rep(i,N){ auto res=allprod*a[i]; for(auto p:bp[i])res/=gcd(b[i],g[p][0].first); ans+=res; } debug(ans,allprod); rep1(i,200001){ if(g[i].empty())continue; ll p=g[i][0].first,s=0; vec l; l.reserve(g[i].size()); for(auto [val,id]:g[i])l.emplace_back(b[id]/val%p); auto r=l; rep1(j,l.size())(l[j]*=l[j-1])%=p; brep1(j,r.size())(r[j-1]*=r[j])%=p; for(auto x:g[i]){ auto id=x.second; ll tmp=a[id]%p; if(id)(tmp*=l[id-1])%=p; if(id+1=p)s-=p; } debug(s,p); ans/=gcd(s,p); allprod/=gcd(s,p); } print(ans<<" "<