#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;} #include using mint=atcoder::modint998244353; ostream& operator<<(ostream& os,const mint& v){ return os< 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); rep(i,N){ cin>>a[i]>>b[i]; map mp; j=b[i]; while(j>1){ mp[lpf[j]]++; j/=lpf[j]; } for(auto[p,cnt]:mp){ g[p].emplace_back(modpow(p,cnt),i); } } mint alllcm=1; rep(i,200001){ if(g[i].size()){ vrsort(g[i]); alllcm*=g[i][0].first; } } mint ans; rep(i,N)ans+=a[i]*alllcm/b[i]; debug(ans,alllcm); rep(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]){ debug(val,id); l.emplace_back(b[id]/val%p); } debug(l); auto r=l; rep1(j,l.size())(l[j]*=l[j-1])%=p; brep1(j,r.size())(r[j-1]*=r[j])%=p; debug(l,r); rep(j,g[i].size()){ auto[val,id]=g[i][j]; ll tmp=p/val*a[id]%p; if(j)(tmp*=l[j-1])%=p; if(j+1