#include using namespace std; using Int = long long; template inline void chmin(T1 &a,T2 b){if(a>b) a=b;} template inline void chmax(T1 &a,T2 b){if(a struct Mint{ static constexpr T mod = MOD; T v; Mint():v(0){} Mint(signed v):v(v){} Mint(long long t){v=t%MOD;if(v<0) v+=MOD;} Mint pow(long long k){ Mint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } static Mint add_identity(){return Mint(0);} static Mint mul_identity(){return Mint(1);} Mint inv(){return pow(MOD-2);} Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;} Mint& operator/=(Mint a){return (*this)*=a.inv();} Mint operator+(Mint a) const{return Mint(v)+=a;}; Mint operator-(Mint a) const{return Mint(v)-=a;}; Mint operator*(Mint a) const{return Mint(v)*=a;}; Mint operator/(Mint a) const{return Mint(v)/=a;}; Mint operator-() const{return v?Mint(MOD-v):Mint(v);} bool operator==(const Mint a)const{return v==a.v;} bool operator!=(const Mint a)const{return v!=a.v;} bool operator <(const Mint a)const{return v constexpr T Mint::mod; template ostream& operator<<(ostream &os,Mint m){os< V compress(V v){ sort(v.begin(),v.end()); v.erase(unique(v.begin(),v.end()),v.end()); return v; } template map dict(const vector &v){ map res; for(Int i=0;i<(Int)v.size();i++) res[v[i]]=i; return res; } map dict(const string &v){ return dict(vector(v.begin(),v.end())); } template struct FormalPowerSeries{ using Poly = vector; using Conv = function; Conv conv; FormalPowerSeries(Conv conv):conv(conv){} Poly pre(const Poly &as,Int deg){ return Poly(as.begin(),as.begin()+min((Int)as.size(),deg)); } Poly add(Poly as,Poly bs){ Int sz=max(as.size(),bs.size()); Poly cs(sz,T(0)); for(Int i=0;i<(Int)as.size();i++) cs[i]+=as[i]; for(Int i=0;i<(Int)bs.size();i++) cs[i]+=bs[i]; return cs; } Poly sub(Poly as,Poly bs){ Int sz=max(as.size(),bs.size()); Poly cs(sz,T(0)); for(Int i=0;i<(Int)as.size();i++) cs[i]+=as[i]; for(Int i=0;i<(Int)bs.size();i++) cs[i]-=bs[i]; return cs; } Poly mul(Poly as,Poly bs){ return conv(as,bs); } Poly mul(Poly as,T k){ for(auto &a:as) a*=k; return as; } // F(0) must not be 0 Poly inv(Poly as,Int deg){ assert(as[0]!=T(0)); Poly rs({T(1)/as[0]}); for(Int i=1;ias.size()) return Poly(); reverse(as.begin(),as.end()); reverse(bs.begin(),bs.end()); Int need=as.size()-bs.size()+1; Poly ds=pre(mul(as,inv(bs,need)),need); reverse(ds.begin(),ds.end()); return ds; } // F(0) must be 1 Poly sqrt(Poly as,Int deg){ assert(as[0]==T(1)); T inv2=T(1)/T(2); Poly ss({T(1)}); for(Int i=1;i class Enumeration{ private: static vector fact,finv,invs; public: static void init(Int n){ n=min(n,M::mod-1); Int m=fact.size(); if(n=m;i--) finv[i-1]=finv[i]*M(i); for(Int i=m;i<=n;i++) invs[i]=finv[i]*fact[i-1]; } static M Fact(Int n){ init(n); return fact[n]; } static M Finv(Int n){ init(n); return finv[n]; } static M Invs(Int n){ init(n); return invs[n]; } static M C(Int n,Int k){ if(n > D(Int n,Int m){ vector< vector > dp(n+1,vector(m+1,0)); dp[0][0]=M(1); for(Int i=0;i<=n;i++){ for(Int j=1;j<=m;j++){ if(i-j>=0) dp[i][j]=dp[i][j-1]+dp[i-j][j]; else dp[i][j]=dp[i][j-1]; } } return dp; } static M B(Int n,Int k){ if(n==0) return M(1); k=min(k,n); init(k); vector dp(k+1); dp[0]=M(1); for(Int i=1;i<=k;i++) dp[i]=dp[i-1]+((i&1)?-finv[i]:finv[i]); M res(0); for(Int i=1;i<=k;i++) res+=M(i).pow(n)*finv[i]*dp[k-i]; return res; } static M montmort(Int n){ init(n); M res(0); for(Int k=2;k<=n;k++){ if(k&1) res-=finv[k]; else res+=finv[k]; } return res*=fact[n]; } static M LagrangePolynomial(vector &y,M t){ Int n=y.size()-1; if(t.v<=n) return y[t.v]; init(n+1); vector dp(n+1,1),pd(n+1,1); for(Int i=0;i0;i--) pd[i-1]=pd[i]*(t-M(i)); M res(0); for(Int i=0;i<=n;i++){ M tmp=y[i]*dp[i]*pd[i]*finv[i]*finv[n-i]; if((n-i)&1) res-=tmp; else res+=tmp; } return res; } }; template vector Enumeration::fact=vector(); template vector Enumeration::finv=vector(); template vector Enumeration::invs=vector(); constexpr Int bmds(Int x){ const Int v[] = {1012924417, 924844033, 998244353, 897581057, 645922817}; return v[x]; } constexpr Int brts(Int x){ const Int v[] = {5, 5, 3, 3, 3}; return v[x]; } template struct NTT{ static constexpr Int md = bmds(X); static constexpr Int rt = brts(X); using M = Mint; vector< vector > rts,rrts; void ensure_base(Int n){ if((Int)rts.size()>=n) return; rts.resize(n);rrts.resize(n); for(Int i=1;i &as,bool f,Int n=-1){ if(n==-1) n=as.size(); assert((n&(n-1))==0); ensure_base(n); for(Int i=0,j=1;j+1>1;k>(i^=k);k>>=1); if(i>j) swap(as[i],as[j]); } for(Int i=1;i multiply(vector as,vector bs){ Int need=as.size()+bs.size()-1; Int sz=1; while(sz multiply(vector as,vector bs){ vector am(as.size()),bm(bs.size()); for(Int i=0;i<(Int)am.size();i++) am[i]=M(as[i]); for(Int i=0;i<(Int)bm.size();i++) bm[i]=M(bs[i]); vector cm=multiply(am,bm); vector cs(cm.size()); for(Int i=0;i<(Int)cs.size();i++) cs[i]=cm[i].v; return cs; } }; template constexpr Int NTT::md; template constexpr Int NTT::rt; struct ArbitraryModConvolution{ using ll = long long; static NTT<0> ntt0; static NTT<1> ntt1; static NTT<2> ntt2; static constexpr Int pow(Int a,Int b,Int md){ Int res=1; a=a%md; while(b){ if(b&1) res=(ll)res*a%md; a=(ll)a*a%md; b>>=1; } return res; } static constexpr Int inv(Int x,Int md){ return pow(x,md-2,md); } inline void garner(Int &c0,Int c1,Int c2,Int m01,Int MOD){ static constexpr Int r01=inv(ntt0.md,ntt1.md); static constexpr Int r02=inv(ntt0.md,ntt2.md); static constexpr Int r12=inv(ntt1.md,ntt2.md); c1=(ll)(c1-c0)*r01%ntt1.md; if(c1<0) c1+=ntt1.md; c2=(ll)(c2-c0)*r02%ntt2.md; c2=(ll)(c2-c1)*r12%ntt2.md; if(c2<0) c2+=ntt2.md; c0+=(ll)c1*ntt0.md%MOD; if(c0>=MOD) c0-=MOD; c0+=(ll)c2*m01%MOD; if(c0>=MOD) c0-=MOD; } inline void garner(vector< vector > &cs,Int MOD){ Int m01 =(ll)ntt0.md*ntt1.md%MOD; Int sz=cs[0].size(); for(Int i=0;i multiply(vector as,vector bs,Int MOD){ vector< vector > cs(3); cs[0]=ntt0.multiply(as,bs); cs[1]=ntt1.multiply(as,bs); cs[2]=ntt2.multiply(as,bs); size_t sz=as.size()+bs.size()-1; for(auto& v:cs) v.resize(sz); garner(cs,MOD); return cs[0]; } template decltype(auto) multiply(vector< Mint > am, vector< Mint > bm){ using M = Mint; vector as(am.size()),bs(bm.size()); for(Int i=0;i<(Int)as.size();i++) as[i]=am[i].v; for(Int i=0;i<(Int)bs.size();i++) bs[i]=bm[i].v; vector cs=multiply(as,bs,MOD); vector cm(cs.size()); for(Int i=0;i<(Int)cm.size();i++) cm[i]=M(cs[i]); return cm; } }; NTT<0> ArbitraryModConvolution::ntt0; NTT<1> ArbitraryModConvolution::ntt1; NTT<2> ArbitraryModConvolution::ntt2; //INSERT ABOVE HERE signed main(){ Int n; cin>>n; vector as(n),bs(n); for(Int i=0;i>as[i]>>bs[i]; vector vs; for(Int a:as) vs.emplace_back(a); for(Int b:bs) vs.emplace_back(b); vs.emplace_back(0); vs.emplace_back(1e9+6); vs=compress(vs); auto dc=dict(vs); Int sz=dc.size(); const Int MOD = 1e9+7; using M = Mint; ArbitraryModConvolution arb; FormalPowerSeries FPS([&](auto as,auto bs){return arb.multiply(as,bs);}); using Poly = FormalPowerSeries::Poly; Poly sum({1,1,500000004,333333336,208333335,933333340,384722225,953769848,884027784,28425375,878389832,120295265,667416506,229082322,168690037,792301837,189791907,537322580,270492550,482909819,434964639,603347984,256069033,40542057,910866921,438756389,689225591,456092267,413439436,942741942,190664686,782031312,604476028,573671381,838163729,26381583,992375502,930241799,68659206,750162938,475025082,44106509,953003110,354749308,929548052,773716788,337410579,936852063,239751572,561034786,757300345,866130835,553348107,173690227,339768055,709994974,599133150,808467741,396950722,936881852,933909478,737746550,781678380,976953545,580850150,325446247,537865815,281759879,678254613,501070706,851777585,443897119,629314534,760221421,466210161,508261591,65379122,70860701,553561602,854155236,407075847,92305888,282144425,99940577,300342438,587223921,290386237,874023958,985911658,291238936,785218916,678035252,407108295,192101397,507631876,885193819,934834163,385372845,417450165,966951672,684237800,52565350,530411501,135801688,482549358,210734100,761667073,954034475,693540720,576600855,148510276,919026764,583465058,956106104,181054957,41348431,224860616,517912143,860599260,727279538,906355640,153963332,118864415,34582699,44891509,32565076,105784827,928923967,903694428,235385416,883778964,689231689,547905546,909455137,465865460,662952760,195582959,432129855,680896262,758700879,501176266,776382822,454182726,365978689,459511347,816227295,999967985,931726294,294000060,267169976,42254724,349482774,808670797,253898299,508920118,703775403,785503876,423332329,660157859,247972241,450442033,165002242,361442380,392196376,978825741,920083817,560637228,355209713,832930192,440150331,375967478,305763913,635609914,188334856,10887821,335431951,444798249,529525353,226380424,33966925,136881343,434803890,922586534,569205127,117755704,850230335,9409131,93257910,499343559,777515079,650212468,412857608,653792744,679126849,627912655,420312949,612153221,845955439,166961824,673224688,890626117,315980351,994489857,197421005,255024280,293965643,551312195,954953948,756212493,145912941,421627841,799494402,930555555,355649848,186846433,48886853,726884935,842271550,621329810,400463499,99728277,259919265,910183168,345461687,647722720,465173355,355332005,670027204,429411872,891988152,9169256,451160948,499408796,131168601,198918642,129056918,498922473,98755571,915188909,895498700,154447049,565728210,321328855,10010840,606569580,973703597,842226469,741226137,421029601,247331280,864146768,199266677,950280814,999665342,469919529,13609624}); /* const Int deg = 1<<8; { for(Int l=0;l; E::init(deg); for(Int i=0;i > dp(n+1,vector(sz,0)); for(Int j=0;j+1 > nx(n+1,vector(sz,0)); if(i&1){ for(Int l=1;l=0;k--) nx[1][k]+=sum[l]*dp[l][j] *M(as[i]<=vs[k]&&vs[k+1]<=bs[i])*M(vs[k+1]-vs[k])*rev; } } } swap(dp,nx); } M ans{0}; for(Int i=1;i<=n;i++) for(Int j=0;j+1