#include<bits/stdc++.h> using namespace std; #define ll long long #define pb push_back #define inx int I=h[u],v=edge[I].v;I;I=edge[I].nx,v=edge[I].v inline int read(){int x=0,f=1;char c=getchar();while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}while(c>='0'&&c<='9')x=x*10+c-'0',c=getchar();return x*f;} const int MAXN=300010,Mod=1000000007; struct Edge{int v,nx;}edge[MAXN<<1];int h[MAXN],CNT;void add_side(int u,int v){edge[++CNT]={v,h[u]};h[u]=CNT;edge[++CNT]={u,h[v]};h[v]=CNT;} int n,m,a[MAXN],b[MAXN]; ll sm,ny[MAXN]; ll Pow(ll x,int y){ll rt=1;while(y){if(y&1)rt=rt*x%Mod;x=x*x%Mod,y>>=1;}return rt;} int vis[MAXN],zx,sz,tp; int getsz(int u,int lst){ if(vis[u])return 0; int res=1; for(inx)if(v!=lst){ res+=getsz(v,u); } return res; } int getzx(int u,int lst){ if(vis[u])return 0; int res=1,mx=0; for(inx)if(v!=lst){ int tmp=getzx(v,u); res+=tmp;mx=max(mx,tmp); } mx=max(mx,sz-res); if(mx<tp)tp=mx,zx=u; return res; } ll ans; #define lson (pos<<1) #define rson (pos<<1|1) struct treearray{ ll C[MAXN]; int lb(int x){return x&(-x);} void upd(int x,ll y){for(int i=x;i<=m;i+=lb(i))C[i]=(C[i]+y)%Mod;} ll qry(int x){ll res=0;for(int i=x;i>=1;i-=lb(i))res=(res+C[i])%Mod;return res;} }; struct segmenttree{ treearray t1,t2; void update(int l,int r,ll x){ t1.upd(l,x); t1.upd(r+1,-x); t2.upd(l,x*(l-1)%Mod); t2.upd(r+1,-x*r%Mod+Mod); return ; } ll query(int l,int r){return ((t1.qry(r)*r%Mod-t1.qry(l-1)*(l-1)%Mod-t2.qry(r)+t2.qry(l-1))%Mod+Mod)%Mod;} }D,Y; void count(int u,int lst,int d){ if(vis[u])return; ans=(ans+d*sm%Mod*ny[b[u]-a[u]+1]%Mod*Y.query(a[u],b[u])%Mod)%Mod; ans=(ans+sm%Mod*ny[b[u]-a[u]+1]%Mod*D.query(a[u],b[u])%Mod)%Mod; // cout<<u<<" "<<a[u]<<" "<<b[u]<<":"<<d*sm%Mod*ny[b[u]-a[u]+1]%Mod<<" "<<Y.query(1,1,m,a[u],b[u])%Mod<<" "; // cout<<sm%Mod*ny[b[u]-a[u]+1]%Mod<<" "<<D.query(1,1,m,a[u],b[u])%Mod<<endl; for(inx)if(v!=lst){ count(v,u,d+1); } } void add(int u,int lst,int d,int lf){ if(vis[u])return; D.update(a[u],b[u],(Mod+lf*d*ny[b[u]-a[u]+1]%Mod)%Mod); // cout<<"+"<<u<<" "<<a[u]<<" "<<b[u]<<" "<<d*ny[b[u]-a[u]+1]<<endl; Y.update(a[u],b[u],(Mod+lf*ny[b[u]-a[u]+1]%Mod)%Mod); // cout<<"+"<<u<<" "<<a[u]<<" "<<b[u]<<" "<<ny[b[u]-a[u]+1]<<endl; for(inx)if(v!=lst){ add(v,u,d+1,lf); } } void getans(int u){ Y.update(a[u],b[u],ny[b[u]-a[u]+1]); // cout<<"+"<<u<<" "<<a[u]<<" "<<b[u]<<" "<<ny[b[u]-a[u]+1]<<endl; for(inx)if(!vis[v]){ count(v,u,1); add(v,u,1,1); } for(inx)if(!vis[v]){ add(v,u,1,-1); } Y.update(a[u],b[u],(Mod-ny[b[u]-a[u]+1])%Mod); } void dfz(int u,int lst){ sz=getsz(u,lst);tp=n; int tmp=getzx(u,lst); getans(zx); vis[zx]=1; u=zx; for(inx)if(!vis[v]){ dfz(v,u); } } void slv(){ n=read(); for(int i=1;i<MAXN-5;i++)ny[i]=Pow(i,Mod-2); sm=1; for(int i=1;i<=n;i++)a[i]=read(),b[i]=read(),m=max(m,b[i]),sm=sm*(b[i]-a[i]+1)%Mod; for(int i=1;i<n;i++){ int u=read(),v=read(); add_side(u,v); } dfz(1,1); printf("%lld",ans); } signed main(){ slv(); return 0; }