#include<iostream> #include<cstring> #include<cstdio> #include<vector> #include<queue> #define int LL #define LL long long #define mod 1000000007 #define MAXN 500010 using namespace std; struct edge { int u,v,nxt; #define u(x) ed[x].u #define v(x) ed[x].v #define n(x) ed[x].nxt #define u2(x) ed2[x].u #define v2(x) ed2[x].v #define n2(x) ed2[x].nxt }ed[1000000],ed2[1000000]; int first[MAXN],num_e; #define f(x) first[x] int first2[MAXN],num_e2; #define f2(x) first2[x] int n,du[MAXN]; int x[MAXN],r[MAXN]; int dfn[MAXN],low[MAXN],cnt; int stack[MAXN],top; int belong[MAXN],tot; bool v[MAXN]; vector<int> scc[MAXN]; void tarjan(int x) { dfn[x]=low[x]=++cnt; stack[++top]=x;v[x]=1; for(int i=f(x);i;i=n(i)) if(!dfn[v(i)])tarjan(v(i)),low[x]=min(low[x],low[v(i)]); else if(v[v(i)])low[x]=min(low[x],dfn[v(i)]); if(low[x]==dfn[x]) { ++tot;v[x]=0; while(stack[top]!=x) { v[stack[top]]=0; belong[stack[top]]=tot; scc[tot].push_back(stack[top--]); } belong[x]=tot; scc[tot].push_back(stack[top--]); } } int L[MAXN],R[MAXN]; inline void add(int u,int v); inline void add2(int u,int v); signed main() { // freopen("in.txt","r",stdin); scanf("%lld",&n); for(int i=1;i<=n;i++) scanf("%lld%lld",&x[i],&r[i]); for(int i=1;i<=n;i++) { for(int j=i-1;j;j--) if(x[i]<=x[j]+r[j]){add(i,j);break;} for(int j=i+1;j<=n;j++)if(x[i]>=x[j]-r[j]){add(i,j);break;} } for(int i=1;i<=n;i++) if(!dfn[i])tarjan(i); for(int i=1;i<=num_e;i++) if(belong[u(i)]!=belong[v(i)]) add2(belong[u(i)],belong[v(i)]),du[belong[v(i)]]++; memset(L,0x7f,sizeof(L)); memset(R,-0x7f,sizeof(R)); for(int i=1;i<=tot;i++) for(int j=0;j<scc[i].size();j++) L[i]=min(L[i],scc[i][j]),R[i]=max(R[i],scc[i][j]); queue<int> q; for(int i=1;i<=tot;i++) if(!du[i])q.push(i); while(!q.empty()) { int k=q.front();q.pop(); for(int i=f2(k);i;i=n2(i)) { du[v2(i)]--; if(!du[v2(i)])q.push(v2(i)); L[v2(i)]=min(L[v2(i)],L[k]); R[v2(i)]=max(R[v2(i)],R[k]); } } LL ans=0; for(int i=1;i<=n;i++) ans=(ans+i*(R[belong[i]]-L[belong[i]]+1))%mod; printf("%lld\n",ans); } inline void add(int u,int v) { ++num_e; u(num_e)=u; v(num_e)=v; n(num_e)=f(u); f(u)=num_e; } inline void add2(int u,int v) { ++num_e2; u2(num_e2)=u; v2(num_e2)=v; n2(num_e2)=f2(u); f2(u)=num_e2; } 