#include<vector>
#include<algorithm>
using namespace std;
typedef long long ll;
struct in
{
ll x, y, Vn, Hn, vc, hc;
in() {}
in(ll a, ll b) : x(a), y(b) {}
};
bool cmp1(const in &a, const in &b)
{
return a.x<b.x || (a.x==b.x && a.y<b.y);
}
bool cmp2(const in &a, const in &b)
{
return a.y<b.y || (a.y==b.y && a.x<b.x);
}
ll n;
in m[100005];
ll Vcnt[100005], Hcnt[100005];
vector<ll> Vlst[100005], Hlst[100005];
ll res;
const ll MOD=1e9;
ll dfs(ll v, ll prev, vector<ll> *lst, ll *cnt)
{
ll s=cnt[v];
for(int i=0 ; i<lst[v].size() ; i++)
{
ll nxt=lst[v][i];
if(nxt!=prev) s+=dfs(nxt,v,lst,cnt);
}
(res+=(n-s)*s)%=MOD;
return s;
}
int DistanceSum(int N, int *X, int *Y)
{
n=N;
for(int i=1 ; i<=n ; i++) m[i].x=X[i-1], m[i].y=Y[i-1];
//make vertical node
sort(m+1,m+1+n,cmp1);
ll ncnt=0;
for(int i=1 ; i<=n ; i++)
{
if(m[i].x!=m[i-1].x || (m[i].x==m[i-1].x && m[i].y-m[i-1].y>1)) ncnt++;
m[i].Vn=ncnt;
Vcnt[ncnt]++;
m[i].vc=Vcnt[ncnt];
}
//make horizontal node and vertical edge
sort(m+1,m+1+n,cmp2);
ncnt=0;
for(int i=1 ; i<=n ; i++)
{
if(m[i].y!=m[i-1].y || (m[i].y==m[i-1].y && m[i].x-m[i-1].x>1)) ncnt++;
m[i].Hn=ncnt;
Hcnt[ncnt]++;
m[i].hc=Hcnt[ncnt];
if(m[i].y==m[i-1].y && m[i].x-m[i-1].x==1 && (m[i].vc==Vcnt[m[i].Vn] || m[i-1].vc==Vcnt[m[i-1].Vn]))
Vlst[m[i].Vn].push_back(m[i-1].Vn), Vlst[m[i-1].Vn].push_back(m[i].Vn);
}
//make horizontal edge
sort(m+1,m+1+n,cmp1);
for(int i=1 ; i<=n ; i++)
{
if(m[i].x==m[i-1].x && m[i].y-m[i-1].y==1 && (m[i].hc==Hcnt[m[i].Hn] || m[i-1].hc==Hcnt[m[i-1].Hn]))
Hlst[m[i].Hn].push_back(m[i-1].Hn), Hlst[m[i-1].Hn].push_back(m[i].Hn);
}
dfs(1,0,Vlst,Vcnt);
dfs(1,0,Hlst,Hcnt);
int ret=res;
return ret;
}
