#include <bits/stdc++.h>
// just testing
#define ff first
#define ss second
using namespace std;
const int maxn = 1e5+10;
const int mod = 1e9;
typedef pair<int, int> pii;
int n;
pii pt[maxn];
int vert[maxn], A[maxn];
vector<int> grafo[maxn];
map<pii, int> ind, conecta;
int nivel[maxn];
bool comp(pii a, pii b)
{
if (a.ss == b.ss) return a.ff < b.ff;
return a.ss < b.ss;
}
void init()
{
ind.clear(); conecta.clear();
for (int i = 1; i <= n; i++)
grafo[i].clear(), A[i] = 0;
}
int make_tree1(void)
{
sort(pt+1, pt+n+1);
for (int i = 1; i <= n; i++)
ind[pt[i]] = i;
int atual = 1;
vert[1] = 1, A[1] = 1;
for (int i = 2; i <= n; i++)
{
if (pt[i].ff > pt[i-1].ff || pt[i].ss-pt[i-1].ss > 1)
{
vert[i] = ++atual;
A[atual]++;
continue;
}
vert[i] = atual;
A[atual]++;
}
for (int i = 1; i <= n; i++)
{
if (ind.find({pt[i].ff-1, pt[i].ss}) != ind.end())
{
int u = i, v = ind[{pt[i].ff-1, pt[i].ss}];
u = vert[u], v = vert[v];
if (!conecta[{u, v}])
{
conecta[{u, v}] = conecta[{v, u}] = 1;
grafo[u].push_back(v), grafo[v].push_back(u);
}
}
}
return atual;
}
int make_tree2(void)
{
sort(pt+1, pt+n+1, comp);
for (int i = 1; i <= n; i++)
ind[pt[i]] = i;
int atual = 1;
vert[1] = 1, A[1] = 1;
for (int i = 2; i <= n; i++)
{
if (pt[i].ss > pt[i-1].ss || pt[i].ff-pt[i-1].ff > 1)
{
vert[i] = ++atual;
A[atual]++;
continue;
}
vert[i] = atual;
A[atual]++;
}
for (int i = 1; i <= n; i++)
{
if (ind.find({pt[i].ff, pt[i].ss-1}) != ind.end())
{
int u = i, v = ind[{pt[i].ff, pt[i].ss-1}];
u = vert[u], v = vert[v];
if (!conecta[{u, v}])
{
conecta[{u, v}] = conecta[{v, u}] = 1;
grafo[u].push_back(v), grafo[v].push_back(u);
}
}
}
return atual;
}
void dfs(int u, int p)
{
for (auto v: grafo[u])
{
if (v == p) continue;
nivel[v] = nivel[u]+1;
dfs(v, u);
}
}
int DistanceSum(int N, int *X, int *Y)
{
int ans = 0;
n = N;
for (int i = 1; i <= n; i++)
pt[i] = {X[i-1], Y[i-1]};
int m = make_tree1();
for (int i = 1; i <= m; i++)
{
nivel[i] = 0;
dfs(i, 0);
for (int j = 1; j < i; j++)
{
long long soma = (1ll*A[j]*nivel[j]*A[i])%mod;
ans = (ans+soma)%mod;
}
}
init();
m = make_tree2();
for (int i = 1; i <= m; i++)
{
nivel[i] = 0;
dfs(i, 0);
for (int j = 1; j < i; j++)
{
long long soma = (1ll*A[j]*nivel[j]*A[i])%mod;
ans = (ans+soma)%mod;
}
}
return ans;
}
