#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define pii pair<int, int>
#define F first
#define S second
const int N = 100005;
vector<int> a[N];
int w[N], sub[N], used[N];
ll m;
set <pii> s;
void DFS(int node){
used[node] = 1;
sub[node] = w[node];
for(int i : a[node]){
if(!used[i]){
DFS(i);
sub[node] += sub[i];
}
}
}
ll getans(int node){
ll res = sub[node] * (m - sub[node]);
used[node] = 2;
for(int i : a[node]){
if(used[i] != 2){
res += getans(i);
}
}
return res;
}
int DistanceSum(int n, int *x, int *y) {
for(int i = 0; i < n; i++){
s.insert({x[i], y[i]});
}
map<pii, int> mp;
int idx = (*s.begin()).F;
int idy = (*s.begin()).S;
int sz = 1, nn = 1;
s.erase(s.begin());
mp[{idx, idy}] = nn;
while(s.size() > 0){
int curx = (*s.begin()).F;
int cury = (*s.begin()).S;
s.erase(s.begin());
if(curx == idx){
if(cury == idy + sz) {
sz++;
mp[{curx, cury}] = nn;
}
else{
idy = cury;
w[nn] = sz;
sz = 1;
nn++;
mp[{curx, cury}] = nn;
}
}
else{
w[nn] = sz;
sz = 1;
nn++;
idy = cury;
idx = curx;
mp[{curx, cury}] = nn;
}
}
w[nn] = sz;
for(auto i : mp){
int curx = i.F.F;
int cury = i.F.S;
int u = mp[{curx, cury}];
if(mp[{curx - 1, cury}]){
int v = mp[{curx - 1, cury}];
if(mp[{curx - 1, cury}] == mp[{curx - 1, cury - 1}] && mp[{curx, cury}] == mp[{curx, cury - 1}]) continue;
a[u].pb(v);
a[v].pb(u);
}
}
DFS(1);
m = sub[1];
ll ans = getans(1);
for(int i = 1; i <= nn; i++){
a[i].clear();
used[i] = 0;
sub[i] = 0;
w[i] = 0;
}
mp.clear();
for(int i = 0; i < n; i++){
s.insert({y[i], x[i]});
}
idx = (*s.begin()).F;
idy = (*s.begin()).S;
sz = 1, nn = 1;
s.erase(s.begin());
mp[{idx, idy}] = nn;
while(s.size() > 0){
int curx = (*s.begin()).F;
int cury = (*s.begin()).S;
s.erase(s.begin());
if(curx == idx){
if(cury == idy + sz) {
sz++;
mp[{curx, cury}] = nn;
}
else{
idy = cury;
w[nn] = sz;
sz = 1;
nn++;
mp[{curx, cury}] = nn;
}
}
else{
w[nn] = sz;
sz = 1;
nn++;
idy = cury;
idx = curx;
mp[{curx, cury}] = nn;
}
}
w[nn] = sz;
for(auto i : mp){
int curx = i.F.F;
int cury = i.F.S;
int u = mp[{curx, cury}];
if(mp[{curx - 1, cury}]){
int v = mp[{curx - 1, cury}];
if(mp[{curx - 1, cury}] == mp[{curx - 1, cury - 1}] && mp[{curx, cury}] == mp[{curx, cury - 1}]) continue;
a[u].pb(v);
a[v].pb(u);
}
}
DFS(1);
m = sub[1];
return ans + getans(1);
}
/*
11
2 5
2 6
3 3
3 6
4 3
4 4
4 5
4 6
5 3
5 4
5 6
*/
