#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9;
ll ans = 0;
int cur_seg = 0;
int seg_ind[100000];
pii seg[200000];
vi graph[200000];
ll n;
int dfs_ans(int v, int pop)
{
ll val = seg[v].ss - seg[v].ff+1;
forall(it,graph[v])
{
if(pop != it)
{
ll new_val = dfs_ans(it,v);
ans += new_val * (n - new_val);
val += new_val;
}
}
ans += val * (n-val);
return val;
}
void solve(int* X, int* Y)
{
map<pii,int> ind_map;
rep(i,n) ind_map[{X[i],Y[i]}] = i;
int beg_seg = cur_seg;
rep(i,n)
{
if(ind_map.find({X[i],Y[i]+1}) == ind_map.end())
{
int cur_y = Y[i];
while(ind_map.find({X[i],cur_y}) != ind_map.end())
{
seg_ind[ind_map[{X[i],cur_y}]] = cur_seg;
cur_y--;
}
seg[cur_seg] = {cur_y+1,Y[i]};
cur_seg++;
}
}
set<pii> existing_edges;
rep(i,n)
{
if(ind_map.find({X[i]-1,Y[i]}) != ind_map.end() && existing_edges.find({seg_ind[i],seg_ind[ind_map[{X[i]-1,Y[i]}]]}) == existing_edges.end())
{
int new_ = ind_map[{X[i]-1,Y[i]}];
graph[seg_ind[i]].pb(seg_ind[new_]);
graph[seg_ind[new_]].pb(seg_ind[i]);
existing_edges.insert({seg_ind[i],seg_ind[new_]});
existing_edges.insert({seg_ind[new_],seg_ind[i]});
}
if(ind_map.find({X[i]+1,Y[i]}) != ind_map.end() && existing_edges.find({seg_ind[i],seg_ind[ind_map[{X[i]+1,Y[i]}]]}) == existing_edges.end())
{
int new_ = ind_map[{X[i]+1,Y[i]}];
graph[seg_ind[i]].pb(seg_ind[new_]);
graph[seg_ind[new_]].pb(seg_ind[i]);
existing_edges.insert({seg_ind[i],seg_ind[new_]});
existing_edges.insert({seg_ind[new_],seg_ind[i]});
}
}
dfs_ans(beg_seg,beg_seg);
}
int DistanceSum(int N, int *X, int *Y)
{
n = N;
solve(X,Y);
solve(Y,X);
return (ans/2)%MOD;
}
