#include <bits/stdc++.h>
#define ll long long
#define ld long double
#define pii pair<int, int>
#define pll pair<ll, ll>
#define vt vector
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define sz(x) (int) (x).size()
#pragma GCC optimize ("O3")
#pragma GCC optimize ("O2")
#define F first
#define S second
//#define endl '\n'
//#define int long long
const int MOD = 1e9;
using namespace std;
map<pii, bool> filled;
map<pii, int> dist;
int bfs(pii start, int i)
{
dist.clear();
for(auto x : filled)
if (x.S) dist[x.F] = INT_MAX;
queue<pii> q;
q.push(start);
dist[start] = 0;
while(!q.empty())
{
pii v = q.front();
q.pop();
int d = dist[{v.F, v.S}];
if (filled[{v.F + 1, v.S}])
{
if (dist[{v.F + 1, v.S}] > d + 1)
q.push({v.F + 1, v.S}), dist[{v.F + 1, v.S}] = d + 1;
}
if (filled[{v.F, v.S + 1}])
{
if (dist[{v.F, v.S + 1}] > d + 1)
q.push({v.F, v.S + 1}), dist[{v.F, v.S + 1}] = d + 1;
}
if (filled[{v.F - 1, v.S}])
{
if (dist[{v.F - 1, v.S}] > d + 1)
q.push({v.F - 1, v.S}), dist[{v.F - 1, v.S}] = d + 1;
}
if (filled[{v.F, v.S - 1}])
{
if (dist[{v.F, v.S - 1}] > d + 1)
q.push({v.F, v.S - 1}), dist[{v.F, v.S - 1}] = d + 1;
}
}
int ans = 0;
int j = 0;
for(auto x : dist)
{
if (j > i) ans = (1ll * ans + x.S) % MOD;
j++;
}
return ans;
}
int subtask12(int N, int* X, int* Y)
{
for(int i = 0; i < N; i++)
filled[{*(X + i), *(Y + i)}] = 1;
int ans = 0;
for(int i = 0; i < N; i++)
ans = (1ll * ans + bfs({*(X + i), *(Y + i)}, i)) % MOD;
return ans;
}
int DistanceSum(int N, int* X, int* Y)
{
if (N <= 2000) return subtask12(N, X, Y);
}
/*
11
2 5
2 6
3 3
3 6
4 3
4 4
4 5
4 6
5 3
5 4
5 6
*/
