#pragma GCC target("avx2")
#pragma GCC optimization("O3")
#pragma GCC optimization("unroll-loops")
#include<bits/stdc++.h>
//#include "job.h"
#define rc(x) return cout<<x<<endl,0
#define pb push_back
#define mkp make_pair
#define in insert
#define er erase
#define fd find
#define fr first
#define sc second
typedef long long ll;
typedef long double ld;
const ll INF=0x3f3f3f3f3f3f3f3f;
const ll llinf=(1LL<<62);
const int inf=(1<<30);
const int nmax=1e5+50;
const ll mod=1e9;
using namespace std;
int dx[]={-1,0,0,1},dy[]={0,-1,1,0};
int i,j,a,b,x[nmax],y[nmax],di[nmax],vz[nmax],n,rs,sx,sy;
vector<int>g[nmax];
queue<int>q;
map<pair<int,int>,int>mp;
void ad(int &x,int y)
{
x+=y;
if(x>=mod)x-=mod;
if(x<0)x+=mod;
}
void rec(int a,int b)
{
int c=mp[mkp(a,b)],d;
if(vz[c])return;
vz[c]=1;
for(int i=0;i<4;i++)
{
d=mp[mkp(a+dx[i],b+dy[i])];
if(!d)continue;
g[c].pb(d);
rec(a+dx[i],b+dy[i]);
}
}
int DistanceSum(int N,int X[],int Y[])
{
n=N;
for(i=1;i<=n;i++)
{
x[i]=X[i-1],y[i]=Y[i-1];
mp[mkp(x[i],y[i])]=i;
}
rec(x[1],y[1]);
if(n<=2000)
{
for(i=1;i<=n;i++)
{
while(!q.empty())q.pop();
q.push(i);
for(j=1;j<=n;j++)vz[j]=di[j]=0;
vz[i]=1;
while(!q.empty())
{
a=q.front();
q.pop();
if(a>i)ad(rs,di[a]);
for(j=0;j<g[a].size();j++)
{
b=g[a][j];
if(!vz[b])
{
vz[b]=1;
q.push(b);
di[b]=di[a]+1;
}
}
}
}
}
else
{
sort(x+1,x+n+1);
sort(y+1,y+n+1);
for(i=1;i<=n;i++)
{
ad(sx,x[i]);
ad(sy,y[i]);
}
for(i=n;i>=1;i--)
{
ad(rs,((1LL*x[i]*i%mod)-sx+mod)%mod);
ad(rs,((1LL*y[i]*i%mod)-sy+mod)%mod);
ad(sx,-x[i]);
ad(sy,-y[i]);
}
}
return rs;
}
