This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
//#include "grader.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int N = 5e5+50;
const ll oo = 1e18;
const ll mod = 1e9;
int cost[2010][2010],r[2010][2010];
ll ans = 0;
int cur;
int dx[] = {1,-1,0,0};
int dy[] = {0,0,1,-1};
void bfs(pair<int,int> st){
queue<pair<int,int>> q;
q.push(st);
int fr = r[st.first][st.second];
cost[fr][fr] = 0;
while(q.size()){
pair<int,int> u = q.front();
q.pop();
int bf = r[u.first][u.second];
if(fr < bf)ans += cost[fr][bf];
for(int i=0;i<4;i++){
pair<int,int> v = {u.first+dx[i],u.second+dy[i]};
int idx = r[v.first][v.second];
if(idx==-1 || cost[fr][idx]!=-1)continue;
cost[fr][idx] = cost[fr][bf]+1;
q.push(v);
}
}
}
int DistanceSum(int N, int *X, int *Y) {
if(N<=2000){
int mn1=-1,mn2=-1;
for(int i=0;i<N;i++){
if(mn1==-1||mn1 > X[i])mn1=X[i];
if(mn2==-1||mn2 > Y[i])mn2=Y[i];
}
for(int i=0;i<2000;i++)
for(int j=0;j<2000;j++)
r[i][j] = cost[i][j] = -1;
for(int i=0;i<N;i++){
X[i]-=mn1;
Y[i]-=mn2;
r[X[i]][Y[i]]=i;
}
for(int i=0;i<N;i++)bfs({X[i],Y[i]});
return ans;
}
sort(X,X+N);
int sum=0,ret=0,lst=X[0];
for(int i=0;i<N;i++){
if(X[i]!=lst){
ret = (ret + (X[i]-lst)*1ll*(sum*1ll*(N-sum))%mod)%mod;
lst = X[i];
}
sum++;
}
ans = ret;
sort(Y,Y+N);
sum=0;ret=0;lst=Y[0];
for(int i=0;i<N;i++){
if(Y[i]!=lst){
ret = (ret + (Y[i]-lst)*1ll*(sum*1ll*(N-sum))%mod)%mod;
lst = Y[i];
}
sum++;
}
ans = (ans+ret)%mod;
return ans;
}
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