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;
map<pair<ll,ll>,bool> r,vis,cost;
ll ans = 0;
int dx[] = {1,-1,0,0};
int dy[] = {0,0,1,-1};
void bfs(int sx,int sy){
queue<pair<pair<int,int>,int>> q;
q.push({{sx,sy},0});
while(q.size()){
pair<int,int> u = q.front().first;
int cst = q.front().second;
q.pop();
if(vis[u])continue;
vis[u]=1;
for(int i=0;i<4;i++){
pair<int,int> v = {u.first+dx[i],u.second+dy[i]};
if(cost[v])continue;
cost[v]=1;
ans = (ans+cst+1)%mod;
q.push({v,cst+1});
}
}
}
int DistanceSum(int N, int *X, int *Y) {
if(N<=2000){
for(int i=0;i<N;i++)r[{X[i],Y[i]}]=1;
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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