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#include<iostream>
#include<map>
#include<vector>
#include<set>
#include<algorithm>
#define pi pair < int,int >
#define mp(a,b) make_pair(a,b)
#define rep(i,a,b) for(int i = a;i < b;i++)
#define MAXN 100004
using namespace std;
int seg[4*MAXN][2];
int id[MAXN];
map < int,int > mapper;
int mod = 1000000000;
void update(int low,int high,int pos,int slow)
{
if(low==slow&&low==high)
{
seg[pos][0]++;
seg[pos][1]+=id[slow];
return;
}
if(low>slow||high<slow)
return;
int mid = (low+high) / 2;
update(low,mid,pos*2+1,slow);
update(mid+1,high,pos*2+2,slow);
rep(id,0,2)
seg[pos][id] = (seg[pos*2+1][id] + seg[pos*2+2][id])%mod;
return;
}
pi query(int low,int high,int pos,int slow,int shigh)
{
if(low >= slow && high <= shigh)
return mp(seg[pos][0],seg[pos][1]);
if(low>shigh||high<slow)
return mp(0,0);
int mid = (low+high)/2;
pi q1 = query(low,mid,pos*2+1,slow,shigh);
pi q2 = query(mid+1,high,pos*2+2,slow,shigh);
q1.first = (q1.first+q2.first)%mod;
q1.second = (q1.second+q2.second)%mod;
return q1;
}
int DistanceSum(int N, int *X, int *Y)
{
vector < pi > points;
set < int > ys;
rep(i,0,N)
{
points.push_back(mp(X[i],Y[i]));
ys.insert(Y[i]);
}
int cnt = 0;
for(set < int >::iterator it = ys.begin();it != ys.end();it++)
{
id[cnt] = *it;
mapper[*it] = cnt++;
}
sort(points.begin(),points.end());
int ans = 0;
int sum = 0;
rep(i,0,N)
{
int x = points[i].first;
int y = mapper[points[i].second];
ans = (ans+x*i-sum)%mod;
sum = (sum+x)%mod;
//cout << "here " << x << " " << y << " " << ans << " -> ";
pi q = query(0,cnt,0,0,y);
ans = (ans + q.first*id[y] - q.second)%mod;
q = query(0,cnt,0,y,cnt);
ans = (ans - q.first*id[y] + q.second)%mod;
update(0,cnt,0,y);
// cout << "and here " << x << " " << y << " " << ans << endl;
}
return ans;
}
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