#include "aliens.h"
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
const int N=1e5+5;
const int M=1e6+5;
const bool dbg=false;
const ll inf=1e18;
int n;
ll l[N],r[N];
ll overlap[N];
int mn[M];
stack<pair<int,int>> s;
bool querymode=false;
struct line{
ll m,c;
int cnt;
line():m(0),c(-inf){}
line(ll m,ll c,int cnt):m(m),c(c),cnt(cnt){}
ll get(ll x){
return m*x+c;
}
};
bool bad(line l1,line l2,line l3){
return (l3.c-l1.c)*(l1.m-l2.m)<=(l2.c-l1.c)*(l1.m-l3.m);
}
pair<ll,int> calc(ll lambda){
ll dp=0;
int cnt=0;
deque<line> dq;
dq.emplace_back(line(l[1],-l[1]*l[1],0));
for(int i=1;i<=n;i++){
ll x=2*(r[i]+1);
while(dq.size()>1&&dq[0].get(x)<dq[1].get(x))dq.pop_front();
dp=(r[i]+1)*(r[i]+1)+lambda-overlap[i]-dq[0].get(x);
cnt=dq[0].cnt+1;
if(i==n)break;
line ln(l[i+1],-dp-l[i+1]*l[i+1],cnt);
while(dq.size()>1&&bad(dq[dq.size()-2],dq.back(),ln))dq.pop_back();
dq.emplace_back(ln);
}
return make_pair(dp,cnt);
}
long long take_photos(int N, int m, int k, vector<int> R, vector<int> C) {
n=N;
for(int i=0;i<m;i++)mn[i]=m;
for(int i=0;i<n;i++){
int x=R[i],y=C[i];
int st=min(x,y),ed=max(x,y);
mn[ed]=min(mn[ed],st);
}
for(int i=0;i<m;i++){
if(mn[i]==m)continue;
while(!s.empty()&&s.top().first>=mn[i])s.pop();
s.emplace(mn[i],i);
}
n=s.size();
for(int i=n;i>=1;i--){
tie(l[i],r[i])=s.top();
s.pop();
}
for(int i=1;i<n;i++){
ll res=max(0ll,r[i]-l[i+1]+1);
overlap[i]=res*res;
}
k=min(k,n);
ll lo=0,hi=1ll*m*m+1;
ll ans=1;
while(lo<hi){
ll mid=(lo+hi)/2;
auto [val,cnt]=calc(mid);
if(cnt<=k)hi=mid,ans=val-mid*k;
else lo=mid+1;
}
return ans;
}
