#include "aliens.h"
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#define AquA cin.tie(0);ios_base::sync_with_stdio(0);
#define fs first
#define sc second
#define p_q priority_queue
#define sz(a) ((int)(a.size()))
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pll;
vector<ll> v,nxt;
int lst=0,mn;
int n;
bool check1(pll a,pll b,int c){
return a.fs*c+a.sc>b.fs*c+b.sc;
}
bool check2(pll a,pll b,pll c){
return (b.sc-a.sc)*(b.fs-c.fs)<=(b.sc-c.sc)*(b.fs-a.fs);
}
ll get(ll p,bool x){
vector<pair<pll,int> > dq;
vector<pll> dp(n);
int l=0;
dq.push_back({{1-mn,1ll*(1-mn)*(1-mn)},0});
//cout << p << ":\n";
for(int i=0;i<n;i++){
if(v[i]==n){
continue;
}
while(sz(dq)-l>1 && check1(dq[l].fs,dq[l+1].fs,2*i)){
l++;
}
dp[i].fs=2ll*i*dq[l].fs.fs+dq[l].fs.sc+1ll*i*i+p;
dp[i].sc=dq[l].sc+1;
ll xf=0;
if(i>=nxt[i]){
xf=-(i-nxt[i]+1)*(i-nxt[i]+1);
}
ll a=(1-nxt[i]),b=dp[i].fs+(1ll*(1-nxt[i])*(1-nxt[i]))+xf;
while(sz(dq)-l>1 && check2(dq[sz(dq)-1].fs,dq[sz(dq)-2].fs,{a,b})){
dq.pop_back();
}
dq.push_back({{a,b},dp[i].sc});
/*
cout << i << "\n";
cout << "from: " << dq[l].fs.fs << " " << dq[l].fs.sc << "\n";
for(int j=l;j<sz(dq);j++){
cout << dq[j].fs.fs << " " << dq[j].fs.sc << "\n";
}
*/
}
/*
for(int i=0;i<n;i++){
cout << dp[i].fs << " " << dp[i].sc << "\n";
}
cout << "\n";
*/
if(x==0){
return dp[lst].sc;
}
else{
return dp[lst].fs;
}
}
ll take_photos(int N, int M, int k, vector<int> R, vector<int> C) {
n=M;
int m=N;
v.resize(n+1,n);
nxt.resize(n);
for(int i=0;i<m;i++){
if(R[i]<C[i]){
swap(R[i],C[i]);
}
v[R[i]]=min(v[R[i]],(ll)C[i]);
}
mn=n;
for(int i=n-1;i>=0;i--){
if(v[i]<mn){
nxt[i]=mn;
if(mn==n){
lst=i;
}
mn=v[i];
}
else{
v[i]=n;
}
}
ll l=0,r=2e14;
while(r>l){
ll mid=(l+r)/2;
if(get(mid,0)<=k){
r=mid;
}
else{
l=mid+1;
}
}
return get(l,1)-l*k;
}
