#include "aliens.h"
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair<ll,ll>
#define X first
#define Y second
const int maxn = 1e3 + 5;
struct line {
ll m,c,val;
line(ll _m = 0, ll _c = 0, ll _val = 0) {
m = _m; c = _c; val = _val;
}
};
int n,m,k,sz;
pii p[maxn];
pii dp[maxn];
line cht[maxn];
ll getpow(ll x) {
return x*x;
}
double cut(int x, int y) {
if(x==0 || y==0) return -2e16;
return (double)(cht[y].c-cht[x].c)/(cht[x].m-cht[y].m);
}
void solve(ll cost) {
int len = 0;
// printf("solve %lld\n",cost);
cht[++len] = line(-2*p[0].X,getpow(p[0].X),1);
for(int x=0;x<sz;x++) {
int pos = 1;
for(int i=1;i<=len;i++) {
if(cht[i].m*p[x].Y+cht[i].c < cht[pos].m*p[x].Y+cht[pos].c) pos = i;
else if(cht[i].m*p[x].Y+cht[i].c == cht[pos].m*p[x].Y+cht[pos].c && cht[i].val<cht[pos].val) pos = i;
}
dp[x] = {cht[pos].m*p[x].Y + cht[pos].c + getpow(p[x].Y) + cost, cht[pos].val};
//update
line t = line(-2*p[x+1].X, dp[x].X - getpow(max(0LL,p[x].Y-p[x+1].X)) + getpow(p[x+1].X), dp[x].Y+1);
cht[++len] = t;
// printf("dp %d = {%lld, %lld}\n",x,dp[x].X,dp[x].Y);
}
}
bool cmp(pii x, pii y) {
if(x.X!=y.X) return x.X<y.X;
return x.Y>y.Y;
}
long long take_photos(int N, int M, int K, std::vector<int> R, std::vector<int> C) {
n = N; m = M; k = K;
//prep
for(int i=0;i<n;i++) {
p[i] = {R[i],C[i]};
if(p[i].X>p[i].Y) swap(p[i].X,p[i].Y);
p[i].Y++;
}
sort(p,p+n,cmp);
ll cur = -1;
for(int i=0;i<n;i++) {
if(p[i].Y<=cur) continue;
p[sz++] = p[i];
cur = p[i].Y;
}
//solve
ll l = 0, r = 1e13, mid, pos;
ll ans;
while(l<r) {
mid = (l+r)/2;
solve(mid);
if(dp[sz-1].Y<=k) pos = mid, r = mid-1;
else l = mid+1;
}
solve(pos);
return dp[sz-1].X - pos*dp[sz-1].Y;
}
