#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 = 1e5 + 5;
struct line {
ll m,c;
int cnt;
line(ll _m = 0, ll _c = 0, int _cnt = 0) {
m = _m; c = _c; cnt = _cnt;
}
};
int n,m,k;
pii p[maxn];
int r[maxn], c[maxn];
ll dp[maxn];
int cnt[maxn];
line cht[maxn];
bool cmp(pii x, pii y) {
if(x.X!=y.X) return x.X<y.X;
return x.Y>y.Y;
}
ll p2(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);
}
long long func(line t, ll x) {
return t.m*x + t.c;
}
int solve(ll cost) {
int st = 1, ft = 0;
for(int x=1;x<=n;x++) {
cht[++ft] = line(-2*r[x], p2(r[x]) + dp[x-1] - p2(max(0,c[x-1]-r[x])), cnt[x-1]+1);
while(ft-st+1>=3 && cut(ft-1,ft)<cut(ft-2,ft)) cht[ft-1] = cht[ft], ft--;
while(ft-st+1>=2 && func(cht[st],c[x])>func(cht[st+1],c[x])) st++;
dp[x] = cht[st].m*c[x] + cht[st].c + p2(c[x]) + cost;
cnt[x] = cht[st].cnt;
// printf("dp %d = %lld %d\n",x,dp[x],cnt[x]);
}
// printf("cost = %lld : %d dp = %lld\n",cost,cnt[n],dp[n]);
return cnt[n];
}
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);
}
sort(p,p+n,cmp);
ll cur = -1, sz = 0;
for(int i=0;i<n;i++) {
if(p[i].Y<=cur) continue;
sz++;
r[sz] = p[i].X; c[sz] = p[i].Y+1;
cur = p[i].Y;
}
n = sz;
//solve
ll l = 0, r = 2e16, mid;
while(l<r) {
mid = (l+r)/2;
if(solve(mid)<=k) r = mid;
else l = mid+1;
}
solve(l);
return dp[n] - l*k;
}
