#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pll = pair<ll, ll>;
using pli = pair<ll, int>;
#define fi first
#define se second
int c[100009];
ll D[100009];
inline ll p(ll x) { return x*x; }
struct line {
ll a, b;
int idx;
};
line stk[100009]; int t, j;
inline bool del(line P, line Q, line R) {
return (R.a - P.a) * (Q.b - R.b) < (R.a - Q.a) * (P.b - R.b);
}
void add(line P) {
while(1<=t && del(stk[t-1], stk[t], P)) --t, j = min(j, t);
stk[++t] = P;
}
pli DP(vector<pll>& A, ll lambda) {
int N = (int)A.size() - 1;
for(int i=1; i<N; i++) D[i] = 1LL * 1e18, c[i] = 0;
t = -1; add((line){-2LL * A[1].fi, p(A[1].fi) - 2*A[1].fi, 0});
j = 0;
for(int i=1; i<N; i++) {
while(j<t && A[i].se * stk[j].a + stk[j].b > A[i].se * stk[j+1].a + stk[j+1].b) ++j;
ll nw = A[i].se * stk[j].a + stk[j].b + p(A[i].se) + 2*A[i].se + 1 + lambda;
if(D[i] > nw) D[i] = nw, c[i] = c[stk[j].idx] + 1;
add({-2LL * A[i+1].fi, D[i] + p(A[i+1].fi) - 2*A[i+1].fi - p(max(0LL, A[i].se - A[i+1].fi + 1)), i});
}
return {D[N-1], c[N-1]};
}
long long take_photos(int n, int m, int k, vector<int> r, vector<int> c) {
vector<pll> A, B;
for(int i=0; i<n; i++) {
if(r[i] > c[i]) swap(r[i], c[i]);
A.push_back({r[i], c[i]});
}
sort(A.begin(), A.end(), [&](pll P, pll Q) {
if(P.se == Q.se) return P.fi > Q.fi;
return P.se < Q.se;
});
B.push_back({-1, -1});
for(int i=0; i<n; i++) {
while(B.size() && B.back().fi >= A[i].fi) B.pop_back();
B.push_back(A[i]);
} B.push_back({0, 0});
long long L = 0, R = 1LL*1e12, f = 0;
while(L <= R) {
long long m = L+R >> 1, v; int cnt;
tie(v, cnt) = DP(B, m);
if(cnt > k) L = m+1;
else R = m-1, f = v - m * k;
}
return f;
}
