#include "aliens.h"
#include <vector>
#include <iostream>
#include <algorithm>
#include <cassert>
using namespace std;
#define ll long long
#define pb push_back
#define ii pair<int, int>
#define f1 first
#define s2 second
vector<ii> interval;
//cost for interval [i, j], assuming interval [0, i-1] have been fulfilled
inline ll getCost(int i, int j)
{
ll res = 1LL * (interval[j].s2 - interval[i].f1 + 1) * (interval[j].s2 - interval[i].f1 + 1);
if (i)
{
if (interval[i-1].s2 >= interval[i].f1)
res -= 1LL * (interval[i-1].s2 - interval[i].f1 + 1) * (interval[i-1].s2 - interval[i].f1 + 1);
}
return res;
}
vector<ll> dp[2];
inline void dnc(int k, int l, int r, int optL, int optR)
{
if (l > r)
return;
int mid = (l + r) / 2;
ll optVal = 1e18;
int optIdx = -1;
for (int i = optL; i <= mid && i <= optR; ++i)
{
ll val = (i ? dp[(k+1) & 1][i-1] : 0) + getCost(i, mid);
if (optVal > val)
{
optVal = val;
optIdx = i;
}
}
dp[k&1][mid] = optVal;
dnc(k, l, mid-1, optL, optIdx-1);
dnc(k, mid+1, r, optIdx+1, optR);
}
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
vector<ii> v(n);
for (int i = 0; i < n; ++i)
v[i] = {min(r[i], c[i]), max(r[i], c[i])};
sort(v.begin(), v.end(), [](const ii &x, const ii &y){
return x.f1 < y.f1 || (x.f1 == y.f1 && x.s2 > y.s2);
});
interval.pb(v[0]);
for (int i = 1; i < n; ++i)
{
if (interval.back().f1 <= v[i].f1 && v[i].s2 <= interval.back().s2)
continue;
interval.pb(v[i]);
}
for (int i = 0; i+1 < interval.size(); ++i)
assert(interval[i].f1 < interval[i+1].f1 && interval[i].s2 < interval[i+1].s2);
dp[0].resize(interval.size());
dp[1].resize(interval.size());
for (int i = 0; i < interval.size(); ++i)
dp[1][i] = getCost(0, i);
for (int j = 2; j <= k; ++j)
dnc(j, 0, interval.size() - 1, 0, interval.size() - 1);
return dp[k & 1].back();
}
