#include<bits/stdc++.h>
#include "aliens.h"
#define F first
#define S second
#define PB push_back
#define sz(s) (int(s.size()))
#define bit(n, k) (((n)>>(k)) & 1)
using namespace std;
typedef pair<int, int> pii;
typedef long long ll;
typedef pair<ll, ll> pll;
const int maxn = 1e5 + 10, mod = 1e9 + 7;
const ll inf = 1e13 + 10, INF = 1e18;
pll dp[maxn];
int mn[maxn];
ll f(int ln){
return 1ll * ln * ln;
}
pll solve(int n, ll c){
for(int i = n-1; i >= 0; i--){
if(mn[i] > i){
dp[i] = dp[i+1];
continue;
}
dp[i] = {inf, inf};
for(int j = i; j < n; j++)
dp[i] = min(dp[i], (pll){ dp[j+1].F + f(j - mn[i] + 1) - f(i - mn[i]) + c, dp[j+1].S + 1 });
}
return dp[0];
}
ll take_photos(int m, int n, int k, vector<int> X, vector<int> Y){
for(int i = 0; i <= n; i++){
mn[i] = n + 10;
}
for(int i = 0; i < m; i++){
if(X[i] > Y[i])
swap(X[i], Y[i]);
mn[Y[i]] = min(mn[Y[i]], X[i]);
}
for(int i = n-1; i >= 0; i--){
mn[i] = min(mn[i], mn[i+1]);
}
ll l = -1, r = inf;
while(r-l > 1){
ll mid = (l+r) >> 1;
pll p = solve(n, mid);
if(p.S > k)
l = mid;
else
r = mid;
}
pll p = solve(n, r);
return 1ll * p.F - 1ll * k * r;
}
