#include <bits/stdc++.h>
#define ent '\n'
#define f first
#define s second
typedef long long ll;
using namespace std;
const int maxn = 1e6+12;
pair<ll, int> dp[maxn];
vector<int> g[maxn];
bool was[maxn];
vector<int> t;
int L[maxn];
int R[maxn];
int n, m;
struct line{
ll k, b;
int c;
};
bool check(line nw, line last, line prl){
if((nw.b - prl.b) * (prl.k - last.k) <= (last.b - prl.b) * (prl.k - nw.k))return 1;
return 0;
}
int ptr = 0;
vector<line> l;
void add(line x){
while(l.size() && l.back().k == x.k && l.back().b > x.b){
l.pop_back();
}
if(l.size() && l.back().k == x.k && l.back().b <= x.b){
return;
}
while(l.size()>1 && check(x, l.back(), l[l.size()-2])){
l.pop_back();
}
l.push_back(x);
}
pair<ll, int> get(ll x){
if(!l.size()){
return {1e18, 1e9};
}
if(ptr >= l.size()){
ptr = l.size()-1;
}
while(ptr + 1 < l.size() && l[ptr].k * x + l[ptr].b > l[ptr+1].k * x + l[ptr+1].b){
ptr++;
}
return {l[ptr].k * x + l[ptr].b, l[ptr].c + 1};
}
int check(ll k){
add({0, 0, 0});
for(int &i:t){
dp[i] = get(i);
dp[i].f += i * 1ll * i + k;
for(int &j:g[i]){
ll b = j * 1ll * j + dp[R[j]].f, c = dp[R[j]].s;
if(R[j] > j) b -= (R[j] - j) * 1ll * (R[j] - j);
add(line(-2 * j, b, c));
}
}
l.clear();
ptr = 0;
return dp[m].s;
}
long long take_photos(int N, int M, int k, vector<int> r, vector<int> c){
n = N, m = M;
for(int i=1;i<=m;i++){
L[i] = 1e9;
}
m = 0;
for(int i=0;i<n;i++){
if(r[i] < c[i]){
swap(r[i], c[i]);
}
r[i]++, c[i]++;
L[r[i]] = min(L[r[i]], c[i]);
R[c[i]] = max(R[c[i]], r[i]);
for(int x=-1;x<=0;x++){
was[r[i]+x] = was[c[i]+x] = 1;
}
m = max(m, r[i]);
}
was[1] = 1;
for(int i=1;i<=m;i++){
R[i] = max(R[i], R[i-1]);
if(!was[i]) continue;
t.push_back(i);
g[max(R[i], i)].push_back(i);
}
ll val = 0;
for(ll l = -2e12, r = 2e12; l <= r;){
ll mid = l + r >> 1;
if(check(mid) < k){
val = mid;
r = mid - 1;
}
else l = mid + 1
}
check(val);
return dp[m].f - dp[m].s * val;
}