#include <bits/stdc++.h>
#define x first
#define y second
using namespace std;
using ll=long long;
using ld=long double;
using pp=pair<ll, ll>;
const int Nmax=100010;
ll N, NN, M, K, DP[Nmax], C[Nmax];
pp A[Nmax], B[Nmax];
struct line {
ll a, b;
int idx;
ll f(ll x) {return a*x+b;}
ld cross(line r) {return (b-r.b)/(r.a-a);}
}L[Nmax];
void Dynamic(ll v) {
int fr=0, re=0;
fill(C+1, C+N+1, 0);
for(int i=1; i<=N; i++) {
line tmp={-2*A[i].x, DP[i-1]+A[i].x*A[i].x-2*A[i].x, i};
while(fr<re && L[re-1].cross(tmp)>=L[re-1].cross(L[re])) re--;
L[++re]=tmp;
while(fr<re && L[fr].f(A[i].y)>=L[fr+1].f(A[i].y)) fr++;
DP[i]=L[fr].f(A[i].y)+A[i].y*A[i].y+v+2*A[i].y+1;
C[i]=C[L[fr].idx-1]+1;
}
}
ll take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
NN=n, M=m, K=k;
for(int i=1; i<=NN; i++) {
B[i].x=min(r[i-1], c[i-1]), B[i].y=max(r[i-1], c[i-1]);
}
sort(B+1, B+NN+1);
for(int i=NN; i>=1; i--) {
while(N && A[N].y<=B[i].y) N--;
A[++N]=B[i];
}
reverse(A+1, A+N+1); K=min(K, N);
{
ll l=0, r=N+1, lv, rv;
for(ll s=0, e=M*M; s<=e;) {
ll mid=(s+e)/2;
Dynamic(mid);
if(C[N]==K) {
return DP[N]-mid*C[N];
}
else if(C[N]>K) {
s=mid+1;
if(r>C[N]) r=C[N], rv=DP[N]-mid*C[N];
}
else {
e=mid-1;
if(l<C[N]) l=C[N], lv=DP[N]-mid*C[N];
}
}
return rv+(lv-rv)/(r-l)*(r-K);
}
}
