#include <bits/stdc++.h>
#include "vision.h"
using namespace std;
#define ll long long
//#define int long long
#define all(x) x.begin(), x.end()
#define siz(x) ((int)x.size())
#define yes cout << "YES\n"
#define no cout << "NO\n"
#define f first
#define s second
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<class T>
using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
*/
const int mod = 1e9+7;
const int N = 20005;
const long long inf = 1e12+12;
double eps = 1e-9;
vector<vector<int>> hi;
int cur;
int h, w, k;
vector<vector<int>> meto ( ) {
vector<array<int,2>>vect;
for(int i=0;i<h;++i){
for(int j=0;j<w;++j){
vect.push_back({i,j});
}
}
vector<vector<int>> ans( siz(vect)+3 );
for(int i =0;i<vect.size();++i){
for(int j =i+1;j<vect.size();++j){
int sz = abs(vect[i][0]-vect[j][0])+abs(vect[i][1]-vect[j][1]);
if(sz==k)
ans[i].push_back(j);
}
}
return ans;
}
vector<int> r(int i) {
vector<int> ans;
for (int j=0; j<w; j++) ans.push_back( i*w+j );
return ans;
}
vector<int> c(int j) {
vector<int> ans;
for (int i=0; i<h; i++) ans.push_back( i*w+j );
return ans;
}
void normal () {
vector<int> can;
for (int i=0; i<h*w; i++) {
if ( siz( hi[i] ) == 0 ) continue;
add_or( hi[i] );
add_and( {cur+1, i} );
cur+=2;
can.push_back(cur);
}
add_or( can );
}
void subtask_6 ( ) {
vector<int> can;
vector<int> tmp = r(0);
auto cc = c(0);
tmp.insert( tmp.end(), all(cc) );
for ( auto& i : tmp) {
if ( siz( hi[i] ) == 0 ) continue;
add_or( hi[i] );
add_and( {cur+1, i} );
cur+=2;
can.push_back(cur);
}
add_or( can );
}
void subtask_7 () {
vector<int> rs(h), cs(w); // rs[i] = id of Xor row i, cs[i] = id of Xor col i
int nr, nc; // nr -> id of Not(OR(Xor rows)) ,id nc Not(OR(Xor col))
for (int i=0; i<h; i++) {
vector<int> tmp = r(i);
add_xor( tmp );
rs[i] = ++cur;
}
for (int i=0; i<w; i++) {
vector<int>tmp = c(i);
add_xor(tmp);
cs[i] = ++cur;
}
add_or( rs );
add_not(++cur);
nr = ++cur;
add_or(cs);
add_not( ++cur );
nc = ++cur;
vector<int> can;
for (int i=0; i<h-1; i++) {
add_and( {rs[i], rs[i+1], nc} );
can.push_back( ++cur );
}
for (int i=0; i<w; i++) {
add_and( {cs[i], cs[i+1], nr} );
can.push_back( ++cur );
}
add_or(can);
}
/*
add_and(Ns);
add_or(Ns);
add_xor(Ns);
add_not(c);
*/
void construct_network(int H, int W, int K) {
h = H;
w = W;
k = K;
hi = meto();
cur = h*w-1;
if ( (max(h, w) > 30) && (k == 1) ) {
subtask_7();
return;
}
if ( max(h, w) > 30 ) {
subtask_6();
return;
}
normal();
}
