#include "vision.h"
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
#define F first
#define S second
#define all(x) (x).begin(), (x).end()
template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p)
{
return os << "(" << p.F << "," << p.S << ")";
}
template<typename T>
void print(const T &v, int lim = 1e9)
{
for(auto x : v)
if(lim-- > 0) cout << x << " ";
cout << endl;
}
template<typename T>
void print(T *begin, const T *end)
{
for(T *it = begin; it < end; it++)
cout << *it << " ";
cout << endl;
}
int n, m, k;
inline int idx(int x, int y)
{
return x * m + y;
}
void brute()
{
vector<pair<int, int>> pairs;
for(int i = 0; i < n; i++)
{
for(int j = 0; j < m; j++)
{
for(int x = 0; x <= k; x++)
{
int y = k - x;
if(i + x < n && j + y < m)
pairs.emplace_back(idx(i, j), idx(i + x, j + y));
if(i + x < n && j - y >= 0)
pairs.emplace_back(idx(i, j), idx(i + x, j - y));
}
}
}
vector<int> v;
int j = n * m;
for(auto [idx1, idx2] : pairs)
{
add_and({idx1, idx2});
v.push_back(j++);
}
add_or(v);
}
void sol1()
{
vector<int> rows, cols, row_adj, col_adj;
int it = n * m;
for(int i = 0; i < n; i++)
{
vector<int> v;
for(int j = 0; j < m; j++)
v.push_back(idx(i, j));
add_or(v);
rows.push_back(it++);
}
for(int j = 0; j < m; j++)
{
vector<int> v;
for(int i = 0; i < n; i++)
v.push_back(idx(i, j));
add_or(v);
cols.push_back(it++);
}
for(int i = 0; i < n - 1; i++)
{
add_and({rows[i], rows[i + 1]});
row_adj.push_back(it++);
}
for(int i = 0; i < m - 1; i++)
{
add_and({cols[i], cols[i + 1]});
col_adj.push_back(it++);
}
int cond1, cond2;
add_or(row_adj);
add_xor(cols);
add_and({it, it + 1});
cond1 = it + 2;
it += 3;
add_or(col_adj);
add_xor(rows);
add_and({it, it + 1});
cond2 = it + 2;
it += 3;
add_or({cond1, cond2});
}
void smart()
{
vector<int> rows, cols;
int it = n * m;
for(int i = 0; i < n; i++)
{
vector<int> v;
for(int j = 0; j < m; j++)
v.push_back(idx(i, j));
add_or(v);
rows.push_back(it++);
}
for(int j = 0; j < m; j++)
{
vector<int> v;
for(int i = 0; i < n; i++)
v.push_back(idx(i, j));
add_or(v);
cols.push_back(it++);
}
vector<int> dif_row(k + 1), dif_col(k + 1);
for(int dif = 1; dif <= k; dif++)
{
vector<int> v;
for(int i = 0; i + dif < n; i++)
{
add_and({rows[i], rows[i + dif]});
v.push_back(it++);
}
add_or(v);
dif_row[dif] = it++;
v.clear();
for(int j = 0; j + dif < m; j++)
{
add_and({cols[j], cols[j + dif]});
v.push_back(it++);
}
add_or(v);
dif_col[dif] = it++;
}
add_xor(rows);
dif_row[0] = it++;
add_xor(cols);
dif_col[0] = it++;
vector<int> conds;
for(int x = 0; x <= k; x++)
{
add_and({dif_row[x], dif_col[k - x]});
conds.push_back(it++);
}
add_or(conds);
}
void construct_network(int H, int W, int K) {
n = H, m = W, k = K;
if(max(n, m) <= 10 || min(n, m) == 1) brute();
else if(k == 1) sol1();
else smart();
}
