#include "bits/extc++.h"
using namespace std;
template <typename T, typename... U>
void dbgh(const T& t, const U&... u) {
cerr << t;
((cerr << " | " << u), ...);
cerr << endl;
}
#ifdef DEBUG
#define dbg(...) \
cerr << "L" << __LINE__ << " [" << #__VA_ARGS__ << "]: "; \
dbgh(__VA_ARGS__)
#else
#define dbg(...)
#define cerr \
if (false) \
cerr
#endif
#define endl "\n"
#define long int64_t
#define sz(x) int(std::size(x))
int add_and(vector<int> Ns);
int add_or(vector<int> Ns);
int add_xor(vector<int> Ns);
int add_not(int N);
void construct_network(int n, int m, int kv) {
auto id_arr = [&](int x, int y) -> int { return x * m + y; };
int b_true = -1, b_false = -1;
auto g_true = [&]() -> int {
if (b_true == -1) {
vector<int> cq;
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
cq.push_back(id_arr(i, j));
}
}
b_true = add_or(cq);
}
return b_true;
};
auto g_false = [&]() -> int {
if (b_false == -1) {
b_false = add_not(g_true());
}
return b_false;
};
auto go_cell = [&](auto cb) -> vector<int> {
map<int, vector<int>> mp;
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
mp[cb(i, j)].push_back(id_arr(i, j));
}
}
vector<int> ans;
for (auto& [_k, v] : mp) {
ans.push_back(add_or(v));
}
return ans;
};
auto has_k_diff = [&](const vector<int>& arr, int kv) -> int {
int n = sz(arr);
if (kv >= n) {
return g_false();
}
vector<int> cq;
for (int i = 0; i + kv < n; i++) {
cq.push_back(add_and({arr[i], arr[i + kv]}));
}
return add_or(cq);
};
auto has_ge_k_diff = [&](const vector<int>& arr, int kv) -> int {
int n = sz(arr);
if (kv >= n) {
return g_false();
}
vector<int> cq;
int suff = arr[0];
for (int i = kv; i < n; i++) {
suff = add_or({suff, arr[i - kv]});
cq.push_back(add_and({arr[i], suff}));
}
return add_or(cq);
};
auto c1 = go_cell([&](int x, int y) -> int { return x + y; }),
c2 = go_cell([&](int x, int y) -> int { return x - y; });
int has_k = add_or({has_k_diff(c1, kv), has_k_diff(c2, kv)}),
has_gt_k =
add_or({has_ge_k_diff(c1, kv + 1), has_ge_k_diff(c2, kv + 1)});
add_and({has_k, add_not(has_gt_k)});
}
