#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define f0r(i, n) for (auto i = 0; i < (n); ++i)
#define fnr(i, n, k) for (auto i = (n); i < (k); ++i)
#define all(v) (v).begin(), (v).end()
#define pb push_back
#define F first
#define S second
#define ctn(x) cout << x << '\n'
#define forl(a, l) for (auto a : l)
#define ctl(l) for (auto &a : (l)) cout << a << ' '; cout << endl;
#define lb(v, x) (lower_bound(all(v), x) - begin(v))
#define ub(v, x) (upper_bound(all(v), x) - begin(v))
#define pq priority_queue
template <class T>
using V = vector<T>;
using ll = long long;
using vi = V<int>;
using vl = V<ll>;
using pi = pair<int, int>;
using ti = tuple<int, int, int>;
using Adj = V<vi>;
using vvi = V<vi>;
#include "vision.h"
int ct = 0;
template<typename F>
void do_oper(int H, int W, int K, vi &args, F &&f) {
auto enc = [=](int x, int y) { return x*W+y; };
auto enc2 = [&]() { return H*W+(ct++); };
map<int, vi> mp;
f0r(r, H) f0r(c, W) mp[f(r, c)].pb(enc(r, c));
map<int, int> mr;
for (auto &p: mp) {
add_or(p.S);
mr[p.F] = enc2();
}
for (auto &p: mr) if (mr.count(p.F + K)) {
add_and({p.S, mr[p.F+K]});
args.pb(enc2());
}
}
void construct_network(int H, int W, int K) {
auto enc2 = [&]() { return H*W+(ct++); };
vi arg;
do_oper(H, W, K, arg, [](int x, int y) { return x+y; });
do_oper(H, W, K, arg, [](int x, int y) { return x-y; });
if (!arg.size()) return;
add_or(arg);
int kk = enc2();
arg = {};
do_oper(H, W, K+1, arg, [](int x, int y) { return x+y; });
do_oper(H, W, K+1, arg, [](int x, int y) { return x-y; });
if (!arg.size()) {
add_and({kk, kk});
return;
}
add_or(arg);
int kk1 = enc2();
add_not(kk1);
int y = enc2();
add_and({kk, y});
return;
auto enc = [=](int x, int y) { return x*W+y; };
ct = 0;
if (H == 1) {
vi c;
f0r(i, W-K) {
add_and({enc(0, i), enc(0, i+K)});
c.pb(enc2());
}
add_or(c);
return;
} else if (W == 1) {
vi c;
f0r(i, H-K) {
add_and({enc(i, 0), enc(i+K, 0)});
c.pb(enc2());
}
add_or(c);
return;
}
vi vt;
f0r(c, W) {
vi cc;
f0r(r, H) cc.pb(enc(r, c));
add_or(cc);
vt.pb(enc2());
}
vi vt2;
f0r(c, W-1) {
add_and({vt[c], vt[c+1]});
vt2.pb(enc2());
}
add_or(vt2);
int ww = enc2();
add_xor(vt);
int ww2 = enc2();
vi ht;
f0r(r, H) {
vi cc;
f0r(c, W) cc.pb(enc(r, c));
add_or(cc);
ht.pb(enc2());
}
vi ht2;
f0r(r, H-1) {
add_and({ht[r], ht[r+1]});
ht2.pb(enc2());
}
add_or(ht2);
int hh = enc2();
add_xor(ht);
int hh2 = enc2();
add_and({ww, hh2});
int a = enc2();
add_and({hh, ww2});
int b = enc2();
add_or({a, b});
if (K==1) return;
/*
// ROW, COL
int cnt = 0;
vi c;
f0r(r1, H) f0r(c1, W) f0r(r2, H) f0r(c2, W) if (r1 <= r2 && (r1 != r2 || c1 <= c2) && abs(r2-r1)+abs(c2-c1) == K) {
add_and({enc(r1, c1), enc(r2, c2)});
c.pb(enc2(cnt++));
}
add_or(c);
return;
if (H == 1) {
vi c;
f0r(i, W-K) {
add_and({enc(0, i), enc(0, i+K)});
c.pb(enc2(i));
}
add_or(c);
} else {
vi c;
f0r(i, H-K) {
add_and({enc(i, 0), enc(i+K, 0)});
c.pb(enc2(i));
}
add_or(c);
}
//std::vector<int> Ns;
//Ns = {0, 1};
//int a = add_and(Ns);
//Ns = {0, a};
//int b = add_or(Ns);
//Ns = {0, 1, b};
//int c = add_xor(Ns);
//add_not(c);
*/
}
