#include<bits/stdc++.h>
#include "vision.h"
using namespace std;
using pii = pair<int,int>;
using ll = long long;
using pll = pair<ll,ll>;
using pli = pair<ll,int>;
using pil = pair<int,ll>;
using ld = long double;
using ui = unsigned int;
using ull = unsigned long long;
using ui128 = __uint128_t;
#define all(x) (x).begin(),(x).end()
#define mp make_pair
#define lc ind<<1
#define rc ind<<1|1
const int MN = 1e5 + 2, LOG = 21, INF = 1e8;
int cur;
int _add_not (int n) {cur++; return add_not(n);}
int _add_and (vector<int> ns) {cur++; return add_and(ns);}
int _add_or (vector<int> ns) {cur++; return add_or(ns);}
int _add_xor (vector<int> ns) {cur++; return add_xor(ns);}
int check_k (int n, int m, int k) {
vector<pii> check;
int pbase = -1, sbase = -1;
for (int nx = 2; nx + k <= n + m; nx++) {
vector<int> on;
for (int x = max(1,nx - m); x <= min(n,nx-1); x++) {
int y = nx - x;
on.push_back((x - 1) * m + y - 1);
}
if (~pbase) {on.push_back(cur-1); _add_or(on);}
else pbase = _add_or(on);
}
for (int nx = n + m; nx - k >= 2; nx--) {
vector<int> on;
for (int x = max(1,nx-m); x <= min(n,nx-1); x++) {
int y = nx - x;
on.push_back((x-1) * m + y - 1);
}
if (~sbase) {on.push_back(cur-1); _add_or(on);}
else sbase = _add_or(on);
check.emplace_back(cur-1,pbase + nx - k - 2);
}
pbase = sbase = -1;
for (int ny = 1 - n; ny + k <= m - 1; ny++) {
vector<int> on;
for (int x = max(1,1 - ny); x <= min(n, m - ny); x++) {
int y = ny + x;
on.push_back((x-1) * m + y - 1);
}
if (~pbase) {on.push_back(cur-1); _add_or(on);}
else pbase = _add_or(on);
}
for (int ny = m-1; ny - k >= 1 - n; ny--) {
vector<int> on;
for (int x = max(1,1 - ny); x <= min(n,m - ny); x++) {
int y = ny + x;
on.push_back((x-1) * m + y - 1);
}
if (~sbase) {on.push_back(cur-1); _add_or(on);}
else sbase = _add_or(on);
check.emplace_back(cur - 1, pbase + ny - k + n - 1);
}
int start = cur;
for (pii p : check) _add_and({p.first,p.second});
vector<int> go;
for (int i = start; i < cur; i++) go.push_back(i);
assert(go.size());
return _add_or(go);
}
void construct_network (int n, int m, int k) { //(x,y) -> (x+y,x-y)
cur = n * m;
if (n + m - 2 == k) check_k(n,m,k);
else _add_and({check_k(n,m,k),_add_not(check_k(n,m,k+1))});
}
