#include "vision.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pi;
typedef vector <int> vi;
typedef vector <pi> vpi;
typedef pair<pi, ll> pii;
typedef set <ll> si;
typedef long double ld;
#define f first
#define s second
#define mp make_pair
#define FOR(i,s,e) for(int i=s;i<=int(e);++i)
#define DEC(i,s,e) for(int i=s;i>=int(e);--i)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define lbd(x, y) lower_bound(all(x), y)
#define ubd(x, y) upper_bound(all(x), y)
#define aFOR(i,x) for (auto i: x)
#define mem(x,i) memset(x,i,sizeof x)
#define fast ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0)
#define maxn 201
#define INF (ll)1e9
#define MOD 1000000007
typedef pair <vi, int> pvi;
typedef pair <int,pi> ipi;
typedef vector <pii> vpii;
int H,W;
bool valid(int x,int y){
return (x >= 0 && x < H && y >= 0 && y < W);
}
int ordiag1[maxn][maxn],ordiag2[maxn][maxn],xordiag1[maxn][maxn],xordiag2[maxn][maxn];
void construct_network(int H, int W, int K) {
vi ans;
::H = H; ::W = W;
// precomp OR and XOR in each diagonal
for (int si=0,sj=W-1;si<H;(sj==0?si++:sj--)){
vi v;
for (int i=si,j=sj;valid(i,j);i++,j++) v.pb(i*W+j);
ordiag1[si][sj] = add_or(v);
xordiag1[si][sj] = add_xor(v);
}
for (int si=0,sj=0;si<H;(sj==W-1?si++:sj++)){ // antidiagonal
vi v;
for (int i=si,j=sj;valid(i,j);i++,j--) v.pb(i*W+j);
ordiag2[si][sj] = add_or(v);
xordiag2[si][sj] = add_xor(v);
}
vi axis1_unstrict_or, axis2_strict_or;
for (int si=0,sj=W-1;si<H;(sj==0?si++:sj--)){
vi orv,xorv;
for (int k=0;k<=K;k++){
int diagi = si+k, diagj = sj;
diagi -= diagj; diagj = 0;
if (!valid(diagi, diagj)){
diagj -= diagi; diagi = 0;
}
if (!valid(diagi, diagj)) continue;
assert(diagi == 0 || diagj == 0);
orv.pb(ordiag1[diagi][diagj]);
xorv.pb(xordiag1[diagi][diagj]);
}
if (orv.empty()) continue;
axis1_unstrict_or.pb(add_and({add_or(orv), add_not(add_xor(xorv))}));
}
int distleqK1 = add_or(axis1_unstrict_or);
for (int si=0,sj=0;si<H;(sj==W-1?si++:sj++)){
int diagi = si+K, diagj = sj;
diagj += diagi; diagi = 0;
if (!valid(diagi, diagj)){
diagi -= (-diagj + W - 1);
diagj = W-1;
}
if (!valid(diagi, diagj)) continue;
int or_idx = add_or({ordiag2[diagi][diagj], ordiag2[si][sj]});
int xor_idx = add_xor({xordiag2[diagi][diagj], xordiag2[si][sj]});
axis2_strict_or.pb(add_and({or_idx, add_not(xor_idx)})); // Whether it is distance K on the axis
}
int distK2 = add_or(axis2_strict_or);
int ok1 = add_and({distleqK1, distK2});
vi axis2_unstrict_or, axis1_strict_or;
for (int si=0,sj=0;si<H;(sj==W-1?si++:sj++)){ // antidiagonal
vi orv,xorv;
for (int k=0;k<=K;k++){
int diagi = si+k, diagj = sj;
diagj += diagi; diagi = 0;
if (!valid(diagi, diagj)){
diagi -= (-diagj + W - 1);
diagj = W-1;
}
if (!valid(diagi, diagj)) continue;
orv.pb(ordiag2[diagi][diagj]);
xorv.pb(xordiag2[diagi][diagj]);
}
axis2_unstrict_or.pb(add_and({add_or(orv), add_not(add_xor(xorv))}));
}
int distleqK2 = add_or(axis2_unstrict_or);
for (int si=0,sj=W-1;si<H;(sj==0?si++:sj--)){ // diagonal
int diagi = si+K, diagj = sj;
diagj -= diagi; diagi = 0;
if (!valid(diagi, diagj)){
diagi -= diagj;
diagj = 0;
}
if (!valid(diagi, diagj)) continue;
int or_idx = add_or({ordiag1[diagi][diagj], ordiag1[si][sj]});
int xor_idx = add_xor({xordiag1[diagi][diagj], xordiag1[si][sj]});
axis1_strict_or.pb(add_and({or_idx, add_not(xor_idx)})); // Whether it is distance K on the axis
}
int distK1 = add_or(axis1_strict_or);
int ok2 = add_and({distleqK2, distK1});
add_or({ok1, ok2});
}
