#include "vision.h"
#include <bits/stdc++.h>
using namespace std;
//add_and
//add_or
//add_xor
//add_not
vector<int> operator + (vector<int> a, vector<int> b) {
vector<int> ans(a.begin(), a.end());
for (int i : b) ans.emplace_back(i);
return ans;
}
struct node {int x, y, idx;
node() {}
node(int _x, int _y, int _idx) : x(_x), y(_y), idx(_idx) {}
};
vector<node> nodes;
vector<int> A, B;
vector<int> C, D;
int solveFirstCase(int H, int W, int K) {
int conditionOne, conditionTwo;
if (1) {
vector<int> p;
for (int i1 = 0, i2 = 0; i1 < C.size(); i1++) {
while (i2 < C.size() && C[i2]-C[i1] <= K) ++i2;
--i2;
if (i1 == i2) continue;
vector<int> o;
for (int i = i1; i <= i2; i++) o.emplace_back(A[i]);
p.emplace_back(add_and({add_not(add_xor(o)), add_or(o)}));
}
conditionTwo = add_or(p + vector<int>{add_xor(A)});
}
if (1) {
vector<int> p, q;
for (int i1 = 0, i2 = 0; i1 < D.size(); i1++) {
while (i2 < D.size() && D[i2]-D[i1] <= K) ++i2;
--i2;
if (D[i2]-D[i1] != K) continue;
vector<int> o;
for (int i = i1; i <= i2; i++) o.emplace_back(B[i]);
p.emplace_back(add_and({add_not(add_xor(o)), add_or(o)}));
}
if (K != 1) {
for (int i1 = 0, i2 = 0; i1 < D.size(); i1++) {
while (i2 < D.size() && D[i2]-D[i1] < K) ++i2;
--i2;
if (i1 == i2) continue;
vector<int> o;
for (int i = i1; i <= i2; i++) o.emplace_back(B[i]);
q.emplace_back(add_and({add_not(add_xor(o)), add_or(o)}));
}
conditionOne = add_and(vector<int>{add_or(p)} + vector<int>{add_not(add_or(q))});
} else conditionOne = add_or(p);
}
return add_and({conditionOne, conditionTwo});
}
int solveSecondCase(int H, int W, int K) {
int conditionOne, conditionTwo;
if (1) {
vector<int> p;
for (int i1 = 0, i2 = 0; i1 < D.size(); i1++) {
while (i2 < D.size() && D[i2]-D[i1] <= K) ++i2;
--i2;
if (i1 == i2) continue;
vector<int> o;
for (int i = i1; i <= i2; i++) o.emplace_back(B[i]);
p.emplace_back(add_and({add_not(add_xor(o)), add_or(o)}));
}
conditionTwo = add_or(p + vector<int>{add_xor(B)});
}
if (1) {
vector<int> p, q;
for (int i1 = 0, i2 = 0; i1 < C.size(); i1++) {
while (i2 < C.size() && C[i2]-C[i1] <= K) ++i2;
--i2;
if (C[i2]-C[i1] != K) continue;
vector<int> o;
for (int i = i1; i <= i2; i++) o.emplace_back(A[i]);
p.emplace_back(add_and({add_not(add_xor(o)), add_or(o)}));
}
if (K != 1) {
for (int i1 = 0, i2 = 0; i1 < C.size(); i1++) {
while (i2 < C.size() && C[i2]-C[i1] < K) ++i2;
--i2;
if (i1 == i2) continue;
vector<int> o;
for (int i = i1; i <= i2; i++) o.emplace_back(A[i]);
q.emplace_back(add_and({add_not(add_xor(o)), add_or(o)}));
}
conditionOne = add_and(vector<int>{add_or(p)} + vector<int>{add_not(add_or(q))});
} else conditionOne = add_or(p);
}
return add_and({conditionOne, conditionTwo});
}
void construct_network(int H, int W, int K) {
nodes.clear();
A.clear();
B.clear();
C.clear();
D.clear();
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++) {
int x = i-j, y = i+j, idx = i*W+j;
nodes.emplace_back(x, y, idx);
}
sort(nodes.begin(), nodes.end(), [&](const node &a, const node &b) {
return a.x < b.x;
});
for (int i2 = 0; i2 < nodes.size();) {
int i1 = i2;
vector<int> nho;
while (i2 < nodes.size() && nodes[i2].x == nodes[i1].x) {
nho.emplace_back(nodes[i2].idx);
++i2;
}
A.emplace_back(add_or(nho));
C.emplace_back(nodes[i1].x);
}
sort(nodes.begin(), nodes.end(), [&](const node &a, const node &b) {
return a.y < b.y;
});
for (int i2 = 0; i2 < nodes.size();) {
int i1 = i2;
vector<int> nho;
while (i2 < nodes.size() && nodes[i2].y == nodes[i1].y) {
nho.emplace_back(nodes[i2].idx);
++i2;
}
B.emplace_back(add_or(nho));
D.emplace_back(nodes[i1].y);
}
add_or({solveFirstCase(H, W, K), solveSecondCase(H, W, K)});
}
