#include "vision.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#define watch(x) cout<<(#x)<<"="<<x<<endl
#define forn(i,a,b) for(int i=(a);i<(b);i++)
#define fore(i,a,b) for(int i=(a);i<=(b);i++)
#define pb push_back
#define F first
#define S second
#define fbo find_by_order
#define ook order_by_key
typedef long long ll;
typedef vector<int> vi;
typedef pair<ll,ll> ii;
typedef vector<ii> vii;
typedef long double ld;
typedef tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update> pbds;
void SD(int t=0){ cout<<"TEST "<<t<<endl; }
const int MAXN = 405;
const int MOD = 1e9+7;
bool DEBUG=0;
/*
int add_and(std::vector<int> Ns);
int add_or(std::vector<int> Ns);
int add_xor(std::vector<int> Ns);
int add_not(int N);
*/
int dist(ii a, ii b)
{
return abs(a.F-b.F)+abs(a.S-b.S);
}
vi v;
int off;
vector<int> d1[MAXN],d2[MAXN];
int t1[2],t2[2];
void construct_network(int n, int m, int K)
{
if(n*m==2){
add_or({0,1});
return;
}
off=m-1;
vi all;
for(int i=0;i<n;i++) for(int j=0;j<m;j++)
{
all.pb(i*m+j);
d1[i+j].pb(i*m+j);
d2[i-j+off].pb(i*m+j);
}
//create dummy 0 and 1
int zero = add_and(all);
int one = add_or(all);
forn(i,0,m+n-1)
{
int tmp=add_or(d1[i]);
if(i==0) t1[0]=tmp;
if(i==m+n-2) t1[1]=tmp;
}
forn(i,0,m+n-1)
{
int tmp=add_or(d2[i]);
if(i==0) t2[0]=tmp;
if(i==m+n-2) t2[1]=tmp;
}
vi exact,test;
//----------------------------------------------
//d1 K, d2 large
for(int i=t1[0];i+K<=t1[1];i++)
{
v={i,i+K};
exact.pb(add_and(v)); if(DEBUG) cout<<"exact: "<<exact.back()<<endl;
}
for(int i=t2[0];i+K+1<=t2[1];i++)
{
v={i};
for(int j=i+K+1;j<=t2[1];j++) v.pb(j);
test.pb(add_and(v)); if(DEBUG) cout<<"test: "<<test.back()<<endl;
}
int f1,f2;
int final1, final2;
if(DEBUG){
cout<<"exact.size()="<<exact.size()<<endl;
cout<<"test.size()="<<test.size()<<endl;
}
f1 = (exact.size() ? add_or(exact) : zero);
f2 = (test.size() ? add_not(add_or(test)) : one);
v = {f1,f2}; if(DEBUG){ watch(f1); watch(f2); }
final1=add_and(v);
//phase 1 end
//----------------------------------------------
exact.clear(); test.clear(); v.clear();
//----------------------------------------------
//d2 exact, d1 large
for(int i=t2[0];i+K<=t2[1];i++)
{
v={i,i+K};
exact.pb(add_and(v)); if(DEBUG) cout<<"exact: "<<exact.back()<<endl;
}
for(int i=t1[0];i+K+1<=t1[1];i++)
{
v={i};
for(int j=i+K+1;j<=t1[1];j++) v.pb(j);
test.pb(add_and(v)); if(DEBUG) cout<<"test: "<<test.back()<<endl;
}
f1 = (exact.size() ? add_or(exact) : zero);
f2 = (test.size() ? add_not(add_or(test)) : one);
v = {f1,f2}; if(DEBUG){ watch(f1); watch(f2); }
final2=add_and(v);
//phase 2 end
//----------------------------------------------
//----------------------------------------------
//check one of them is correct
v = {final1, final2};
add_or(v);
}
