#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1ULL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(abs(a), abs(b));}
ll lcm(ll a, ll b){return abs(a) / gcd(a, b) * abs(b);}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ull mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
#include "abc.h"
const int OP_ZERO = 0; // f(OP_ZERO, x0, x1) = 0
const int OP_NOR = 1; // f(OP_NOR, x0, x1) = !(x0 || x1)
const int OP_GREATER = 2; // f(OP_GREATER, x0, x1) = (x0 > x1)
const int OP_NOT_X1 = 3; // f(OP_NOT_X1, x0, x1) = !x1
const int OP_LESS = 4; // f(OP_LESS, x0, x1) = (x0 < x1)
const int OP_NOT_X0 = 5; // f(OP_NOT_X0, x0, x1) = !x0
const int OP_XOR = 6; // f(OP_XOR, x0, x1) = (x0 ^ x1)
const int OP_NAND = 7; // f(OP_NAND, x0, x1) = !(x0 && x1)
const int OP_AND = 8; // f(OP_AND, x0, x1) = (x0 && x1)
const int OP_EQUAL = 9; // f(OP_EQUAL, x0, x1) = (x0 == x1)
const int OP_X0 = 10; // f(OP_X0, x0, x1) = x0
const int OP_GEQ = 11; // f(OP_GEQ, x0, x1) = (x0 >= x1)
const int OP_X1 = 12; // f(OP_X1, x0, x1) = x1
const int OP_LEQ = 13; // f(OP_LEQ, x0, x1) = (x0 <= x1)
const int OP_OR = 14; // f(OP_OR, x0, x1) = (x0 || x1)
const int OP_ONE = 15; // f(OP_ONE, x0, x1) = 1
int alice(const int n, const char names[][5], const unsigned short numbers[], bool outputs_alice[]) {
for(int i = 0; i < 16; ++i) outputs_alice[i] = GETBIT(numbers[0], i);
return 16;
}
int bob(const int m,const char senders[][5],const char recipients[][5],bool outputs_bob[]) {
for(int i = 0; i < 10; ++i) outputs_bob[i] = GETBIT(m, i);
return 10;
}
struct LogicGate{
int x, y, type;
LogicGate(int x = -1, int y = -1, int type = -1): x(x), y(y), type(type){}
};
vector<LogicGate> gay;
vector<int> add_gate(vector<int> x, int y, int off_set = 0){
for(int it = off_set; it < (int) x.size(); ++it){
int i = x[it];
int j = gay.size();
gay.push_back(LogicGate(i, y, OP_XOR));
int k = gay.size();
gay.push_back(LogicGate(i, y, OP_AND));
x[it] = j;
y = k;
}
return x;
}
vector<int> add_gate(vector<int> x, vector<int> y){
if (x.size() < y.size()) swap(x, y);
for(int i = 0; i < (int) y.size(); ++i){
x = add_gate(x, y[i], i);
}
return x;
}
vector<int> multiply_gate(vector<int> x, vector<int> y){
vector<int> ans;
for(int i = 0; i < (int) x.size(); ++i){
ans.push_back(gay.size());
}
gay.push_back(LogicGate(0, 0, OP_ZERO));
for(int i = 0; i < (int) y.size(); ++i)
for(int j = 0; j < (int) x.size(); ++j){
if (i + j < (int)x.size()){
int k = gay.size();
gay.push_back(LogicGate(y[i], x[j], OP_AND));
ans = add_gate(ans, k, i + j);
}
}
return ans;
}
int circuit(const int la, const int lb, int operations[],int operands[][2],int outputs_circuit[][16]) {
for(int i = 0; i < la + lb; ++i) gay.emplace_back();
vector<int> x(la), y(lb);
for(int i = 0; i < la; ++i) x[i] = i;
for(int j = 0; j < lb; ++j) y[j] = j + la;
vector<int> z = multiply_gate(x, y);
for(int i = la + lb; i < (int) gay.size(); ++i) {
operations[i] = gay[i].type;
operands[i][0] = gay[i].x;
operands[i][1] = gay[i].y;
}
for(int i = 0; i< 16; ++i) outputs_circuit[0][i] = z[i];
return gay.size();
}
