#include <bits/stdc++.h>
using namespace std;
// you may find the definitions useful
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
const int LG = 16;
const int MAXN = 30;
int alice(
const int n,
const char name[][5],
const unsigned short numbers[],
bool outputs_alice[]
) {
map <string, int> hasher;
for (int i = 0; i < n; ++ i)
hasher[name[i]];
int cur = 0;
for (auto &[x, y] : hasher) y = cur ++;
for (int i = 0; i < n; ++ i){
for (int b = 0; b < LG; ++ b)
outputs_alice[hasher[name[i]] * LG + b] = (numbers[i] >> b) & 1;
}
if (n == 1) return LG;
int l = n * LG;
for (int i = 0; i < n; ++ i)
outputs_alice[l + i * MAXN + hasher[name[i]]] = true;
return l + MAXN * n;
}
int bob(
const int m,
const char senders[][5],
const char recipients[][5],
bool outputs_bob[]
) {
map <string, int> hasher;
for (int i = 0; i < m; ++ i)
hasher[senders[i]] = hasher[recipients[i]];
int cur = 0;
for (auto &[x, y] : hasher) y = cur ++;
if (cur == 1) return m;
for (int i = 0; i < m; ++ i)
outputs_bob[hasher[senders[i]] + MAXN * hasher[recipients[i]]] = true;
return 900;
}
int circuit(
const int la,
const int lb,
int operations[],
int operands[][2],
int outputs_circuit[][LG]
) {
int l = la + lb - 1;
int n = la / (LG + MAXN);
if (la == LG) n = 1;
auto calc = [&](int oper, int a, int b){
operations[++ l] = oper;
operands[l][0] = a;
operands[l][1] = b;
return l;
};
auto alloc = [&](){
vector <int> ans(LG);
for (int i = 0; i < LG; ++ i)
ans[i] = calc(OP_ZERO, 0, 0);
return ans;
};
auto add = [&](vector <int> a, vector <int> b){
vector <int> carry(LG);
carry[0] = calc(OP_ZERO, 0, 0);
vector <int> ans(LG);
for (int i = 0; i < LG; ++ i){
ans[i] = calc(OP_XOR, calc(OP_XOR, a[i], b[i]), carry[i]);
if (i == 15) continue;
int tmp1 = calc(OP_AND, a[i], b[i]);
tmp1 = calc(OP_OR, tmp1, calc(OP_AND, a[i], carry[i]));
carry[i + 1] = calc(OP_OR, tmp1, calc(OP_AND, b[i], carry[i]));
}
return ans;
};
auto get_values = [&](vector <int> a, int b){
for (int &i : a)
i = calc(OP_AND, i, b);
return a;
};
auto OR = [&](vector <int> a, vector <int> b){
for (int i = 0; i < LG; ++ i)
a[i] = calc(OP_OR, a[i], b[i]);
return a;
};
if (n == 1){
vector <int> values(LG);
iota(values.begin(), values.end(), 0);
vector <int> myans = alloc();
for (int loops = 0; loops < lb; ++ loops)
myans = add(myans, values);
for (int i = 0; i < LG; ++ i)
outputs_circuit[0][i] = myans[i];
return l + 1;
}
vector <vector <int>> ans(n, alloc());
vector <vector <int>> values(n, vector <int> (LG));
for (int i = 0; i < n; ++ i)
iota(values[i].begin(), values[i].end(), i * LG);
for (int recevier = 0; recevier < n; ++ recevier){
for (int sender = 0; sender < n; ++ sender)
ans[recevier] = add(ans[recevier], get_values(values[sender], la + recevier * MAXN + sender));
}
int f = n * LG;
for (int i = 0; i < n; ++ i){
vector <int> myans = alloc();
for (int j = 0; j < n; ++ j)
myans = OR(myans, get_values(ans[j], f + i * MAXN + j));
for (int j = 0; j < LG; ++ j)
outputs_circuit[i][j] = myans[j];
}
return l + 1;
}
