#include "message.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
vector<vector<bool>> encode(vector<int> A, vector<bool> M){
ll x = 0;
for (int i=0;i<40;i++) if (M[i]) x |= 1LL<<i;
ll fact[16];
fact[0] = 1;
for (int i=1;i<16;i++) fact[i] = fact[i-1] * i;
assert(x < fact[15]);
vector<int> used(15), P;
for (int i=0;i<15;i++){
for (int j=0;j<15;j++) if (!used[j]){
if (x >= fact[14-i]){
x -= fact[14-i];
continue;
}
used[j] = 1;
P.push_back(A[j]);
break;
}
}
P.push_back(A.back());
P.insert(P.begin(), A.back());
vector<vector<bool>> ret(5, vector<bool>(31));
for (int i=0;i<(int)P.size()-1;i++){
for (int j=0;j<5;j++){
if (P[i+1] & (1<<j)) ret[j][P[i]] = true;
else ret[j][P[i]] = false;
}
}
return ret;
}
void send_message(std::vector<bool> M, std::vector<bool> C) {
M.push_back(true);
while(M.size() < 40 || M.size() % 16 != 8) M.push_back(false);
vector<int> A;
for (int i=0;i<31;i++) if (!C[i]) A.push_back(i);
assert(A.size() == 16);
auto ret = encode(A, vector<bool>(M.begin(), M.begin() + 40));
for (auto &V:ret) send_packet(V);
for (int i=40;i<(int)M.size();i+=16){
vector<bool> V(31);
for (int j=0;j<16;j++) V[A[j]] = M[i+j];
send_packet(V);
}
}
pair<vector<int>, vector<bool>> decode(vector<vector<bool>> R){
vector<int> go(31);
for (int i=0;i<5;i++){
for (int j=0;j<31;j++){
if (R[i][j]) go[j] |= 1<<i;
}
}
vector<int> P;
for (int i=0;i<31;i++){
P.clear();
for (int j=i;;j=go[j]){
if (find(P.begin(), P.end(), j) != P.end()) break;
P.push_back(j);
}
if (P.end() - find(P.begin(), P.end(), go[P.back()]) != 16) continue;
P.erase(P.begin(), find(P.begin(), P.end(), go[P.back()]));
rotate(P.begin(), max_element(P.begin(), P.end()), P.end());
rotate(P.begin(), P.begin()+1, P.end());
break;
}
ll x = 0;
ll fact[16];
fact[0] = 1;
for (int i=1;i<16;i++) fact[i] = fact[i-1] * i;
vector<int> A = P, used(P.size());
sort(A.begin(), A.end());
for (int i=0;i<15;i++){
for (int j=0;j<15;j++){
if (P[i] == A[j]){
used[j] = 1;
break;
}
if (!used[j]) x += fact[14-i];
}
}
vector<bool> M(40);
for (int i=0;i<40;i++) if (x&(1LL<<i)) M[i] = true;
return {A, M};
}
std::vector<bool> receive_message(std::vector<std::vector<bool>> R) {
auto [A, M] = decode(vector<vector<bool>>(R.begin(), R.begin() + 5));
for (int i=5;i<(int)R.size();i++){
for (int j=0;j<16;j++){
if (R[i][A[j]]) M.push_back(true);
else M.push_back(false);
}
}
while(!M.back()) M.pop_back();
M.pop_back();
return M;
}
