#include <bits/stdc++.h>
using namespace std ;
vector<bool> send_packet(vector<bool> A);
vector<vector<bool>> encode(int num, const int &d) {
vector<vector<bool>> res ;
for(int i = d - 1; i > -1; i --) {
res.emplace_back(vector<bool>(31, (bool)(num >> i & 1))) ;
}
return res ;
}
void send_message(vector<bool> M, vector<bool> C) {
// SEND C WITH OPTIMIZATIONS
int ma = 0, pos = -1 ;
for(int i = 0; i < 31; i ++) if(!C[i]) {
int j = i ;
while(j < 30 && !C[j + 1]) ++ j ;
if(j - i + 1 > ma) {
ma = j - i + 1 ; pos = i ;
}
i = j ;
}
if(ma == 1) {
vector<vector<bool>> buck = encode(31, 5) ;
for(vector<bool> &cur : buck) {
send_packet(cur) ;
}
}
else {
vector<vector<bool>> buck = encode(pos, 5) ;
for(vector<bool> &cur : buck) {
send_packet(cur) ;
}
int k = pos - 1, l = pos + 2, key = -1 ;
if(!pos) k = l, ++ l ;
else if(pos == 29) l = k, -- k ;
vector<bool> pack(31, false) ;
pack[pos] = C[k] ; pack[pos + 1] = C[l] ;
key = (!C[k] ? k : (!C[l] ? l : -1)) ;
send_packet(pack) ;
vector<int> indices ;
int le = min(pos, k), ri = max(pos + 1, l) ;
for(int i = 0; i < 31; i ++) {
if(i >= le && i <= ri) continue ;
indices.emplace_back(i) ;
// cerr << i << ' ' ;
} //assert
for(int i = 2; i < indices.size(); i += 3) {
int u = indices[i - 2] ;
int v = indices[i - 1], w = indices[i] ;
vector<bool> pack(31, false) ;
pack[pos] = C[u] ; pack[pos + 1] = C[v] ;
// cerr << "-> " << pos << ' ' << u << ' ' << C[u] << ' ' << pos + 1 << ' ' << v << ' ' << C[v] << endl ;
if(key == -1) {
for(int r : indices) pack[r] = C[w] ;
}
else {
pack[key] = C[w] ;
}
send_packet(pack) ;
}
}
// SEND MESSAGE STRAIGHTLY FOWARD
vector<int> idx ;
for(int i = 0; i < 31; i ++) {
if(!C[i]) idx.emplace_back(i) ;
}
int s = (int)M.size() - 1 ;
reverse(M.begin(), M.end()) ;
for(int i = 0; i < 10; i ++) {
M.emplace_back((bool)(s >> i & 1)) ;
}
reverse(M.begin(), M.end()) ;
for(int i = 0; i < M.size();) {
vector<bool> pack(31, false) ;
int x = min((int)M.size() - i, 16) ;
for(int j = 0; j < x; j ++) {
pack[idx[j]] = M[i] ; ++ i ;
}
send_packet(pack) ;
}
}
vector<bool> receive_message(vector<vector<bool>> R) {
// DECODE THE STRING C
int pos = 0 ;
for(int i = 0; i < 5; i ++) {
vector<int> cnt(2, 0) ;
for(int j = 0; j < 31; j ++) {
++ cnt[(int)R[i][j]] ;
}
pos = pos << 1 | ((int)(cnt[1] > cnt[0])) ;
}
vector<bool> C(31, true) ;
int num = 5 ;
if(pos == 31) {
for(int d = 0; d < 31; d += 2) C[d] = false ;
}
else {
num = 15 ;
C[pos] = C[pos + 1] = false ;
int k = pos - 1, l = pos + 2, key = -1 ;
if(!pos) k = l, ++ l ;
else if(pos == 29) l = k, -- k ;
vector<int> indices ;
int le = min(pos, k), ri = max(pos + 1, l) ;
for(int i = 0; i < 31; i ++) {
if(i >= le && i <= ri) continue ;
indices.emplace_back(i) ;
}
C[k] = R[5][pos] ; C[l] = R[5][pos + 1] ;
key = (!C[k] ? k : (!C[l] ? l : -1)) ;
int iter = 2 ;
for(int i = 6; i < num; i ++, iter += 3) {
int u = indices[iter - 2] ;
int v = indices[iter - 1], w = indices[iter] ;
C[u] = R[i][pos] ; C[v] = R[i][pos + 1] ;
// cerr << "<- " << pos << ' ' << u << ' ' << R[i][pos] << ' ' << pos + 1 << ' ' << v << ' ' << R[i][pos + 1] << " | " << w << endl ;
if(key == -1) {
vector<int> cnt(2, 0) ;
for(int r : indices) ++ cnt[(int)R[i][r]] ;
C[w] = (cnt[1] > cnt[0]) ;
}
else {
C[w] = R[i][key] ;
}
}
}
// cerr << "Finished decoding C\n" ;
// DECODE THE SIZE OF MESSAGE AND ITS BITS
vector<int> idx ;
for(int i = 0; i < 31; i ++) {
if(!C[i]) idx.emplace_back(i) ;
}
int numSz = 0 ;
for(int i = 0; i < 10; i ++) {
numSz = numSz << 1 | ((int)R[num][idx[i]]) ;
}
++ numSz ;
int iter = 9 ;
vector<bool> res ;
for(; numSz > 0; numSz --) {
if(++ iter == 16) iter = 0, ++ num ;
res.emplace_back(R[num][idx[iter]]) ;
}
return res ;
}
