#include <bits/stdc++.h>
using namespace std;
//#define int long long
#define double long double
vector<bool> send_packet(vector<bool> A);
void send_message(vector<bool> M, vector<bool> C){
int sz = (int)M.size();
vector<int> blank;
for (int i = 0; i < 31; i++){
if (C[i] == 0){
blank.push_back(i);
}
}
int c1 = 0, c2 = 0;
for (int i = 0; i < 16; i++){
c1 += (1 - C[i]);
}
for (int i = 15; i < 31; i++){
c2 += (1 - C[i]);
}
if (c2 > c1){
vector<bool> send(31);
for (int i = 0; i < 31; i ++){
send[i] = 1;
}
send_packet(send);
for (int i = 0; i < 9; i++){
vector<bool> send(31);
if (C[30 - i] == 1){
for (int i = 1; i < 31; i += 2){
send[i] = 1;
}
}
else{
for (int i = 0; i < 31; i += 2){
send[i] = 1;
}
}
send_packet(send);
}
int culm = 9;
reverse(blank.begin(), blank.end());
for (int i = 2; i < 16; i *= 2){
vector<bool> send(31);
for (int j = 0; j < i; j++){
send[blank[j]] = C[30 - (culm + j)];
}
culm += i;
send_packet(send);
}
vector<bool> snd(31);
for (int j = 0; j < 8; j++){
snd[blank[j]] = C[30 - (culm + j)];
}
send_packet(snd);
}
else{
vector<bool> send(31);
for (int i = 0; i < 31; i++){
send[i] = 0;
}
send_packet(send);
for (int i = 0; i < 9; i++){
vector<bool> send(31);
if (C[i] == 1){
for (int i = 1; i < 31; i += 2){
send[i] = 1;
}
}
else{
for (int i = 0; i < 31; i += 2){
send[i] = 1;
}
}
send_packet(send);
}
int culm = 9;
for (int i = 2; i < 16; i *= 2){
vector<bool> send(31);
for (int j = 0; j < i; j++){
send[blank[j]] = C[culm + j];
}
culm += i;
send_packet(send);
}
vector<bool> snd(31);
for (int j = 0; j < 8; j++){
snd[blank[j]] = C[culm + j];
}
send_packet(snd);
}
vector<bool> send(31);
int cur = 0;
for (int i = 0; i < 31; i++){
if (C[i] == 0){
send[i] = (sz >> cur) & 1;
cur++;
}
}
send_packet(send);
for (int i = 0; i < sz; i += 16){
vector<bool> send(31);
int cur = 0;
for (int j = 0; j < 31; j++){
if (C[j] == 0){
send[j] = M[(i + cur) % sz];
cur++;
}
}
send_packet(send);
}
}
vector<bool> receive_message(vector<vector<bool>> R){
vector<int> C(31);
vector<int> blank;
int c = 0;
for (int i = 0; i < 31; i++){
c += R[0][i];
}
if (c >= 16){
c = 1;
}
else{
c = 0;
}
if (c == 0){
for (int i = 0; i < 9; i++){
int c0 = 0, c1 = 0;
for (int j = 0; j < 31; j++){
if (R[i + 1][j] == 1){
if (j % 2== 1){
c1++;
}
else{
c0++;
}
}
}
if (c1 >= c0){
C[i] = 1;
}
else{
blank.push_back(i);
}
}
int culm = 9;
for (int i = 2; i < 16; i *= 2){
int lg = log2(i);
for (int j = 0; j < i; j++){
C[culm + j] = R[9 + lg][blank[j]];
if (C[culm + j] == 0){
blank.push_back(culm + j);
}
}
culm += i;
}
for (int j = 0; j < 8; j++){
C[culm + j] = R[9 + 4][blank[j]];
if (C[culm + j] == 0){
blank.push_back(culm + j);
}
}
}
else{
for (int i = 0; i < 9; i++){
int c0 = 0, c1 = 0;
for (int j = 0; j < 31; j++){
if (R[i + 1][j] == 1){
if (j % 2== 1){
c1++;
}
else{
c0++;
}
}
}
if (c1 >= c0){
C[30 - i] = 1;
}
else{
blank.push_back(30 - i);
}
}
int culm = 9;
for (int i = 2; i < 16; i *= 2){
int lg = log2(i);
for (int j = 0; j < i; j++){
C[30 - (culm + j)] = R[9 + lg][blank[j]];
if (C[30 - (culm + j)] == 0){
blank.push_back(30 - (culm + j));
}
}
culm += i;
}
for (int j = 0; j < 8; j++){
C[30 - (culm + j)] = R[9 + 4][blank[j]];
if (C[30 - (culm + j)] == 0){
blank.push_back(30 - (culm + j));
}
}
}
int sz = 0;
int cur = 0;
for (int i = 0; i < 31; i++){
if (C[i] == 0){
sz += (1 << cur) * R[14][i];
cur++;
}
}
vector<bool> ans(sz);
cur = 0;
for (int i = 15; i < R.size(); i++){
for (int j = 0; j < 31; j++){
if (C[j] == 0){
ans[cur % sz] = R[i][j];
cur++;
}
}
}
return ans;
}
/*
____ ___ ___ ____ _____ ____ ____ ___
| | | | \ | | /| | | | \
| | | | | |____ | | | _ |____ |___/
| | | | | | | | | | | | \
|____ |___| |___/ |____ | __|__ |____| |____ | \
*/
