#include<bits/stdc++.h>
#include "message.h"
using namespace std;
#define N 1000010
#define int long long
#define db long double
#define pii pair<int,int>
#define st first
#define ed second
#define mkp make_pair
#define pb push_back
#define eps 1e-9
#define mod 998244353
#define mod2 1000000007
#define bs 13131
#define bs2 131
#define INF 0x3f3f3f3f3f3f3f3f
#define il inline
#define vi vector<int>
#define ins insert
#define umap unordered_map
#define uset unordered_set
#define R(x) x.begin(),x.end()
#define B(x) x.begin()
#define E(x) x.end()
#define lb lower_bound
#define ub upper_bound
il int read(){
int x=0,f=1;
char ch=getchar();
while(ch<'0'||ch>'9'){
if(ch=='-')f=-1;
ch=getchar();
}
while(ch>='0'&&ch<='9'){
x=(x<<1)+(x<<3)+(ch^48);
ch=getchar();
}
return x*f;
}
void send_message(std::vector<bool> M, std::vector<bool> C){
M.pb(1),M.resize(1025,0);
vector<int> p;
vector<int> d(16);
for(int i=0;i<31;i++)if(!C[i])p.pb(i);
for(int i=0;i<16;i++)d[i]=(p[(i+1)%16]-p[i]+31)%31;
vector<vector<bool>> data(66,vector<bool>(31,0));
int pos=0;
for(int i=0;i<16;i++){
for(int j=0;j<d[i]-1;j++)data[p[i]][j]=0;
data[p[i]][d[i]-1]=1;
for(int j=d[i];j<66;j++)data[j][p[i]]=M[pos++];
}
for(int i=0;i<66;i++)send_packet(data[i]);
}
std::vector<bool> receive_message(std::vector<std::vector<bool>> R){
vector<int> to(31,0),vis(31,0);
for(int i=0;i<31;i++)
for(int j=0;j<66;j++)
if(R[j][i]){
to[i]=(i+j+j)%31;
break;
}
vector<int> p,tmp;
for(int i=0;i<31;i++){
if(vis[i])continue;
tmp.clear();
int now=i;
do{tmp.pb(now),now=to[now],vis[now]=1;}while(now!=i);
if(tmp.size()==16){
p=tmp;
break;
}
}
vector<bool> ans;
for(auto x:p)
for(int i=0;i<66;i++)
if(R[i][x]){
for(int j=i+1;j<66;j++)
ans.pb(R[j][x]);
break;
}
while(!ans.back())ans.pop_back();
ans.pop_back();
return ans;
}