#include <bits/stdc++.h>
#define SIZE(x) int(x.size())
using namespace std;
std::vector<int> get_attachment(std::vector<int> source)
{
vector<int>cal;
vector<int>ag, ag2;
int pot=1, i, pos=0,cP=0, j, un;
for(i=0; pos<SIZE(source); i++)
{
if(i+1==pot)
{
pot*=2;
cP++;
cal.push_back(2);
}
else
{
cal.push_back(source[pos]);
pos++;
}
}
pot=1;
for(i=0; i<cP; i++)
{
un=0;
for(j=pot-1; j<SIZE(cal); j++)
{
if((j+1)&pot)
{
if(cal[j]==1)
un++;
}
}
if(un%2==0)
ag.push_back(0);
else
ag.push_back(1);
pot*=2;
}
for(i=SIZE(ag)-1; i>=0; i--)
{
ag2.push_back(ag[i]);
}
return ag2;
}
std::vector<int> retrieve(std::vector<int> data)
{
vector<int>ret(SIZE(data)), comp(SIZE(data)), ag, ag2;
int pot=1, pos=0, i, cP=0, j, un;
for(i=0; i<SIZE(ret); i++)
{
if(i+1==pot)
{
ret[i]=data[SIZE(data)-1];
comp[i]=2;
cP++;
ag2.push_back(ret[i]);
data.pop_back();
pot*=2;
}
else
{
ret[i]=data[pos];
comp[i]=ret[i];
pos++;
}
}
pot=1;
for(i=0; i<cP; i++)
{
un=0;
for(j=pot-1; j<SIZE(comp); j++)
{
if((j+1)&pot)
{
if(comp[j]==1)
un++;
}
}
if(un%2==0)
ag.push_back(0);
else
ag.push_back(1);
pot*=2;
}
vector<bool>bus(cP,1);
for(i=0; i<SIZE(ag); i++)
{
if(ag[i]!=ag2[i])
{
bus[i]=0;
}
}
pot=1;
int arr=0;
for(auto k:bus)
{
if(k==0)
{
arr=arr|pot;
}
pot*=2;
}
for(i=0; i<SIZE(ret); i++)
{
if(i+1==arr)
{
ret[i]=!ret[i];
}
}
vector<int>ans;
pot=1;
for(i=0; i<SIZE(ret); i++)
{
if(i+1==pot)
{
pot*=2;
}
else
{
ans.push_back(ret[i]);
}
}
return ans;
}
