#ifndef hwe
#include "transfer.h"
#endif
#include <bits/stdc++.h>
using namespace std;
#define popcount(n) (__builtin_popcountll((n)))
#define clz(n) (__builtin_clzll((n)))
#define ctz(n) (__builtin_ctzll((n)))
#define lg(n) (63 - __builtin_clzll((n)))
#define BIT(n, i) (((n) >> (i)) & 1ll)
#define MASK(i) (1ll << (i))
#define FLIP(n, i) ((n) ^ (1ll << (i)))
#define ON(n, i) ((n) | MASK(i))
#define OFF(n, i) ((n) & ~MASK(i))
#define Int __int128
#define fi first
#define se second
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef pair<long long, int> pli;
typedef pair<int, long long> pil;
typedef vector<pair<int, int>> vii;
typedef vector<pair<long long, long long>> vll;
typedef vector<pair<long long, int>> vli;
typedef vector<pair<int, long long>> vil;
template <class T1, class T2>
bool maximize(T1 &x, T2 y) {
if (x < y) {
x = y;
return true;
}
return false;
}
template <class T1, class T2>
bool minimize(T1 &x, T2 y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <class T>
void remove_duplicate(vector<T> &ve) {
sort (ve.begin(), ve.end());
ve.resize(unique(ve.begin(), ve.end()) - ve.begin());
}
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
template <class T> T random(T l, T r) {
return uniform_int_distribution<T>(l, r)(rng);
}
template <class T> T random(T r) {
return rng() % r;
}
const int N = 1e6 + 5;
const int MOD = 1e9 + 7;
const int inf = 1e9;
const ll INF = 1e18;
vector<int> get_attachment(vector<int> source) {
int Xor = 0;
for (auto &x : source) Xor ^= x;
source.emplace_back(Xor);
int lim = lg(source.size());
for (int bit = 0; bit < lim; ++bit) {
int cur_xor = 0;
for (int i = 0; i < MASK(lim); ++i) if (BIT(i, bit)) cur_xor ^= source[i];
source.emplace_back(cur_xor);
}
return vector<int>(source.begin() + MASK(lim) - 1, source.end());
}
vector<int> retrieve(vector<int> data) {
int Xor = 0, lim = lg(data.size());
for (int i = 0; i < MASK(lim); ++i) Xor ^= data[i];
if (Xor != 0) {
int wrong_spot = 0;
for (int bit = 0; bit < lim; ++bit) {
int cur_xor = 0;
for (int i = 0; i < MASK(lim); ++i) if (BIT(i, bit)) cur_xor ^= data[i];
if (cur_xor != data[bit + MASK(lim)]) wrong_spot = ON(wrong_spot, bit);
}
data[wrong_spot] = !data[wrong_spot];
}
return vector<int>(data.begin(), data.begin() + MASK(lim) - 1);
}
#ifdef hwe
// signed main() {
// vector<int> data = get_attachment({1, 0, 1});
// vector<int> ans = retrieve(data);
// for (auto &x : ans) cerr << x << ' ';
// cerr << '\n';
// cerr << '\n'; return 0;
// }
#endif
