#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1ULL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(abs(a), abs(b));}
ll lcm(ll a, ll b){return abs(a) / gcd(a, b) * abs(b);}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ull mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
// mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
mt19937_64 rng(1);
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
double rngesus_d(double l, double r){
double cur = rngesus(0, MASK(60) - 1);
cur /= MASK(60) - 1;
return l + cur * (r - l);
}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
#include "squares.h"
ostream& operator << (ostream &os, pair<int, int> x){
return os << "(" << x.first << ", " << x.second << ")";
}
namespace Sigma{
int n;
vector<vector<int>> graphIn, graphOut;
vector<bool> visited;
vector<int> res;
int cnt = 0;
bool check = false;
string s;
void Try(int u){
visited[u] = true;
res[cnt] = u;
cnt++;
if (cnt == MASK(n)){
check = true;
s = string(n - 1, '0');
for(int i = 0; i<MASK(n); ++i)
if (res[i] % 2 == 0) s += "0";
else s += "1";
return;
}
for(int v:graphOut[u]){
if (check) return;
if (!visited[v])
Try(v);
}
cnt--;
visited[u] = false;
res[cnt] = 0;
}
void main(int _n){
n = _n;
graphIn.resize(MASK(n));
graphOut.resize(MASK(n));
visited.resize(MASK(n));
res.resize(MASK(n));
long t = MASK(n) - 1;
for(long i = 0; i < MASK(n); ++i){
long a = (i << 1) & t;
long b = a + 1;
if (a != i) {
graphOut[i].push_back(a);
graphIn[a].push_back(i);
}
if (b != i){
graphOut[i].push_back(b);
graphIn[b].push_back(i);
}
}
Try(0);
}
}
vector<int> paint(int n){
Sigma::main(10);
string s = Sigma::s;
vector<int> ans;
for(int i = 0; i < n; ++i) ans.push_back(s[i] - '0');
ans.push_back(10);
return ans;
}
int find_location(int n, vector<int> c){
Sigma::main(10);
string s = Sigma::s;
vector<int> ans;
for(int i = 0; i < n; ++i) ans.push_back(s[i] - '0');
while(ans.size() > n) ans.pop_back();
for(int i = 0; i < 10; ++i) ans.push_back(-1);
for(int i = 0; i < n; ++i){
bool check = true;
for(int j = 0; j < 10; ++j) if (ans[i + j] != c[j]){
check = false;
break;
}
if (check) return i;
}
return -1;
}
