Q. Prims and Permutation

#include <bits/stdc++.h>
using namespace std;
#define cin(vec) for(auto& i : vec) cin >> i
#define cin_2d(vec, n, m) for(int i=0; i<n; i++) for(int j=0; j<m && cin >> vec[i][j]; j++);
#define cout(vec) for(auto& i : vec) cout << i << " "; cout << "\n";
#define cout_2d(vec, r, c) for(int i=0; i<r; i++, cout << "\n") for(int j=0; j<c && cout << vec[i][j] << " "; j++);
#define cout_map(mp) for(auto& [f, s] : mp) cout << f << " : " << s << "\n";
#define matrix(grid, n, m) vector < vector <ll> > grid(n, vector <ll> (m));
#define Time cerr << "Time Taken: " << (float)clock() / CLOCKS_PER_SEC << " Secs" << "\n";
#define ceil(n, m) (((n) / (m)) + ((n) % (m) ? 1 : 0))
#define fixed(n) cout << fixed << setprecision(n)
#define Num_of_Digits(n) ((int)log10(n)+1)
#define getline(s) getline(cin >> ws, s)
#define to_decimal(bin) stoi(bin, nullptr, 2)
#define TC int t; cin >> t; while(t--)
#define rall(s) s.rbegin(), s.rend()
#define all(s) s.begin(), s.end()
#define sz(x) int(x.size())
#define Pair pair <int, int>
#define fi first
#define se second
#define ll long long
#define PI acos(-1)
#define Mod 1'000'000'007
#define INF 2'000'000'000
#define EPS 1e-9

void Anwar_Rizk(){
  ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
  #ifndef ONLINE_JUDGE    // Anwar Rizk 🥇🖤
    freopen("input.txt", "r", stdin), freopen("output.txt", "w", stdout);
  #endif
  Time
}

bool is_prime(ll n){
  if(n < 2 || (n % 2 == 0 && n != 2)) return false;
  for(int i = 3; i <= sqrt(n); i += 2)
      if(n % i == 0) return false;
  return true;
}

bool is_good(vector <int>& v){
  for(int i = 1; i < sz(v); i++){
    if(!is_prime(v[i] + v[i - 1]))  return false;
  }
  return true;
}

int n;
set < vector < int > > answer;
vector < int > nums;

void permut(int l, int r){
  if(l == r){
    if(nums.front() == 1 && is_good(nums))
    answer.emplace(nums);
    return;
  }
  for(int i = l; i <= r; i++){
    swap(nums[l], nums[i]);
    permut(l + 1, r);
    swap(nums[l], nums[i]);
  }
}

int main()
{   Anwar_Rizk();

    cin >> n;
    nums.resize(n);
    for(int i = 0; i < n; i++)  nums[i] = i + 1;
    permut(0, n - 1);
    for(auto& v : answer){
      cout(v);
    }

  return 0;
}