#include "prison.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using lld = long double;
using pii = pair<int,int>;
using pll = pair<ll, ll>;
using vi = vector<int>;
using vll = vector<ll>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using vlld = vector<lld>;
// #define endl '\n'
#define all(x) x.begin(),x.end()
#define lsb(x) x&(-x)
#define gcd(a,b) __gcd(a,b)
#define sz(x) (int)x.size()
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define fls cout.flush()
#define fore(i,l,r) for(auto i=l;i<r;i++)
#define fo(i,n) fore(i,0,n)
#define forex(i,r,l) for(auto i=r; i>=l;i--)
#define ffo(i,n) forex(i,n-1,0)
bool cmin(ll &a, ll b) { if(b<a){a=b;return 1;}return 0; }
bool cmax(ll &a, ll b) { if(b>a){a=b;return 1;}return 0; }
void valid(ll in) { cout<<((in)?"YES\n":"NO\n"); }
ll lcm(ll a, ll b) { return (a/gcd(a,b))*b; }
ll gauss(ll n) { return (n*(n+1))/2; }
vector<vector<int>> devise_strategy(int N) {
vector<vector<int>> ans;
vector<int> ar(N+1);
ar[0] = 0;
fore (j, 1, N+1) {
if (j&(1<<12)) ar[j] = 2;
else ar[j] = 1;
}
ans.pb(ar);
ll x = 0, idx = 1;
forex (b, 12, 0) {
x ^= 1;
ar[0] = x;
fore (j, 1, N+1) {
ll t = (j&(1<<b)) ? 1 : 0;
if (t) ar[j] = (x == 1 ? -1 : -2);
else if (b >= 1) ar[j] = idx+2 + ((j&(1<<(b-1))) ? 1 : 0);
else ar[j] = -2;
}
ans.pb(ar);
idx++;
ar[0] = x;
fore (j, 1, N+1) {
ll t = (j&(1<<b)) ? 1 : 0;
if (t) {
if (b >= 1) ar[j] = idx + 1 + ((j&(1<<(b-1))) ? 1 : 0);
else ar[j] = -2;
} else ar[j] = (x == 1 ? -2 : -1);
}
ans.pb(ar);
idx++;
}
return ans;
}
