#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>     
#include <ext/pb_ds/tree_policy.hpp>  
#define pii pair<int,int>
#define pll pair<ll,ll>
#define fi first
#define se second
#define endl "\n"
#define rep(a,b,c) for(ll a=b; a<c; a++)
#define rep2(a,b,c,d) for(ll a=b; a<c; a+=d)
#define repr(a,b,c) for(ll a=b-1; a>c-1; a--)
#define repa(a,b) for(const auto &a: b)
#define multicase() int t; cin>>t; while(t--)
#define fastIO() ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define valid(c) cout<<(c ? "YES" : "NO")<<endl;
#define valid2(c,a,b) cout<<(c ? a : b)<<endl;
#define pq_min(a) priority_queue<a, vector<a>, greater<a>>
#define pq_max(a) priority_queue<a>
#define pb push_back
#define ppb pop_back
#define pf push_front
#define ppf pop_front
#define mid ((l+r)>>1)
#define flush endl<<flush
#define all(a) a.begin(), a.end()
#include "prison.h"
#include <vector>
using namespace std;
using namespace __gnu_pbds;
using vi = vector<int>;
using ll = long long;
template <typename T>
using vec = vector<T>;
template <typename T>
using ordered_set = tree<T, null_type,less<T>, rb_tree_tag,tree_order_statistics_node_update>;
mt19937_64 rnd(chrono::steady_clock::now().time_since_epoch().count());
vec<vi> devise_strategy(int N) {
	vec<vi> a;
	a.resize(27);
	int b=13, x=-1, y=-2, z;
	rep(i,0,27){
		a[i].resize(N+1);
		if(i&1) b--, swap(x,y);
		a[i][0]=b&1;
		z=i+(i&1);
		rep(j,1,N+1){
			if((i&1) != ((j>>b)&1)){
				if(j&(1<<b)) a[i][j]=x;
				else a[i][j]=y;
			}else{
				if(j&(1<<(b-1))) a[i][j]=z+1;
				else a[i][j]=z+2;
			}
			if(a[i][j]==28) a[i][j]=-1;
		}
	}
	return a;
}
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