#include "prison.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define sz(a) (int)a.size()
#define all(a) begin(a),end(a)
using ll = long long;
using vi = vector<int>;
const int mxN = (int)1e5+10;
const ll LINF = (ll)2e18;
const int B = 6;
int Pow[B+1][100];
vector<vi> devise_strategy(int N) {
for(int j = 1; j <= B; j++){
Pow[j][0] = 1;
for(int i = 1; i < 20; i++)
Pow[j][i]=Pow[j][i-1]*j;
}
int tot = 1, mxX = 1;
while(tot*B<=5000) tot*=B, mxX++;
int lim = mxX-1; mxX*=B;
vector<vi> ans(mxX+1,vi(N+1,0));
int fi = 1, cur = 0;
ans[0][0] = 0; // if we are at 0, inspect A.
for(int i = 1; i <= N; i++)
ans[0][i] = 1+i/Pow[B][lim];
for(int i = lim; i>=0; i--){
cur^=1;
for(int j = fi; j < fi+B; j++){
ans[j][0] = cur;
for(int k = 1; k <= N; k++){
int curA=(k%Pow[B][i+1])/Pow[B][i], curB = j-fi;
if(cur) swap(curA,curB);
if(curA<curB) ans[j][k]=-1;
else if(curA>curB) ans[j][k]=-2;
else if(i) ans[j][k] = fi+B+(k%Pow[B][i])/Pow[B][i-1];
}
}
fi+=B;
}
return ans;
}
