#include "prison.h"
#include <bits/stdc++.h>
using namespace std;
#define ll int
#define sz(x) (ll)x.size()
#define F first
#define S second
#define pb push_back
#define MID ((l+r)/2)
#define dbg(x) cout<<#x<<": "<<x<<endl;
#define dbg2(x,y) cout<<#x<<": "<<x<<" "<<#y<<": "<<y<<endl;
#define dbg3(x,y,z) cout<<#x<<": "<<x<<" "<<#y<<": "<<y<<" "<<#z<<": "<<z<<endl;
#define dbg5(x,y,z,a,b) cout<<#x<<": "<<x<<" "<<#y<<": "<<y<<" "<<#z<<": "<<z<<" "<<#a<<": "<<a<<" "<<#b<<": "<<b<<endl;
typedef vector <ll> vi;
typedef pair <ll,ll> ii;
typedef vector <ii> vii;
typedef pair<ii,ii> i4;
typedef pair <ll, i4> i5;
void printVct(vi &v, string s = ""){
cout<<s<<": ";
for (ll i=0; i<sz(v); i++){
cout<<v[i]<<" ";
}
cout<<endl;
}
void printVct2D(vector <vi> &v, string s = ""){
cout<<s<<": "<<endl;
for (ll i=0; i<sz(v); i++){
cout<<i<<": ";
for (ll j =0; j<sz(v[i]); j++){
cout<<v[i][j]<<" ";
}
cout<<endl;
}
cout<<endl;
}
vector <vi> s;
ll next_free = 0;
queue<i5> q;
void addQ(ll a, ll b, ll c, ll d, ll e){
q.push(i5(a, i4(ii(b,c), ii(d,e))));
next_free ++;
}
bool calc(ll u, ll l, ll r, ll resVal){
ll new_range= (r-l+1);
ll val = next_free;
if (new_range == 1)
val = resVal;
for (ll i=l; i<=r; i++)
s[u][i] = val;
return (new_range>1);
}
vector<vi> devise_strategy(int n) {
addQ(0,1,n,1,n);
i5 f;
ll u, al,ar,bl,br;
ll mid;
while (!q.empty()){
f = q.front();
q.pop();
u = f.F;
al = f.S.F.F;
ar = f.S.F.S;
bl = f.S.S.F;
br = f.S.S.S;
// dbg5(u,al,ar,bl,br);
s.pb(vi(n+1));
ll range_a = ar - al + 1;
ll range_b = br - bl + 1;
if (range_a == range_b){
//check A
s[u][0] = 0;
if (range_a > 2){
mid = (al + ar) / 2;
if (calc(u, al, mid, -1))
addQ(next_free, al, mid, bl, br);
if (calc(u, mid+1, ar, -2))
addQ(next_free, mid+1, ar, bl, br);
}
else{
//place -1,-2
s[u][al] = -1;
s[u][ar] = -2;
}
}
else{
//check B
s[u][0] = 1;
if (range_b > 2){
mid = (bl + br) / 2;
if (calc(u, bl, mid,-2))
addQ(next_free, al, ar, bl, mid);
if (calc(u, mid+1, br, -1))
addQ(next_free, al, ar, mid+1, br);
}
else{
//place -1,-2
s[u][bl] = -2;
s[u][br] = -1;
}
}
}
// printVct2D(s, "s");
return s;
}
