#pragma GCC target ("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
#define endl '\n'
using namespace std;
int count(int n){
int ans = 0, m = 1;
while(m <= n) m *= 2, ans++;
return ans;
}
vector<vector<int>> devise_strategy(int N) {
int lg = count(N);
vector<vector<int>> s(lg * 2 + 1, vector<int>(N + 1, 0));
for(int i = 0; i <= 2 * lg; i++){
int d = i / 2;
int bit = i % 2;
if(d % 2 == 0) s[i][0] = 0;
else s[i][0] = 1;
for(int j = 1; j <= N; j++){
int _bit = (j & (1<<(lg - d)));
if(bit < _bit){
if(d % 2 == 0) s[i][j] = -2;
else s[i][j] = -1;
}else if(bit > _bit){
if(d % 2 == 0) s[i][j] = -1;
else s[i][j] = -2;
}else if(d == lg){
s[i][j] = -1;
}else{
s[i][j] = (d + 1) * 2 + (j & (1<<(lg - 1 - d)));
}
}
}
return s;
}
