#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1ULL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(abs(a), abs(b));}
ll lcm(ll a, ll b){return abs(a) / gcd(a, b) * abs(b);}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ull mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
#include "prison.h"
int split_percent[] = {0, 1, 2, 2, 3, 3, 3, 3, 3};
int block[] = {2, 4, 10, 22, 68, 206, 620, 1862, 5588};
int get_next(int desired_range, int cur_range, int layer, int num, int side){
// cout << desired_range << " " << cur_range << " " << layer << " " << num << " " << side << endl;
if (num == 0){
if (side == 0) return -1;
else return -2;
}
if (num == cur_range - 1){
if (side == 1) return -1;
else return -2;
}
if (desired_range < cur_range){
num--;
num %= block[layer - 1];
return get_next(desired_range, block[layer - 1], layer - 1, num, side);
}
else{
num--;
num /= block[layer - 1];
int sum = 1;
for(int i = 0; i <= 8; ++i) if (block[i] < desired_range) sum += split_percent[i];
sum += num;
return sum;
}
}
vector<vector<int>> devise_strategy(int N) {
vector<vector<int>> ans(21, vector<int>(N+1));
for(int i = 1; i <= N; ++i){
ans[0][i] = get_next(5588, 5588, 8, i-1, 0);
}
for(int j = 1; j <= 20; ++j){
int current_bit = -1, turn = -1, last_digit = -1;
int sum = 0;
for(int i = 1; i <= 8; ++i){
sum += split_percent[i];
if (sum >= j){
current_bit = i;
last_digit = j - sum + split_percent[i];
break;
}
}
turn = current_bit % 2;
if (turn == 0){
ans[j][0] = 1;
for(int i = 1; i <= N; ++i){
int cur = get_next(block[current_bit], 5588, 8, i-1, 1);
if (cur < 0) ans[j][i] = cur;
else if (cur > j){
ans[j][i] = -1;
}
else if (cur < j){
ans[j][i] = -2;
}
else{
ans[j][i] = get_next(block[current_bit - 1], 5588, 8, i-1, 1);
}
}
}
else{
ans[j][0] = 0;
for(int i = 1; i <= N; ++i){
int cur = get_next(block[current_bit], 5588, 8, i-1, 0);
if (cur < 0) ans[j][i] = cur;
else if (cur > j){
ans[j][i] = -2;
}
else if (cur < j){
ans[j][i] = -1;
}
else{
ans[j][i] = get_next(block[current_bit - 1], 5588, 8, i-1, 0);
}
}
}
}
return ans;
}
