#ifndef SorahISA
#define SorahISA
#include SorahISA __FILE__ SorahISA
int N;
vector<int> mem;
int query(int mask) {
mask &= ((1 << N) - 1);
// cerr << "query: " << bitset<16>(mask).to_string() << "\n";
if (mem[mask] != -2) return mem[mask];
// cerr << " +\n";
vector<int> ask;
for (int i = 0; i < N; ++i) {
if (mask >> i & 1) ask.eb(i);
}
return mem[mask] = run_diagnostic(ask);
}
vector<int> malfunctioning_cores(int _N) {
N = _N, mem.assign(1<<N, -2);
mem[0] = -1, mem.back() = 1;
int thres = 0;
for (int delta = (1 << __lg(N)); delta; delta >>= 1) {
int mask = 0;
for (int bit = 0; bit < thres+delta; ++bit) mask |= (1 << bit);
if (query(mask) == -1) thres += delta;
}
int parity = query((1 << (thres+1)) - 1);
vector<int> ans(N, -1);
ans[thres] = 1;
int left = N-1;
int L = 0, R = thres, mask = (1 << (R+1)) - (1 << L);
while (left > 1) {
if (query(mask) != -1) {
mask &= ~(1 << L);
if (ans[L] != -1) mem[mask] = (ans[L] ? -1 : 1);
else ans[L] = (query(mask) == -1), --left;
L = (L + 1) % N;
}
else {
R = (R + 1) % N;
mask |= (1 << R);
if (ans[R] != -1) mem[mask] = (ans[R] ? 1 : -1);
else ans[R] = (query(mask) != -1), --left;
}
}
int left_id = -1;
for (int i = 0; i < N; ++i) {
if (ans[i] == -1) left_id = i;
else parity ^= ans[i];
}
ans[left_id] = parity;
return ans;
}
#else
#include "coreputer.h"
#pragma GCC optimize("Ofast", "unroll-loops")
#include <bits/stdc++.h>
using namespace std;
// #define int int64_t
// #define double __float80
using pii = pair<int, int>;
template <typename T> using Prior = std::priority_queue<T>;
template <typename T> using prior = std::priority_queue<T, vector<T>, greater<T>>;
// #define X first
// #define Y second
#define eb emplace_back
#define ef emplace_front
#define ee emplace
#define pb pop_back
#define pf pop_front
#define ALL(x) begin(x), end(x)
#define RALL(x) rbegin(x), rend(x)
#define SZ(x) ((int)(x).size())
#ifdef local
#define fastIO() void()
#define debug(...) \
fprintf(stderr, "%sAt [%s], line %d: (%s) = ", "\u001b[33m", __FUNCTION__, __LINE__, #__VA_ARGS__), \
_do(__VA_ARGS__), fprintf(stderr, "%s", "\u001b[0m")
template <typename T> void _do(T &&_t) {cerr << _t << "\n";}
template <typename T, typename ...U> void _do(T &&_t, U &&..._u) {cerr << _t << ", ", _do(_u...);}
#else
#define fastIO() ios_base::sync_with_stdio(0), cin.tie(0)
#define debug(...) void()
#endif
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
template <typename T, typename U> bool chmin(T &lhs, U rhs) {return lhs > rhs ? lhs = rhs, 1 : 0;}
template <typename T, typename U> bool chmax(T &lhs, U rhs) {return lhs < rhs ? lhs = rhs, 1 : 0;}
#endif
