#include "machine.h"
#include <bits/stdc++.h>
using namespace std;
int n;
bool validate(const vector<int>& candidate, const vector<int>& S) {
vector<int> sortedCandidate = candidate, sortedS = S;
sort(sortedCandidate.begin(), sortedCandidate.end());
sort(sortedS.begin(), sortedS.end());
return sortedCandidate == sortedS;
}
vector<int> find_permutation(int N) {
n = N;
vector<int> A(N), S(N);
if (N % 2 == 1) {
for (int i = 0; i < N; i++) {
A[i] = i + 1;
S[i] = i + 1;
}
} else {
for (int i = 0; i < N - 2; i++) {
A[i] = i;
S[i] = i;
}
A[N - 2] = N + 1;
A[N - 1] = N + 2;
S[N - 2] = N + 1;
S[N - 1] = N + 2;
}
vector<int> B = use_machine(A);
int trueX = -1;
vector<int> candidateArr(N);
for (int x = 0; x < 256; x++) {
for (int i = 0; i < N; i++) {
candidateArr[i] = B[i] ^ x;
}
if (validate(candidateArr, S)) {
trueX = x;
break;
}
}
if (trueX < 0)
return vector<int>();
for (int i = 0; i < N; i++) {
candidateArr[i] = B[i] ^ trueX;
}
unordered_map<int, int> pos;
for (int j = 0; j < N; j++) {
pos[A[j]] = j;
}
vector<int> P(N);
for (int i = 0; i < N; i++) {
P[i] = pos[candidateArr[i]];
}
return P;
}
