#include "doll.h"
#include <bits/stdc++.h>
using namespace std;
using ii = pair<int, int>;
#define pb push_back
#define eb emplace_back
vector<ii> construct(int x) {
assert(x >= 2);
if (x == 2) {
vector<ii> ret;
ret.eb(-1, -1);
return ret;
}
// construct a sequence of switches that goes to exactly x outputs
if (x % 2 == 0) {
auto lh = construct(x / 2), rh = lh;
// relabel nodes in rh
for (auto &i : rh) {
if (i.first != -1) i.first += lh.size();
if (i.second != -1) i.second += lh.size();
}
vector<ii> lrh;
for (auto i : lh) lrh.pb(i);
for (auto i : rh) lrh.pb(i);
// create new switch
lrh.eb(lh.size() - 1, lh.size() + rh.size() - 1);
return lrh;
} else {
auto lh = construct((x + 1) / 2), rh = lh;
// relabel nodes in rh
for (auto &i : rh) {
if (i.first != -1) i.first += lh.size();
if (i.second != -1) i.second += lh.size();
}
// reroute last switch of left half
for (int i = (int)lh.size() - 1; i >= 0; i--) {
if (lh[i].second == -1) {
lh[i].second = lh.size() * 2;
break;
}
}
vector<ii> lrh;
for (auto i : lh) lrh.pb(i);
for (auto i : rh) lrh.pb(i);
// create new switch
lrh.eb(lh.size() - 1, lh.size() + rh.size() - 1);
return lrh;
}
}
void create_circuit(int M, vector<int> A) {
int N = A.size();
vector<int> C, X, Y;
auto XY = construct(N);
for (auto &i : XY) {
if (i.first == -1) i.first = 1;
else i.first = -(i.first + 1);
if (i.second == -1) i.second = 1;
else i.second = -(i.second + 1);
}
for (auto i : XY) {
X.pb(i.first);
Y.pb(i.second);
}
C.pb(1);
C.pb(-X.size());
for (int i = (int)Y.size() - 1; i >= 0; i--) {
if (Y[i] == 1) {
Y[i] = 0;
break;
}
}
answer(C, X, Y);
}
