#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define pb emplace_back
#define AI(i) begin(i), end(i)
template<class T> bool chmin(T &a, T b) { return b < a && (a = b, true); }
template<class T> bool chmax(T &a, T b) { return a < b && (a = b, true); }
#ifdef KEV
#define DE(args...) kout("[ " + string(#args) + " ] = ", args)
void kout() { cerr << endl; }
template<class T, class ...U> void kout(T a, U ...b) { cerr << a << ' ', kout(b...); }
template<class T> void debug(T l, T r) { while (l != r) cerr << *l << " \n"[next(l)==r], ++l; }
#else
#define DE(...) 0
#define debug(...) 0
#endif
const int MAX_N = 300010, inf = 1e9;
#include "doll.h"
void create_circuit(int M, std::vector<int> A) {
int n = A.size();
// C is the place where the ith trigger connect to
vector<int> C(M + 1), X, Y;
auto new_s = [&]() {
int ret = X.size();
X.pb(-1), Y.pb(-1);
return ret;
};
auto addf = [&](vector<int> a, int f) {
a.insert(begin(a), f);
return a;
};
auto sid = [&](int id) { return - (id+1); };
int P = inf;
function<vector<int>(vector<int>)> solve = [&](vector<int> target) {
int osz = target.size(), sz = osz;
while (osz != (osz&-osz))
osz += osz&-osz;
int more = osz - sz;
vector<int> allid(sz-1); iota(AI(allid), 0);
vector<int> pos;
function<void(int,vector<int>)> gen = [&](int more, vector<int> allid) {
DE(more, allid.size());
if (more == 0) return ;
if (more == allid.size()) {
pos.insert(end(pos), AI(allid));
return;
}
vector<int> L, R;
for (int i = 0;i < allid.size();++i) {
(i&1?R:L).pb(allid[i]);
}
int sz = L.size(), lm = min(more, sz), rm = more - lm;
gen(lm, L), gen(rm, R);
};
gen(more, allid);
DE(sz, osz, pos.size());
vector<int> val(osz);
vector<int> ban(osz);
for (int i : pos) {
ban[i] = true;
val[i] = P;
}
for (int i = 0, j = 0;i < sz;++i) {
while (ban[j]) ++j;
val[j++] = target[i];
}
return val;
};
function<int(vector<int>)> create = [&](vector<int> target) {
if (target.size() == 1) {
return target[0];
}
int cur = new_s();
if (count(AI(target), target[0]) == target.size()) {
X[cur] = target[0], Y[cur] = target[0];
return sid(cur);
}
vector<int> L, R;
for (int i = 0;i < target.size();++i) {
(i&1?R:L).pb(target[i]);
}
int a = create(L), b = create(R);
X[cur] = a, Y[cur] = b;
return sid(cur);
};
A.pb(0);
vector<vector<int>> pos(M + 1);
for (int i = 0;i < n;++i)
pos[ A[i] ].pb(i);
C[0] = A[0];
vector<int> tar = solve(vector<int>(begin(A)+1, end(A)));
assert(tar.back() == 0);
int g = create(tar);
for (int i = 1;i <= M;++i)
C[i] = g;
for (int i = 0;i < X.size();++i) {
if (X[i] == P) X[i] = g;
if (Y[i] == P) Y[i] = g;
}
debug(AI(C));
DE(n, X.size(), Y.size());
//assert(X.size() <= n + __lg(n) + 10);
answer(C, X, Y);
}
