#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using db = double;
using str = string; // yay python!
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
#define tcT template <class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT > using V = vector<T>;
tcT, size_t SZ > using AR = array<T, SZ>;
tcT > using PR = pair<T, T>;
// pairs
#define mp make_pair
#define f first
#define s second
// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pb push_back
#define eb emplace_back
#define pf push_front
#define lb lower_bound
#define ub upper_bound
tcT > int lwb(V<T> &a, const T &b) { return int(lb(all(a), b) - bg(a)); }
// loops
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define F0R(i, a) FOR(i, 0, a)
#define ROF(i, a, b) for (int i = (b) - 1; i >= (a); --i)
#define R0F(i, a) ROF(i, 0, a)
#define trav(a, x) for (auto &a : x)
const int MOD = 1e9 + 7; // 998244353;
const int MX = 2e5 + 5;
const ll INF = 1e18; // not too close to LLONG_MAX
const ld PI = acos((ld)-1);
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
// bitwise ops
// also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(int x) { // assert(x >= 0); // make C++11 compatible until
// USACO updates ...
return x == 0 ? 0 : 31 - __builtin_clz(x);
} // floor(log2(x))
constexpr int p2(int x) { return 1 << x; }
constexpr int msk2(int x) { return p2(x) - 1; }
ll cdiv(ll a, ll b) {
return a / b + ((a ^ b) > 0 && a % b);
} // divide a by b rounded up
ll fdiv(ll a, ll b) {
return a / b - ((a ^ b) < 0 && a % b);
} // divide a by b rounded down
tcT > bool ckmin(T &a, const T &b) { return b < a ? a = b, 1 : 0; } // set a = min(a,b)
tcT > bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }
tcTU > T fstTrue(T lo, T hi, U f) {
hi++;
assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
T mid = lo + (hi - lo) / 2;
f(mid) ? hi = mid : lo = mid + 1;
}
return lo;
}
tcTU > T lstTrue(T lo, T hi, U f) {
lo--;
assert(lo <= hi); // assuming f is decreasing
while (lo < hi) { // find first index such that f is true
T mid = lo + (hi - lo + 1) / 2;
f(mid) ? lo = mid : hi = mid - 1;
}
return lo;
}
tcT > void remDup(vector<T> &v) { // sort and remove duplicates
sort(all(v));
v.erase(unique(all(v)), end(v));
}
tcTU > void erase(T &t, const U &u) { // don't erase
auto it = t.find(u);
assert(it != end(t));
t.erase(it);
} // element that doesn't exist from (multi)set
// INPUT
#define tcTUU tcT, class... U
tcT > void re(complex<T> &c);
tcTU > void re(pair<T, U> &p);
tcT > void re(V<T> &v);
tcT, size_t SZ > void re(AR<T, SZ> &a);
tcT > void re(T &x) { cin >> x; }
void re(db &d) {
str t;
re(t);
d = stod(t);
}
void re(ld &d) {
str t;
re(t);
d = stold(t);
}
tcTUU > void re(T &t, U &...u) {
re(t);
re(u...);
}
tcT > void re(complex<T> &c) {
T a, b;
re(a, b);
c = {a, b};
}
tcTU > void re(pair<T, U> &p) { re(p.f, p.s); }
tcT > void re(V<T> &x) { trav(a, x) re(a); }
tcT, size_t SZ > void re(AR<T, SZ> &x) { trav(a, x) re(a); }
tcT > void rv(int n, V<T> &x) {
x.rsz(n);
re(x);
}
// TO_STRING
#define ts to_string
str ts(char c) { return str(1, c); }
str ts(const char *s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) {
#ifdef LOCAL
return b ? "true" : "false";
#else
return ts((int)b);
#endif
}
tcT > str ts(complex<T> c) {
stringstream ss;
ss << c;
return ss.str();
}
str ts(V<bool> v) {
str res = "{";
F0R(i, sz(v)) res += char('0' + v[i]);
res += "}";
return res;
}
template <size_t SZ> str ts(bitset<SZ> b) {
str res = "";
F0R(i, SZ) res += char('0' + b[i]);
return res;
}
tcTU > str ts(pair<T, U> p);
tcT > str ts(T v) { // containers with begin(), end()
#ifdef LOCAL
bool fst = 1;
str res = "{";
for (const auto &x : v) {
if (!fst) res += ", ";
fst = 0;
res += ts(x);
}
res += "}";
return res;
#else
bool fst = 1;
str res = "";
for (const auto &x : v) {
if (!fst) res += " ";
fst = 0;
res += ts(x);
}
return res;
#endif
}
tcTU > str ts(pair<T, U> p) {
#ifdef LOCAL
return "(" + ts(p.f) + ", " + ts(p.s) + ")";
#else
return ts(p.f) + " " + ts(p.s);
#endif
}
// OUTPUT
tcT > void pr(T x) { cout << ts(x); }
tcTUU > void pr(const T &t, const U &...u) {
pr(t);
pr(u...);
}
void ps() { pr("\n"); } // print w/ spaces
tcTUU > void ps(const T &t, const U &...u) {
pr(t);
if (sizeof...(u)) pr(" ");
ps(u...);
}
// DEBUG
void DBG() { cerr << "]" << endl; }
tcTUU > void DBG(const T &t, const U &...u) {
cerr << ts(t);
if (sizeof...(u)) cerr << ", ";
DBG(u...);
}
#ifdef LOCAL // compile with -DLOCAL, chk -> fake assert
#define dbg(...) \
cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#define chk(...) \
if (!(__VA_ARGS__)) \
cerr << "Line(" << __LINE__ << ") -> function(" << __FUNCTION__ \
<< ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", \
exit(0);
#else
#define dbg(...) 0
#define chk(...) 0
#endif
void setPrec() { cout << fixed << setprecision(15); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
// FILE I/O
void setIn(str s) { freopen(s.c_str(), "r", stdin); }
void setOut(str s) { freopen(s.c_str(), "w", stdout); }
void setIO(str s = "") {
unsyncIO();
setPrec();
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) setIn(s + ".in"), setOut(s + ".out"); // for USACO
}
int n, p[MX];
int par[MX];
vi val[MX], child[MX];
int qmin(int x) {
if (!par[x]) {
assert(p[x]);
return p[x];
}
assert(p[x] == 0);
x = par[x];
int res = MOD;
while (x) {
assert(sz(val[x]));
trav(t, val[x]) ckmin(res, t);
if (sz(val[x]) == 2) {
assert(!par[x]);
break;
} else {
assert(sz(val[x]) == 1 && par[x]);
x = par[x];
}
}
assert(res != MOD);
return res;
}
void delChild(int a, int b) {
assert(a && par[b] == a);
auto it = find(all(child[a]), b);
assert(it != end(child[a]));
child[a].erase(it);
par[b] = 0;
}
void setChild(int a, int b) {
assert(a);
child[a].pb(b);
par[b] = a; // assert(p[b]);
p[b] = 0;
}
void setEq(int x) {
if (p[x]) return;
int v = qmin(x);
vi trail = {x};
while (find(all(val[trail.bk]), v) == end(val[trail.bk])) {
assert(trail.bk);
trail.pb(par[trail.bk]);
}
for (; sz(trail) > 1; trail.pop_back()) {
int t = trail.bk;
assert(sz(val[t]) && sz(child[t]) == 2);
int c = trail[sz(trail) - 2], C = child[t][0] + child[t][1] - c;
val[c].pb(v);
delChild(t, c);
delChild(t, C);
if (sz(val[t]) == 2) {
val[C].pb(val[t][0] + val[t][1] - v);
} else {
int P = par[t];
delChild(P, t);
setChild(P, C);
}
}
}
int main() {
setIO();
re(n);
FOR(i, 1, n + 1) re(p[i]);
FOR(i, 1, n + 1) {
if (!par[i] && sz(val[i])) {
assert(sz(val[i]) == 1 && p[i] == 0);
p[i] = val[i][0];
val[i] = {};
}
int x = qmin(i);
int mn = x;
if (2 * i <= n) ckmin(mn, p[2 * i]);
if (2 * i + 1 <= n) ckmin(mn, p[2 * i + 1]);
if (mn == x) setEq(i); // just remove the min
else if (mn == p[2 * i]) { // don't touch p[2*i+1]
if (!par[i]) p[2 * i] = p[i];
else {
int P = par[i];
delChild(P, i);
setChild(P, 2 * i);
}
} else {
if (!par[i]) val[i] = {p[i], p[2 * i]};
else val[i] = {p[2 * i]};
setChild(i, 2 * i), setChild(i, 2 * i + 1);
}
pr(mn, ' ');
}
// you should actually read the stuff at the bottom
}
