//#pragma GCC optimize("Ofast,no-stack-protector")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
#pragma GCC optimize("unroll-loops")
/*#pragma GCC optimize("section-anchors")
#pragma GCC optimize("profile-values,profile-reorder-functions,tracer")
#pragma GCC optimize("vpt")
#pragma GCC optimize("rename-registers")
#pragma GCC optimize("move-loop-invariants")
#pragma GCC optimize("unswitch-loops")
#pragma GCC optimize("function-sections")
#pragma GCC optimize("data-sections")
#pragma GCC optimize("branch-target-load-optimize")
#pragma GCC optimize("branch-target-load-optimize2")
#pragma GCC optimize("btr-bb-exclusive")*/
//#pragma comment(linker, "/STACK:367077216")
#define _CRT_SECURE_NO_WARNINGS
#include <chrono>
#include <set>
#include <map>
#include <deque>
#include <string>
#include <cstdint>
#include <cmath>
#include <queue>
#include <cassert>
#include <random>
#include <bitset>
#include <iomanip>
#include <numeric>
#include <time.h>//////////////
#include <ctime>
#include <string>
#include <cstdio>
#include <vector>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <unordered_map>
#include <unordered_set>
//++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++
//#define endl '\n'
#define mp make_pair
#define pbc push_back
#define pob pop_back()
#define empb emplace_back
#define queuel queue<long long>
#define sqr(a) ((a) * (a))
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define pin(p) cin >> p.first >> p.second;
#define uniq(a) sort(all(a));(a).resize(unique(all(a)) - a.begin());
#define rev(v) reverse(v.begin(), v.end());
#define sout(s, c) for (auto i : s) cout << i << c;
#define pout(p) cout << p.first << " " << p.second;
#define er(v, l, r) erase(v.begin() + l, v.begin() + r);
#define vin(v) for (ll i = 0; i < v.size(); ++i) cin >> v[i];
#define vout(v, c) for (int i = 0; i < v.size(); ++i) cout << v[i] << c;
#define pushi(v, a) for (int i = 0; i < a.size(); ++i) v.push_back(a[i]);
#define fastio() ios_base::sync_with_stdio(0); cout.tie(0); cin.tie(0); srand(time(NULL))
#define dab(v) for(auto i:v)cout<<i<<' ';
#define sp system("pause")
//++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++
using namespace std;
//++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
//++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++--++
mt19937 rnd(time(0) + 228 + 'k' + 'e' + 'k' + 'e' + 'r' + 'o' + 'f' + 'e' + 'y');
const ld EPS = 1e-10;
bool check(int x)
{
	for (int i = 2; i * i <= x; ++i) if (x % i == 0) return 0;
	return 1;
}
const ld PI = acos(-1);
const int MOD7 = 1000000007;
const int MOD9 = 1000000009;
int mod = MOD7;
const int inf = 1e9;
pair<int, int> merge(pair<int, int> a, pair<int, int> b)
{
	vector<int> keks = { a.first, b.first, a.second, b.second };
	uniq(keks);
	sort(rall(keks));

	return { keks[0], keks[1] };
}
int kekor(vector<int> a)
{
	//return a[0] | a[1];
	int ans = 0;
	for (int bt = 19; bt >= 0; --bt)
	{
		int cnt = 0;

		for (int i = 0; i < a.size(); ++i)
		{
			if (!(a[i] & (1 << bt)))++cnt;
		}
		if (cnt > 1)
		{
			vector<int> ta;
			for (int i = 0; i < a.size(); ++i)
			{
				if (!(a[i] & (1 << bt)))ta.pbc(a[i]);
			}
			a = ta;
		}
		else ans |= (1 << bt);
	}
	return ans;
}
signed main()
{
	fastio();
	int n;
	cin >> n;
	vector<int> a(1 << n);
	vin(a);
	vector<pair<int, int>> dp(1 << n, { -inf,-inf });
	map<int, vector<int>> indices;
	for (int i = 0; i < a.size(); ++i) indices[a[i]].pbc(i);
	set<int> cnt;
	vector<int> pmax(1 << n);
	for (int i = 0; i < (1 << n); ++i)
	{
		if (cnt.count(a[i]))continue;
		if (dp[i].first == -inf)
		{
			dp[i].first = a[i];
			continue;
		}
		if (dp[i].second == -inf)
		{
			dp[i].second = a[i];
		}
		cnt.insert(a[i]);
	}
	for (auto i : indices)
	{
		if (i.second.size() > 1)
		{
			pmax[kekor(i.second)] = max(2 * i.first, pmax[kekor(i.second)]);
		}
	}
	for (int mask = 0; mask < (1 << n); ++mask)
	{
		for (int bt = 0; bt < n; ++bt)
		{
			if ((1 << bt) & mask) continue;
			int tmask = (mask | (1 << bt));
			dp[mask | (1 << bt)] = merge(dp[mask], dp[mask | (1 << bt)]);
		}
	}
	for (int i = 1; i < (1 << n); ++i)
	{
		pmax[i] = max({ pmax[i], pmax[i - 1], dp[i].first + dp[i].second });
	}
	for (int i = 1; i < (1 << n); ++i)
	{
		cout << pmax[i] << '\n';
	}
	//	sp;
}


Measured memory_bytes: 36200