#include <iostream>
#include <iomanip>
#include <fstream>
#include <string>
#include <array>
#include <vector>
#include <deque>
#include <list>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <stack>
#include <queue>
#include <bitset>
#include <tuple>
#include <cmath>
#include <complex>
#include <algorithm>
#include <utility>
#include <regex>
#include <cstdint>
#include <numeric>
#include <functional>
#include <cassert>

using namespace std;
using ll = long long;
using ull = unsigned long long;

constexpr ll INF = 1'000'000'000'000'000'000;
namespace utils{
#define ALL(x) begin(x), end(x)
#define rALL(x) rbegin(x), rend(x)
    template<class T, class Compare> using p_queue = priority_queue<T, vector<T>, Compare>;
    template<class T> using min_queue = p_queue<T, greater<T>>;
    template<class T> using max_queue = p_queue<T, less<T>>;

    template<class T> bool min_update(T& X, const T& A){ if(X > A) {X = A; return true;} return false; }
    template<class T> bool max_update(T& X, const T& A){ if(X < A) {X = A; return true;} return false; }
    using V_Set = unordered_set<int>;
    using E_Set = unordered_map<int, V_Set>;

    ll operator"" _64(unsigned long long x){ return ll(x); }
    ull operator"" _64u(unsigned long long x){ return ull(x); }

    template<class T>
    vector<T> make_vector(int n, T t){
        return vector<T>(n, t);
    }
    template<class ...Ts>
    auto make_vector(int n, Ts ... ts){
        return vector<decltype(make_vector(ts...))>(n, make_vector(ts...));
    }

    template<class T>
    ostream& operator<<(ostream& os, const vector<T>& v){
        for (auto &&x : v) { os << x << ' '; } cout << endl; return os ;
    }
}
using namespace utils;

class solver{
    istream& is;
    ostream& os;
    vector<ll> A;

public:
    solver(istream& I, ostream& O) :is(I), os(O) {}

    void update(pair<ll, ll>& x, const pair<ll, ll>& p){
        auto xl = A[x.first], xr = A[x.second];
        auto pl = A[p.first], pr = A[p.second];
        if(xl < pl){
            x.second = x.first;
            x.first = p.first;
            xr = A[x.second];
            if(xr < pr){
                x.second = p.second;
            }
        }
        else if(x.first != p.first and xr < pl){
            x.second = p.first;
        }
    }

    ll Asum(pair<ll, ll> x){
        return A[x.first] + A[x.second];
    }

    void run(){
        ll N;
        is >> N;
        if(!is) return;
        A.resize(1 << N);
        for (auto &&a : A) {
            is >> a;
        } // end a
        auto inf = A.size();
        A.push_back(-1);
        vector<pair<ll, ll>> dp(1<<N, {inf, inf});
        for (int i = 0; i < dp.size(); ++i) {
            update(dp[i], {i, inf});
            for (int j = 1; j < dp.size(); j *= 2) {
                if(i & j) continue;
                update(dp[i|j], dp[i]);
            } // end j
        } // end i

        ll mx = -1;
        for (int k = 1; k < dp.size(); ++k) {
            mx =  max(mx, Asum(dp[k]));
            cout << mx << endl;
        } // end k
    }

    ll mK(int K){
        ll ans = 0;
        for (int i = 0; i <= K; ++i) {
            for (int j = i + 1; j <= K; ++j) {
                if((i | j) <= K){
                    ans = max(ans, A[i] + A[j]);
                }
            } // end j
        } // end i
        return ans;
    }
};

int main(int argc, char *argv[]) {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << setprecision(16) << scientific;
#ifdef DEBUG
    string test_cases = "test_OrPlusMax.txt";
    cerr << test_cases << " -->" << endl;
    auto fs = fstream(test_cases, fstream::in);
    int loop = 0;
    while(fs) {
        loop++;
        cout << '#' << loop << "#------\n";
        solver(fs, cout).run();
    }
    if(loop <= 1) {
        cout << "===" << endl;
        while(cin) solver(cin, cout).run();
    }
#else
    solver(cin, cout).run();
#endif
    return 0;
}


Measured memory_bytes: 11132