#include <bits/stdc++.h>
#define int long long
#define lint long long
#define pii pair<int,int>
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(c) (c).begin(),(c).end()
#define ZERO(a) memset(a,0,sizeof(a))
#define MINUS(a) memset(a,0xff,sizeof(a))
#define MINF(a) memset(a,0x3f,sizeof(a))
#define POW(n) (1LL<<(n))
#define IN(i,a,b) (a <= i && i <= b)
using namespace std;
template <typename T> inline bool CHMIN(T& a,T b) { if(a>b) { a=b; return 1; } return 0; }
template <typename T> inline bool CHMAX(T& a,T b) { if(a<b) { a=b; return 1; } return 0; }
template <typename T> inline void SORT(T& a) { sort(ALL(a)); }
template <typename T> inline void REV(T& a) { reverse(ALL(a)); }
template <typename T> inline void UNI(T& a) { sort(ALL(a)); a.erase(unique(ALL(a)),a.end()); }
template <typename T> inline T LB(vector<T>& v, T a) { return *lower_bound(ALL(v),a); }
template <typename T> inline int LBP(vector<T>& v, T a) { return lower_bound(ALL(v),a) - v.begin(); }
template <typename T> inline T UB(vector<T>& v, T a) { return *upper_bound(ALL(v),a); }
template <typename T> inline int UBP(vector<T>& v, T a) { return upper_bound(ALL(v),a) - v.begin(); }
template <typename T1, typename T2> ostream& operator<< (ostream& os, const pair<T1,T2>& p) { os << p.first << " " << p.second; return os; }
template <typename T1, typename T2> istream& operator>> (istream& is, pair<T1,T2>& p) { is >> p.first >> p.second; return is; }
template <typename T> ostream& operator<< (ostream& os, const vector<T>& v) { REP(i,v.size()) { if (i) os << " "; os << v[i]; } return os; }
template <typename T> istream& operator>> (istream& is, vector<T>& v) { for(T& in : v) is >> in; return is; }
template <typename T = int> vector<T> make_v(size_t a) { return vector<T>(a); }
template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts) { return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...)); }
template <typename T, typename V> typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) { t = v; }
template <typename T, typename V> typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e,v); }
const lint MOD = 1000000007;
const lint INF = 0x3f3f3f3f3f3f3f3f;
const double EPS = 1e-10;

template <typename T>
vector<T> zeta(function<T(T, T)> func, vector<T> f, bool s_is_subset) {
    int n = f.size();
    int k = (int)log2(n + EPS);
    if (s_is_subset) {  // Sを部分集合としてもつ集合Tについて
        for (int i = 0, m = 1; i < k; ++i, m <<= 1) {
            for (int j = 0; j < n; ++j) {
                if (!(j & m))
                    f[j] = func(f[j], f[j | m]);
            }
        }
    } else {    // Sの部分集合Tについて
        for (int i = 0, m = 1; i < k; ++i, m <<= 1) {
            for (int j = 0; j < n; ++j) {
                if (j & m)
                    f[j] = func(f[j], f[j ^ m]);
            }
        }
    }
    return f;
}

void _main() {
    int N;
    cin >> N;
    vector<int> A(1 << N);
    cin >> A;
    vector<pii> f(1 << N);
    REP(i, 1 << N) f[i] = pii(A[i], -1);
    auto func = [](pii p, pii q) {
        vector<int> tmp;
        tmp.push_back(p.first);
        if (p.second >= 0) tmp.push_back(p.second);
        tmp.push_back(q.first);
        if (q.second >= 0) tmp.push_back(q.second);
        SORT(tmp);
        return pii(tmp[tmp.size() - 1], tmp[tmp.size() - 2]);
    };
    f = zeta<pii>(func, f, false);
    int ans = -INF;
    for (int i = 1; i < 1 << N; i++) {
        CHMAX(ans, f[i].first + f[i].second);
        cout << ans << endl;
    }
}

signed main(signed argc, char **argv) {
    if (argc > 1) {
        freopen("input.txt", "r", stdin);
        freopen("output.txt", "w", stdout);
    }
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    _main();
    return 0;
}

Measured memory_bytes: 10496