#include <bits/stdc++.h>
using namespace std;

#define times(n, i)      uptil(0, n, i)
#define rtimes(n, i)     downto((n) - 1, 0, i)
#define upto(f, t, i)    for(auto i##0_to = (t), i = decltype(t)(f); i <= i##0_to; i++)
#define uptil(f, t, i)   for(auto i##0_to = (t), i = decltype(t)(f); i <  i##0_to; i++)
#define downto(f, t, i)  for(auto i##0_to = decltype(f)(t), i = (f); i >= i##0_to; i--)
#define downtil(f, t, i) for(auto i##0_to = decltype(f)(t), i = (f); i >  i##0_to; i--)
using LD = long double;
#define double LD
#define long long long
#define LL long
#define int long
template<class T> using vec = vector<T>;
using VB = vec<bool>;   using WB = vec<VB>;
using VC = vec<char>;   using WC = vec<VC>;
using VI = vec<int>;    using WI = vec<VI>;
using VD = vec<double>; using WD = vec<VD>;
using VS = vec<string>; using WS = vec<VS>;
using PI = pair<int, int>;  using VPI = vec<PI>; using WPI = vec<VPI>;
using MI = map<int, int>;   using VMI = vec<MI>;

#if defined(EBUG) && !defined(ONLINE_JUDGE)
    #define debug true
    #define _GLIBCXX_DEBUG
    #define _LIBCPP_DEBUG 2
    #define _LIBCPP_DEBUG2 2
    #define ln << endl
    #define dd(x) cerr << #x << " = " << (x) << ", "
    #define ddd(x) cerr << #x << " = " << (x) ln
#else
    #define debug false
    #define ln << '\n'
    #define dd(x) cerr
    #define ddd(x) cerr
#endif
#define tb << '\t'
#define sp << ' '
#define db dd
#define dbg ddd

template<class T>          inline istream& operator>>(istream& s, vec<T>& v) { for(auto&& p : v) s >> p; return s; }
template<class T, class S> inline ostream& operator<<(ostream&, const pair<T, S>&);
template<class T>          inline ostream& operator<<(ostream&, const vec<T>&);
template<class T, class S> inline ostream& operator<<(ostream&, const map<T, S>&);
#define DEFINE_ITER_OUTPUT(s, x, sep) { int i = 0; for(const auto& x##0_elem : x) { if(i++) s << sep; s << x##0_elem; } return s; }
template<class T, class S> inline ostream& operator<<(ostream& s, const pair<T, S>& p) { return s << "(" << p.first << "," << p.second << ")"; }
template<class T>          inline ostream& operator<<(ostream& s, const vec<T>& v) DEFINE_ITER_OUTPUT(s, v, ' ')
template<class T, class S> inline ostream& operator<<(ostream& s, const map<T, S>& m) DEFINE_ITER_OUTPUT(s, m, ' ')
template<class T>          inline ostream& operator<<(ostream& s, const vec<vec<T>>& w) DEFINE_ITER_OUTPUT(s, w, '\n')
template<class T, class S> inline ostream& operator<<(ostream& s, const vec<map<T, S>>& vm) DEFINE_ITER_OUTPUT(s, vm, '\n')


void solve();

signed main() {
    if(!debug) {
        cin.tie(0);
        ios::sync_with_stdio(0);
    }
    cout << fixed << setprecision(20);
    cerr << fixed << setprecision(20);

    solve();

    return 0;
}

void solve() {
// N N(A)
/* <foxy.memo-area> */
int N;cin>>N;
    int NB = 1 << N;
VI A(NB);times(NB,Ri_0){cin>>A[Ri_0];}
/* </foxy.memo-area> */

    WI mx(NB);
    times(NB, i) {
        mx[i].push_back(i);
        times(N, b) {
            int j = i & ~(1 << b);
            if(i == j) continue;
            // cerr << j ln;
            for(int m : mx[j]) {
                mx[i].push_back(m);
            }
        }
        // cerr << i << "* " << mx[i] ln;
        sort(mx[i].begin(), mx[i].end(), [&](int p, int q) { return A[p] > A[q]; });
        mx[i].erase(unique(mx[i].begin(), mx[i].end()), mx[i].end());
        mx[i].resize(2);
        // cerr << i << ": " << mx[i] ln;
    }

    int ans = INT_MIN;
    uptil(1, NB, i) {
        ans = max(ans, A[mx[i][0]] + A[mx[i][1]]);
        cout << ans ln;
    }
}


Measured memory_bytes: 73088