#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <bits/stdc++.h>
/*#pragma GCC optimize("Ofast","unroll-loops","omit-frame-pointer","inline") //Optimization flags
#pragma GCC option("arch=native","tune=native","no-zero-upper") //Enable AVX
#pragma GCC target("avx2")  //Enable AVX*/

using namespace std;

using ll = long long;

#define mp make_pair

const int p = 998244353;


int mul(int a, int b) {
    return (1LL * a * b) % p;
}

int add(int a, int b) {
    int s = (a+b);
    if (s>=p) s-=p;
    return s;
}

int sub(int a, int b) {
    int s = (a+p-b);
    if (s>=p) s-=p;
    return s;
}

int po(int a, int deg)
{
    if (deg==0) return 1;
    if (deg%2==1) return mul(a, po(a, deg-1));
    int t = po(a, deg/2);
    return mul(t, t);
}

int inv(int n)
{
    return po(n, p-2);
}

/*struct DSU {
    vector<int> sz;
    vector<int> parent;

    void make_set(int v) {
        parent[v] = v;
        sz[v] = 1;
    }

    int find_set(int v) {
        if (v == parent[v])
            return v;
        return parent[v] = find_set(parent[v]);
    }

    void union_sets(int a, int b) {
        a = find_set(a);
        b = find_set(b);
        if (a != b) {
            if (sz[a] < sz[b])
                swap(a, b);
            parent[b] = a;
            sz[a] += sz[b];
        }
    }

    DSU(int n) {
        sz.resize(n);
        parent.resize(n);
        for (int i = 0; i < n; i++) make_set(i);
    }
};*/

/*const int N = 1000000;

vector<int> facs(N), invfacs(N);

void init()
{
    facs[0] = 1;
    for (int i = 1; i<N; i++) facs[i] = mul(facs[i-1], i);
    invfacs[N-1] = inv(facs[N-1]);
    for (int i = N-2; i>=0; i--) invfacs[i] = mul(invfacs[i+1], i+1);
}

int C(int n, int k)
{
    return mul(facs[n], mul(invfacs[k], invfacs[n-k]));
}*/



int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(nullptr);

    int n;
    cin>>n;
    int N = (1<<n);
    vector<int> a(N);
    for (int i = 0; i<N; i++) cin>>a[i];

    vector<pair<pair<int, int>, pair<int, int>>> F(N, {{-1, -1}, {-1, -1}});

    for(int i = 0; i<N; ++i)
        F[i].first = mp(a[i], i);



    /*for (int i = 0; i<N; i++)
    {
        cout<<i<<":\n";
        cout<<F[i].first.first<<' '<<F[i].first.second<<endl;
        cout<<F[i].second.first<<' '<<F[i].second.second<<endl;
    }*/



    for(int i = 0;i < n; ++i)
    {
        for(int mask = 0; mask < N; ++mask){
            if(mask & (1<<i))
            {
                set<pair<int, int>> kek({F[mask].first, F[mask].second, F[mask^(1<<i)].first, F[mask^(1<<i)].second});
                F[mask].first = *prev(kek.end());
                F[mask].second = *prev(prev(kek.end()));
            }
        }
        /*cout<<"\nIteration "<<i<<":\n";
        for (int i = 0; i<N; i++)
        {
            cout<<i<<":\n";
            cout<<F[i].first.first<<' '<<F[i].first.second<<endl;
            cout<<F[i].second.first<<' '<<F[i].second.second<<endl;
        }*/

    }




    for (int i = 1; i<N; i++)
    {
        int res = 0;
        for (int bit = n-1; bit>=0; bit--) if (i&(1<<bit))
        {
            int cur = (i^(1<<bit))|((1<<bit)-1);
            res = max(res, F[cur].first.first + F[cur].second.first);
        }
        res = max(res, F[i].first.first + F[i].second.first);
        cout<<res<<'\n';
    }

}




Measured memory_bytes: 8192