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

#define NDEBUG
#ifdef DEBUG
#include "../cout11.h"
#undef NDEBUG
#endif
#include <cassert>

typedef long long ll;
typedef long double Double;
typedef unsigned long long ull;
typedef pair<int,int> ii;
typedef pair<ll,ll> llll;
typedef pair<double,double> dd;

typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<ii> vii;
typedef vector<vector<ii>> vvii;
typedef vector<ll> vll;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<long double> vD;

#define sz(a)  int((a).size())
#define pb  push_back
#define FOR(var,from,to) for(int var=(from);var<=(to);++var)
#define rep(var,n)  for(int var=0;var<(n);++var)
#define rep1(var,n)  for(int var=1;var<=(n);++var)
#define repC2(vari,varj,n)  for(int vari=0;vari<(n)-1;++vari)for(int varj=vari+1;varj<(n);++varj)
#define ALL(c)  (c).begin(),(c).end()
#define RALL(c)  (c).rbegin(),(c).rend()
#define tr(i,c)  for(auto i=(c).begin(); i!=(c).end(); ++i)
#define found(s,e)  ((s).find(e)!=(s).end())
#define mset(arr,val)  memset(arr,val,sizeof(arr))
#define mid(x,y) ((x)+((y)-(x))/2)
#define IN(x,a,b) ((a)<=(x)&&(x)<=(b))
#define cons make_pair


ll gcd(ll a, ll b) { while(a) swap(a, b%=a); return b; }

const ll MOD=1000000007LL;

ll ADD(ll x, ll y) { return (x+y) % MOD; }
ll SUB(ll x, ll y) { return (x-y+MOD) % MOD; }
ll MUL(ll x, ll y) { return x*y % MOD; }
ll POW(ll x, ll e) { ll v=1; for(; e; x=MUL(x,x), e>>=1) if (e&1) v = MUL(v,x); return v; }
ll DIV(ll x, ll y) { /*assert(y%MOD!=0);*/ return MUL(x, POW(y, MOD-2)); }
// ll comb(ll n, ll k) { ll v=1; for(ll i=1; i<=k; i++) v = DIV(MUL(v, n-i+1),i); return v; }
//

#define INTSPACE 12
char _buf[INTSPACE*1000000 + 3];

int loadint() {
    if (fgets(_buf, INTSPACE+3, stdin)==NULL) return 0;
    return atoi(_buf);
}

int loadvec(vector<int>& v, int N=-1) {
    if (N == -1) {
        N = loadint();
        if (N==0) return 0;
    }
    int bufsize = INTSPACE*N + 3;
    if (fgets(_buf, bufsize, stdin)==NULL) return 0;
    v.resize(N);

    int i=0;
    bool last = false;
    for (char *p=&_buf[0]; ;) {
        char *q = p;
        while (*q > ' ') ++q;
        if (*q == 0x0D || *q == 0x0A) last = true;
        *q = 0;
        v[i++] = atoi(p);
        if (last || i == N) break;
        p = q+1;
    }
    // assert(i <= N);
    return i;
}
void read_cr() {
    fgets(_buf, 256, stdin);
}

typedef pair<ii,ii> jj;

// inline ii so(int x, int y) {
//     return ii(max(x,y), min(x,y));
// }
inline ii ou(ii& p, int x) {
    if (p.second > x) return p;
    if (p.first  > x) return ii(p.first, x);
    return ii(x, p.first);
}
inline jj ou(jj& p, ii x) {
    if (p.second.first > x.first) return p;
    if (p.first.first > x.first) return jj(p.first, x);
    return jj(x, p.first);
}
// inline int sm(ii& p) {
//     return p.first + p.second;
// }

inline int ilog2(int x) {
    int y = 0;
    while (x > 1) {
        x /= 2;
        ++y;
    }
    return y;
}

#if 0
template <typename T>
vector<T> zeta(vector<T> f) {
    // get F(S) = Σ(T⊂S)G(T)
    int N = f.size(), K = ilog2(N);
    for (int i=0,m=1; i<K; ++i,m<<=1) {
        for (int j=0; j<N; ++j)
            if (!(j & m)) f[j] += f[j | m];
    }
    return f;
}
#endif
ii mg(ii&p, ii&q) {
    vi tmp;
    tmp.pb(p.first);
    if (p.second >= 0) tmp.pb(p.second);
    tmp.pb(q.first);
    if (q.second >= 0) tmp.pb(q.second);
    sort(ALL(tmp));
    int L = tmp.size();
    return ii(tmp[L-1], tmp[L-2]);
}

vector<ii> zeta(vector<ii> f, bool moebius=false) {
    // get F(S) = Σ(T⊂S)G(T)
    int N = f.size(), K = ilog2(N);
    if (moebius) {
        for (int i=0,m=1; i<K; ++i,m<<=1)
            for (int j=0; j<N; ++j)
                if (j & m)
                    f[j] = mg(f[j], f[j ^ m]);
    } else {
        for (int i=0,m=1; i<K; ++i,m<<=1)
            for (int j=0; j<N; ++j)
                if (!(j & m))
                    f[j] = mg(f[j], f[j | m]);
    }
    return f;
}

void solve(int N,int W,vi& a) {
    vector<ii> u(W);
    rep(i, W) u[i] = ii(a[i], -1);

    vector<ii> zu = zeta(u, true);
#ifdef DEBUG
    cerr << "zeta(u):" << zu << endl;
#endif

    int smax = -1;
    for (int i=1; i<W; ++i) {
#ifdef DEBUG
        cerr << i << ") " << zu[i] << endl;
#endif
        int s = zu[i].first + zu[i].second;
        smax = max(smax, s);
        cout << smax << endl;
    }
}

int main() {
    int N = loadint();
    int W = 1 << N;
    vi a(W);
    loadvec(a, W);
    solve(N,W,a);
    // cout << (solve(N,a) ? "Yes":"No") << endl;
    return 0;
}


Measured memory_bytes: 12288