/* main code starts from line 155. */

/* ---------- STL Libraries ---------- */

// IO library
#include <cstdio>
#include <iomanip>
#include <ios>
#include <iostream>

// algorithm library
#include <algorithm>
#include <cmath>
#include <numeric>

// container library
#include <array>
#include <bitset>
#include <map>
#include <queue>
#include <set>
#include <string>
#include <vector>

/* ---------- Namespace ---------- */

using namespace std;

/* ---------- Type Abbreviation ---------- */

template <typename T>
using V = vector<T>;
template <typename T, typename U>
using P = pair<T, U>;
template <typename T>
using PQ = priority_queue<T>;
template <typename T>
using GPQ = priority_queue<T, vector<T>, greater<T>>;

using ll = long long;

#define fst first
#define snd second
#define pb push_back
#define mp make_pair
#define mt make_tuple

/* ---------- conversion ---------- */

#define INT(c) static_cast<int>(c)
#define CHAR(n) static_cast<char>(n)
#define LL(n) static_cast<ll>(n)
#define DOUBLE(n) static_cast<double>(n)

/* ---------- container ---------- */

#define ALL(v) (v).begin(), (v).end()
#define SIZE(v) (LL((v).size()))

#define FIND(v, k) (v).find(k) != (v).end()
#define VFIND(v, k) find(ALL(v), k) != (v).end()

#define SORT(v) sort(ALL(v))
#define GSORT(v) sort(ALL(v), greater<decltype((v).front())>())
#define gsort(b, e) sort(b, e, greater<decltype(*b)>())

/* ---------- repetition ---------- */

#define FOR(i, a, b) for (ll i = (a); i <= (b); i++)
#define RFOR(i, a, b) for (ll i = (a); i >= (b); i--)

/* ----------- debug ---------- */

template <typename T, typename U>
void testP2(T a, U b) {
    cout << "(" << a << ", " << b << ")" << endl;
    return;
}

template <typename T>
void testV(T v) {
    cout << "[";
    for (auto i : v) {
        cout << i << ", ";
    }
    cout << "\b\b]" << endl;
    return;
}

template <typename T>
void testV2(T v) {
    for (auto sv : v) {
        testV(sv);
    }
    cout << endl;
    return;
}

#define GET_VAR_NAME(variable) #variable
#define test(x) cout << GET_VAR_NAME(x) << " = " << x << endl;
#define testP(p)                      \
    cout << GET_VAR_NAME(p) << " = "; \
    testP2(p.fst, p.snd);

/* ---------- Constants ---------- */

// const ll MOD = 1e9 + 7;
// const int INF = 1 << 25;
// const ll INF = 1LL << 50;
// const double PI = acos(-1);
// const double EPS = 1e-10;
// const ll dx[4] = {0, -1, 1, 0};
// const ll dy[4] = {-1, 0, 0, 1};

/* ---------- Short Functions ---------- */

template <typename T>
T sq(T a) {
    return a * a;
}

template <typename T>
T gcd(T a, T b) {
    if (a > b) return gcd(b, a);
    return a == 0 ? b : gcd(b % a, a);
}

template <typename T, typename U>
T mypow(T b, U n) {
    if (n == 0) return 1;
    if (n == 1) return n /* % MOD */;
    if (n % 2 == 0) {
        return mypow(sq(b) /* % MOD */, n / 2);
    } else {
        return mypow(b, n - 1) * b /* % MOD */;
    }
}

#define fcout cout << fixed << setprecision(10)


/* v-v-v-v-v-v-v-v-v Main Part v-v-v-v-v-v-v-v-v */

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    ll N;
    cin >> N;

    ll dp[1 << N][2];
    // dp[i] = s in iなるsでA[s]が大きいもの上位2つ

    FOR(i, 0, (1 << N) - 1) {
        cin >> dp[i][0];
        dp[i][1] = 0;
    }

    FOR(i, 0, N - 1) {
        FOR(b, 0, (1 << N) - 1) {
            if ((b >> i) & 1) {
                FOR(j, 0, 1) {
                    if (dp[b][1] < dp[b ^ (1 << i)][j]) {
                        dp[b][1] = dp[b ^ (1 << i)][j];
                        gsort(dp[b], dp[b] + 2);
                    }
                }
            }
        }
    }

    ll ans = 0;
    FOR(b, 1, (1 << N) - 1) {
        ans = max(ans, dp[b][0] + dp[b][1]);
        cout << ans << endl;
    }

    return 0;
}


Measured memory_bytes: 7168