///////////////////////////////////////////////////////////////////////////////

#include <iostream>
#include <iomanip>
#include <vector>
#include <map>
#include <unordered_map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <cmath>
#include <typeinfo>
#include <numeric>
#include <cassert>
#include <stdio.h>
#include <unistd.h>
#include <string.h>

using namespace std;

///////////////////////////////////////////////////////////////////////////////

#define pb push_back
#define V vector
#define M unordered_map
#define rep(i,n) for(int i=0;i<n;++i)
#define srep(i,s,n) for(int i=s;i<n;++i)
#define rrep(i,n) for(int i=n-1;i>=0;--i)
#define ALL(a) (a).begin(),(a).end()

typedef long long ll;
typedef unsigned long long ull;
typedef tuple<ll, ll> t2;
typedef tuple<ll, ll, ll> t3;
typedef tuple<ll, ll, ll, ll> t4;

struct UnionFind
{
        ull *parent, *count, *rank;

        UnionFind(ull n) {
                parent = new ull[n+1];
                count = new ull[n+1];
                rank = new ull[n+1];
                for (ull i = 0ULL; i < n+1; ++i) {
                        parent[i] = i;
                        count[i] = 1;
                        rank[i] = 0;
                }
        }

        ull root(ull i) {
                if (parent[i] == i) return i;
                parent[i] = root(parent[i]);
                return parent[i];
        }

        void unite(ull i, ull j) {
                ull rooti = root(i);
                ull rootj = root(j);

                if (rooti == rootj) return;

                if (rank[rootj] < rank[rooti]) {
                        parent[i] = parent[j] = parent[rootj] = rooti;
                        count[rooti] += count[rootj];
                }
                else {
                        parent[i] = parent[j] = parent[rooti] = rootj;
                        count[rootj] += count[rooti];
                        if (rank[rootj] == rank[rooti]) rank[rootj]++;
                }
        }

        bool same(ull i, ull j) {
                return root(i) == root(j);
        }
};

struct BIT
{
        ll *tree;
        ll size;

        BIT(ll n, ll init) {
                tree = new ll[n+1];
                size = n;
                rep (i, n+1) tree[i] = init;
        }

        // idx is 1 origin
        void add(ll idx, ll x) {
                assert(idx > 0LL);
                while (idx <= size) {
                        tree[idx] += x;
                        idx += (idx & (-idx));
                }
        }

        // idx is 1 origin
        ll sum(ll idx) {
                assert(idx > 0LL);
                ll ret = 0LL;
                while (idx > 0LL) {
                        ret += tree[idx];
                        idx -= (idx & (-idx));
                }
                return ret;
        }
};

struct MaxFlow {
        V<ll> links[1005];
        ll capacities[1005][1005];
        ll nodes;

        MaxFlow(ll nodes) {
                // i == 0       --> S
                // i == nodes+1 --> T
                rep (i, nodes+2LL) links[i].clear();
                memset(capacities, 0, sizeof(capacities));
                this->nodes = nodes;
        }

        void add_path(ll a, ll b, ll capacity) {
                links[a].pb(b);
                links[b].pb(a);
                capacities[a][b] = capacity;
                capacities[b][a] = 0LL;
        }

        ll solve(void) {
                deque<V<ll>> q;
                ll ret = 0LL;

                for ( ; ; q.clear()) {

                        V<ll> start;
                        start.pb(0);
                        q.push_front(start);

                        bool checked[nodes+2];
                        memset(checked, 0, sizeof(checked));

                        V<ll> found;

                        for ( ; !(q.empty()); ) {
                                V<ll> path = q.front(); q.pop_front();
                                ll last = path[path.size()-1];

                                if (checked[last]) continue;
                                if (last == nodes+1) {
                                        found = path;
                                        break;
                                }

                                checked[last] = true;
                                for (auto next : (links[last])) {
                                        if (capacities[last][next] == 0) continue;
                                        V<ll> newpath(path);
                                        newpath.pb(next);
                                        q.push_front(newpath);
                                }
                        }

                        if (found.size() == 0) {
                                break;
                        }
                        else {
                                ll flowcount = capacities[found[0]][found[1]];
                                rep (i, found.size()-1) {
                                        ll src = found[i];
                                        ll dst = found[i+1];
                                        flowcount = min(flowcount, capacities[src][dst]);
                                }
                                rep (i, found.size()-1) {
                                        ll src = found[i];
                                        ll dst = found[i+1];
                                        capacities[src][dst] -= flowcount;
                                        capacities[dst][src] += flowcount;
                                }
                                ret += flowcount;
                        }
                }

                return ret;
        }
};

void llin(ll &a)
{
        cin >> a;
}

void llinl1(auto &v, ll count)
{
        for (ll i = 0LL; i < count ; ++i) {
                ll a;
                cin >> a;
                v.push_back(a);
        }
}

void llinl2(auto &v, ll count)
{
        for (ll i = 0LL; i < count ; ++i) {
                ll a, b;
                cin >> a >> b;
                v.push_back(tuple<ll, ll>(a, b));
        }
}

void llinl3(auto &v, ll count)
{
        for (ll i = 0LL; i < count ; ++i) {
                ll a, b, c;
                cin >> a >> b >> c;
                v.push_back(tuple<ll, ll, ll>(a, b, c));
        }
}

void llina(auto &v, ll count)
{
        llinl1(v, count);
}

template <typename T>
T min(const V<T> v)
{
        T ret = v[0];
        for (auto i : v) ret = min(ret, i);
        return ret;
}

template <typename T>
T max(const V<T> v)
{
        T ret = v[0];
        for (auto i : v) ret = max(ret, i);
        return ret;
}

ll absll(ll x)
{
        if (x < 0) return -x;
        return x;
}

ll mod_mlt(ll x, ll y, ll mod)
{
        ll ret = 0LL;
        x %= mod;

        while (y) {
                if (y & 1LL) {
                        ret += x;
                        ret %= mod;
                }
                y >>= 1;
                x <<= 1;
                x %= mod;
        }

        return ret;
}

ll mod_pow(ll base, ll exp, ll mod)
{
        ll ret = 1LL;

        for ( ; exp; ) {
                if (exp & 1LL) {
                        ret *= base;
                        ret %= mod;
                }
                base = (base * base) % mod;
                exp >>= 1;
        }

        return ret;
}

ll mod_inv(ll x, ll mod)
{
        // available only when mod is prime
        return mod_pow(x, mod - 2LL, mod);
}

ll gcm(ll x, ll y)
{
        while (y != 0) {
                ll z = x % y;
                x = y;
                y = z;
        }
        return x;
}

template <typename T>
void sort(V<T> &v)
{
        sort(v.begin(), v.end());
}

template <typename T>
void sort_reverse(V<T> &v)
{
        sort(v.begin(), v.end(), greater<T>());
}

void get_divisors(V<ll> &retlist, ll x)
{
        for (ll i = 1LL; i < sqrt(x) + 3LL; ++i) {
                if (x % i == 0LL) {
                        retlist.push_back(i);
                        retlist.push_back(x / i);
                }
        }
}

void get_factors(V<ll> &retlist, ll x)
{
        for (ll i = 2LL; i < (ll)(sqrt(x)) + 3LL; ++i) {
                while (x % i == 0LL) {
                        retlist.pb(i);
                        x /= i;
                }
        }
        retlist.pb(x);
}

bool is_prime(ll x)
{
        V<ll> factors, factors2;

        get_factors(factors, x);

        for (auto factor : factors) {
                if (factor > 1) factors2.pb(factor);
        }

        return factors2.size() == 1 && x == factors2[0];
}

template <typename T>
void intersection(const set<T> &a, const set<T> &b,
                  set<T> &result)
{
        V<T> resultlist;

        set_intersection(a.begin(), a.end(),
                         b.begin(), b.end(),
                         back_inserter(resultlist));

        set<T> resultset(resultlist.begin(), resultlist.end());
        result = resultset;
}

ull combination(ll x, ll y)
{
        if (y > x / 2LL) y = x - y;

        ull ret = 1LL;
        for (ll i = 0LL; i < y; ++i) {
                ret *= x--;
                ret /= (i + 1LL);
        }

        return ret;
}

ull mod_combination(ll x, ll y, ll mod)
{
        if (y > x / 2LL) y = x - y;

        ll ret = 1;

        for (ll i = 0LL; i < y; ++i) {
                ret = (ret * x--) % mod;
                ret = (ret * mod_inv(i + 1LL, mod)) % mod;
        }

        return ret;
}

void make_linklist(const V<tuple<ll, ll>> &srclist, V<V<ll>> &dstlist)
{
        for (auto src : srclist) {
                ll a = get<0>(src);
                ll b = get<1>(src);
                dstlist[a].pb(b);
                dstlist[b].pb(a);
        }
}

void debug_print(auto x)
{
        cout << x << endl;
}

void debug_print(const t2 &x)
{
        ll x1 = get<0>(x);
        ll x2 = get<1>(x);
        cout << "-- " << x1 << " -- " << x2 << endl;
}

void debug_print(const t3 &x)
{
        ll x1 = get<0>(x);
        ll x2 = get<1>(x);
        ll x3 = get<2>(x);
        cout << "-- " << x1 << " -- " << x2 << " -- " << x3 << endl;
}

void debug_print(const t4 &x)
{
        ll x1 = get<0>(x);
        ll x2 = get<1>(x);
        ll x3 = get<2>(x);
        ll x4 = get<3>(x);
        cout << "-- " << x1 << " -- " << x2
                << " -- " << x3 << " -- " << x4 << endl;
}

template <typename T>
void debug_print(T xarray[], ll n)
{
        rep (i, n) debug_print(xarray[i]);
}

template <typename T>
void debug_print(const V<T> &xlist)
{
        for (auto x : xlist) {
                cout << "-- ";
                debug_print(x);
        }
}

template <typename S, typename T>
void debug_print(const M<S, T> &xlist)
{
        for (auto x : xlist) {
                S k = x.first;
                T v = x.second;
                cout << "====" << endl;
                cout << "K=";
                debug_print(k);
                cout << "V=";
                debug_print(v);
        }
}

int _main();
int main()
{
        cout << setprecision(12);
        return _main();
}

///////////////////////////////////////////////////////////////////////////////

string pp(t2 x)
{
        char rets[256];
        sprintf(rets, "(%lld, %lld)", get<0>(x), get<1>(x));
        string ret(rets);
        return ret;
}

V<ll> a;
t2 dp[300000][20];
bool flag[300000][20];

t2 f(ll i, int bit)
{
        if (flag[i][bit]) {
                return dp[i][bit];
        }

        if ((i & -i) == (1LL << bit)) {
                int j = (i & ~(1LL << bit));
                flag[i][bit] = true;
                return dp[i][bit] = t2(max(a[i], a[j]), min(a[i], a[j]));
        }

        if (!(i & (1LL << bit))) {
                flag[i][bit] = true;
                return dp[i][bit] = f(i, bit - 1);
        }

        t2 ret1, ret2;
        ret1 = f(i, bit - 1);
        ret2 = f(i & ~(1LL << bit), bit - 1);

        ll f1 = get<0>(ret1);
        ll s1 = get<1>(ret1);
        ll f2 = get<0>(ret2);
        ll s2 = get<1>(ret2);

        flag[i][bit] = true;

        if (s1 > f2) return dp[i][bit] = t2(f1, s1);
        if (f1 > f2) return dp[i][bit] = t2(f1, f2);
        if (f1 > s2) return dp[i][bit] = t2(f2, f1);
        return dp[i][bit] = t2(f2, s2);
}

int _main()
{
        ll n;
        llin(n);
        ll m = pow(2, n);

        llina(a, m);

        rep (i, 300000) rep (j, 20) flag[i][j] = false;

        for (ll i = 1LL; i < m; ++i) {
                dp[i][n] = f(i, (int)n);
        }

        ll ans = 0LL;

        for (ll i = 1LL; i < m; ++i) {
                ans = max(ans, get<0>(dp[i][n]) + get<1>(dp[i][n]));
                cout << ans << endl;
        }

        return 0;
}

///////////////////////////////////////////////////////////////////////////////


Measured memory_bytes: 93296