#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
	#include <boost/multiprecision/cpp_int.hpp>
	#include <boost/multiprecision/cpp_dec_float.hpp>
	using bll = boost::multiprecision::cpp_int;
	using bdouble = boost::multiprecision::cpp_dec_float_100;
#endif
#ifdef LOCAL_DEV
	void debug_impl() { std::cerr << '\n'; }
	template<typename Head, typename... Tail> void debug_impl(Head head, Tail... tail) { std::cerr << " " << head << (sizeof...(tail) ? "," : ""); debug_impl(tail...); }
	#define debug(...) do { std::cerr << "(" << #__VA_ARGS__ << ") ="; debug_impl(__VA_ARGS__); } while (false)
#else
	#define debug(...) do {} while (false)
#endif
#ifdef LOCAL_TEST
	#define BOOST_STACKTRACE_USE_ADDR2LINE
	#define BOOST_STACKTRACE_ADDR2LINE_LOCATION /usr/local/opt/binutils/bin/addr2line
	#define _GNU_SOURCE
	#include <boost/stacktrace.hpp>
	namespace std {
		template<typename T> class dvector : public std::vector<T> {
		public:
			dvector() : std::vector<T>() {}
			explicit dvector(size_t n, const T& value = T()) : std::vector<T>(n, value) {}
			dvector(const std::vector<T>& v) : std::vector<T>(v) {}
			dvector(const std::initializer_list<T> il) : std::vector<T>(il) {}
			dvector(const typename std::vector<T>::iterator first, const typename std::vector<T>::iterator last) : std::vector<T>(first, last) {}
			dvector(const std::string::iterator first, const std::string::iterator last) : std::vector<T>(first, last) {}
			T& operator[](size_t n) {
				try { return this->at(n); } catch (const std::exception& e) {
					std::cerr << boost::stacktrace::stacktrace() << '\n'; return this->at(n);
				}
			}
			const T& operator[](size_t n) const {
				try { return this->at(n); } catch (const std::exception& e) {
					std::cerr << boost::stacktrace::stacktrace() << '\n'; return this->at(n);
				}
			}
		};
	}
	class dbool {
	private:
		bool boolvalue;
	public:
		dbool() : boolvalue(false) {}
		dbool(bool b) : boolvalue(b) {}
		dbool(const dbool& b) : boolvalue(b.boolvalue) {}
		operator bool&() { return boolvalue; }
		operator const bool&() const { return boolvalue; }
	};
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::dvector<T>& v) {
		for (size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::dvector<std::dvector<T>>& vv) {
		s << "\n"; for (size_t i = 0; i < vv.size(); ++i){ s << vv[i] << "\n"; } return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::set<T>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::multiset<T>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
	template <typename T, size_t N> std::ostream& operator<<(std::ostream& s, const std::array<T, N>& a) {
		s << "{ "; for (size_t i = 0; i < N; ++i){ s << a[i] << "\t"; } s << "}"; return s; }
	template<typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::map<T1, T2>& m) {
		s << "{\n"; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << "\n"; } s << "}"; return s; }
	template<typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::pair<T1, T2>& p) {
		return s << "(" << p.first << ", " << p.second << ")"; }
	#define vector dvector
	#define bool dbool
	class SIGFPE_exception : std::exception {};
	class SIGSEGV_exception : std::exception {};
	void catch_SIGFPE(int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGFPE_exception();	}
	void catch_SIGSEGV(int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGSEGV_exception(); }
	signed convertedmain();
	signed main() { signal(SIGFPE, catch_SIGFPE); signal(SIGSEGV, catch_SIGSEGV); return convertedmain(); }
	#define main() convertedmain()
#endif
//#define int long long
using ll = long long;
//constexpr int INF = 1e9;//INT_MAX=(1<<31)-1=2147483647
constexpr ll INF = (ll)1e18;//(1LL<<63)-1=9223372036854775807
constexpr ll MOD = (ll)1e9 + 7;
constexpr double EPS = 1e-9;
constexpr ll dx[4] = {1LL, 0LL, -1LL, 0LL};
constexpr ll dy[4] = {0LL, 1LL, 0LL, -1LL};
constexpr ll dx8[8] = {1LL, 0LL, -1LL, 0LL, 1LL, 1LL, -1LL, -1LL};
constexpr ll dy8[8] = {0LL, 1LL, 0LL, -1LL, 1LL, -1LL, 1LL, -1LL};
#define rep(i, n)   for(ll i=0, i##_length=(n); i< i##_length; ++i)
#define repeq(i, n) for(ll i=1, i##_length=(n); i<=i##_length; ++i)
#define rrep(i, n)   for(ll i=(n)-1; i>=0; --i)
#define rrepeq(i, n) for(ll i=(n)  ; i>=1; --i)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
void p() { std::cout << '\n'; }
template<typename Head, typename... Tail> void p(Head head, Tail... tail) { std::cout << head << (sizeof...(tail) ? " " : ""); p(tail...); }
template<typename T> inline void pv(std::vector<T>& v) { for(ll i=0, N=v.size(); i<N; i++) std::cout << v[i] << " \n"[i==N-1]; }
template<typename T> inline T gcd(T a, T b) { return b ? gcd(b,a%b) : a; }
template<typename T> inline T lcm(T a, T b) { return a / gcd(a,  b) * b; }
template<typename T> inline bool chmax(T& a, T b) { return a < b && (a = b, true); }
template<typename T> inline bool chmin(T& a, T b) { return a > b && (a = b, true); }
template<typename T> inline void uniq(std::vector<T>& v) { v.erase(std::unique(v.begin(), v.end()), v.end()); }

/*-----8<-----template-----8<-----*/

template< typename Monoid, typename F >
class SegmentTree {
public:
	ll sz;
	vector< Monoid > seg;
	const F f;
	const Monoid M1;

	SegmentTree(ll n, const F f, const Monoid &M1) : f(f), M1(M1) {
		sz = 1;
		while(sz < n) sz <<= 1;
		seg.assign(2 * sz, M1);
	}

	void set(ll k, const Monoid &x) {
		seg[k + sz] = x;
	}

	void build() {
		for(ll k = sz - 1; k > 0; k--) {
			seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
		}
	}

	void update(ll k, const Monoid &x) {
		k += sz;
		seg[k] = x;
		while(k >>= 1) {
			seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
		}
	}

	Monoid query(ll a, ll b) {
		Monoid L = M1, R = M1;
		for(a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
			if(a & 1) L = f(L, seg[a++]);
			if(b & 1) R = f(seg[--b], R);
		}
		return f(L, R);
	}

	Monoid operator[](const ll &k) const {
		return seg[k + sz];
	}

	template< typename C >
	ll find_subtree(ll a, const C &check, Monoid &M, bool type) {
		while(a < sz) {
			Monoid nxt = type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
			if(check(nxt)) a = 2 * a + type;
			else M = nxt, a = 2 * a + 1 - type;
		}
		return a - sz;
	}

	template< typename C >
	ll find_first(ll a, const C &check) {
		Monoid L = M1;
		if(a <= 0) {
			if(check(f(L, seg[1]))) return find_subtree(1, check, L, false);
			return -1;
		}
		ll b = sz;
		for(a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
			if(a & 1) {
				Monoid nxt = f(L, seg[a]);
				if(check(nxt)) return find_subtree(a, check, L, false);
				L = nxt;
				++a;
			}
		}
		return -1;
	}

	template< typename C >
	ll find_last(ll b, const C &check) {
		Monoid R = M1;
		if(b >= sz) {
			if(check(f(seg[1], R))) return find_subtree(1, check, R, true);
			return -1;
		}
		ll a = sz;
		for(b += sz; a < b; a >>= 1, b >>= 1) {
			if(b & 1) {
				Monoid nxt = f(seg[--b], R);
				if(check(nxt)) return find_subtree(b, check, R, true);
				R = nxt;
			}
		}
		return -1;
	}
};
template< typename Monoid, typename F >
std::ostream& operator<<(std::ostream& s, SegmentTree<Monoid,F>& seg) { 
	for(ll i=0; i<seg.sz; i++) s << seg[i] << "\t\n"[i==seg.sz-1];
	return s;
}

vector<pair<ll,ll>> zetatransform2(vector<ll> a) {
	auto ilog2 = [](ll x) {
		ll y = 0; while (x > 1) x /= 2, ++y; return y;
	};
	ll N = a.size(), bitsize = ilog2(N);
	vector<pair<ll,ll>> dp(N);
	debug(N,bitsize);
	rep(i,N)dp[i].first=a[i],dp[i].second=0;

	for (ll i=0,b=1; i<bitsize; ++i,b<<=1) { // m = (1<<i)
		for (ll j=0; j<N; ++j) {
			if (j & b) {
				vector<ll> v{dp[j].first, dp[j].second, dp[j ^ b].first, dp[j ^ b].second};
				sort(rall(v));
				dp[j].first=v[0];
				dp[j].second=v[1];
			}
		}
	}
	return dp;
}
/*-----8<-----library-----8<-----*/

void solve() {
	ll N;
	cin>>N;
	vector<ll> a((1LL<<N),0);
	rep(i,1LL<<N)cin>>a[i];


	vector<pair<ll,ll>> dp = zetatransform2(a);
	debug(dp);

	auto F = [](ll x,ll y){return max(x,y);}; //0LL
	SegmentTree<ll,decltype(F)> seg(1LL<<N, F, -INF);
	rep(i,1LL<<N)seg.set(i, dp[i].first+dp[i].second);
	seg.build();
	debug(seg);

	vector<ll> ans(1LL<<N);
	repeq(i,(1LL<<N)-1){
		ll t=seg.query(0,i+1);
		ans[i-1]=t;
	}
	rep(i,(1LL<<N)-1)p(ans[i]);
}

signed main() {
	solve();
	return 0;
}


Measured memory_bytes: 15484