#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define llu unsigned long long
#define ld double
#define llu unsigned long long
#define rep(i,x,y)  for(int i=int(x);i<int(y);++i)
#define For(i,x,y)  for(int i=int(x);i<=int(y);++i)
#define FOr(i,x,y)  for(int i=int(x);i>=int(y);--i)
#define pi acos(-1) 
#define mk make_pair
#define pa pair<ll,ll>
#define lf else if
#define IL inline
#define sqr(x)      ((x)*(x))
#define Mul(x,y)    ((x)=1LL*(x)*(y)%mod)
#define E(x)        return writeln(x),0
#define LL          (long long)
#define p(x)        printf("~%lld~\n",LL(x))
#define pp(x,y)     printf("~~%lld %lld~~\n",LL(x),LL(y))
#define ppp(x,y,z)  printf("~~~%lld %lld %lld~~~\n",LL(x),LL(y),LL(z))
#define pppp(a,b,c,d)   printf("~~~%lld %lld %lld %lld\n",LL(a),LL(b),LL(c),LL(d))
#define f_in(x)     freopen(x".in","r",stdin)
#define f_out(x)    freopen(x".out","w",stdout)
#define open(x)     f_in(x),f_out(x)
#define fi first
#define se second
#define GuYue       puts("\nGuYueNa________________________________________________________________________________")
#define y1          fafa____
typedef complex<double> E;
namespace SHENZHEBEI{
#ifdef LOCAL
    struct _{_(){freopen("cf.in","r",stdin);}}_; 
#endif 
#define NEG 1
    static const int GYN=2333333;
    char SZB[GYN],*SS=SZB,*TT=SZB;
    inline char gc(){   if (SS==TT){  TT=(SS=SZB)+fread(SZB,1,GYN,stdin); if (SS==TT) return '\n';  }   return *SS++;    }
#if NEG
    inline ll read(){    ll x=0,g=1; char ch=gc();   for (;!isdigit(ch);ch=gc()) if (ch=='-') g=-1;  for (;isdigit(ch);ch=gc())  x=x*10-48+ch;   return x*g; }
    inline void write(ll x){    if (x<0) putchar('-'),x=-x;  if (x>=10)   write(x/10);    putchar(x%10+'0');  }
#else
    inline ll read(){    ll x=0; char ch=gc();   for (;!isdigit(ch);ch=gc());    for (;isdigit(ch);ch=gc())  x=x*10-48+ch;   return x;   }
    inline void write(ll x){    if (x>=10)   write(x/10);    putchar(x%10+'0');  }
#endif
    inline char readchar(){ char ch=gc();   for(;isspace(ch);ch=gc());  return ch;  }
    inline ll readstr(char *s){ char ch=gc();   int cur=0;  for(;isspace(ch);ch=gc());      for(;!isspace(ch);ch=gc())  s[cur++]=ch;    s[cur]='\0';    return cur; }
    void Print(long long *a,int s,int t){For(i,s,t)printf("%lld ",a[i]);puts("");}
    void Print(int *a,int s,int t){For(i,s,t)printf("%d ",a[i]);puts("");}
    void Print(char *a,int s,int t){For(i,s,t)putchar(a[i]);puts("");}
    void writeln(ll x){write(x),puts("");}
    void Max(ll &x,ll y){x=x<y?y:x;}
    void Min(ll &x,ll y){x=x>y?y:x;}
    ll min(ll x,ll y){return x<y?x:y;}
}using namespace SHENZHEBEI;
const ll N=800010;
pa mx[N],mn[N],a[10];
ll n,all,ans[N];
bool cmp(pa a,pa b){return a.fi==b.fi?(a.se<b.se):(a.fi>b.fi);}
void merge(ll x,ll y){
	a[1]=mx[x];a[2]=mn[x];a[3]=mx[y];a[4]=mn[y];
	sort(a+1,a+5,cmp);
	ll pos=0;
	mx[x]=mn[x]=mk(0,0);
	For(i,1,4)if (a[i].se!=a[i-1].se){
		if (pos==0)mx[x]=a[i],pos=1;
		lf (pos==1)return mn[x]=a[i],void(0);
	}
}
int main(){
	n=read();all=(1<<n)-1;
	For(i,0,all)mx[i]=mk(read(),i+1);
	For(i,1,all)rep(j,0,n)if (i>>j&1){
		merge(i,i^(1<<j));
	}
	For(i,1,all)ans[i]=max(ans[i-1],mx[i].fi+mn[i].fi);
	For(i,1,all)writeln(ans[i]);
}

Measured memory_bytes: 22272