The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.

The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.

One move is choosing an integer i (1 ≤ i ≤ n) such that ai > 0 and an integer t (t ≥ 0) such that i + 2t ≤ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).

You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 ≤ k < n).

Input

The first input line contains a single integer n. The second line contains n integers ai (0 ≤ ai ≤ 104), separated by single spaces.

The input limitations for getting 20 points are: 

  * 1 ≤ n ≤ 300



The input limitations for getting 50 points are: 

  * 1 ≤ n ≤ 2000



The input limitations for getting 100 points are: 

  * 1 ≤ n ≤ 105

Output

Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams, or the %I64d specifier.

Examples

Input

4
1 0 1 2


Output

1
1
3


Input

8
1 2 3 4 5 6 7 8


Output

1
3
6
10
16
24
40

import java.io.*;
import java.util.*;
public class Main {
          public static void main(String args [])throws IOException{
            
            BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
            int n = Integer.parseInt(f.readLine());
            int num[] = new int [n];
            String s = f.readLine();
            StringTokenizer st= new StringTokenizer(s);
            for(int i =0 ; i< n ;i++){
                num[i]=Integer.parseInt(st.nextToken());            
            }
            int mark[] =new int [n];
            
            int number[] =new int [33];
            number[0] = 1;
            for(int i=1 ; i< 33;i++){
                number[i]=2*number[i-1];
            }
            for(int  i = 1 ; i<n ;i++){
                mark[i-1]=jisuan(i,n,number);
                
            }
//            for(int  i = 1 ; i<n ;i++){
//              System.out.println(mark[i]+" ");
//              
//            }
            long sum = 0 ;
            for(int i = 0 ; i< n/2;i++){
                
                sum=num[i]+sum;
                System.out.println(sum);
            }
            for(int i= n/2;i<n-1;i++){
                //System.out.println(sum+"$$$"+num[i]+"%%%%"+tongji(i+1,mark,num));
                 sum=sum+num[i]+tongji(i+1,mark,num);
                 System.out.println(sum);
            }
     
            
          }
        public static int jisuan(int num,int max,int number[]){
        
            
            for(int i = 0 ; i<32;i++){
                if(num+number[i]<max){
                    if(num+number[i+1]>max){
                        return num+number[i];
                    }
                }
                if(num+number[i]==max){
                    return max;
                }
                
            }
            
            return 0;
        }
        
        public static  long tongji(int n,int mark[],int num[]){
              long number = 0 ;  
            for(int i=0;i<n;i++){
                  if(mark[i]==n){
                      number +=num[i];
                      number+=tongji(i+1,mark,num);
                   }
                  
              }
            
            
            return number;
        }
        
       
          
          
}

