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.util.*;
import java.io.*;
public class A178 {
public static void main(String[] args) throws IOException
{
    FS input = new FS(System.in);
    int n = input.nextInt();
    int[] as = new int[n];
    long[] res = new long[n-1];
    for(int i = 0; i<n-1; i++)
    {
        as[i] += input.nextInt();
        //if(as[i] == 0) continue;
        int max = i+1;
        for(int j = 0; j<20; j++)
        {
            if(i+(1<<j) < n) max = Math.max(max,  i+(1<<j)); 
        }
        res[i] = i == 0 ? 0 : res[i-1];
        res[i] += as[i];
        as[max] += as[i];
        //if(max < n-1)res[max]+=as[i];
        
    }
    //for(int i= 1; i<res.length; i++) res[i] += res[i-1];
    PrintWriter out = new PrintWriter(System.out);
    for(int i = 0; i<n-1; i++) out.println(res[i]);
    out.close();
}
static class FS
{
    BufferedReader br;
    StringTokenizer st;
    
    public FS(InputStream input)
    {
        br = new BufferedReader(new InputStreamReader(input));
        st = new StringTokenizer("");
    }
    
    public FS(File file) throws IOException
    {
        br = new BufferedReader(new FileReader(file));
        st = new StringTokenizer("");
    }
    
    public String next() throws IOException
    {
        if(st.hasMoreTokens())
        {
            return st.nextToken();
        }
        else
        {
            st = new StringTokenizer(br.readLine());
            return next();
        }
    }
    
    public int nextInt() throws IOException
    {
        return Integer.parseInt(next());
    }
}
}
