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.BufferedReader;

import java.io.PrintWriter;

import java.io.InputStreamReader;

import java.io.IOException;

import java.util.StringTokenizer;

public class Main {
    
    static Scanner in = new Scanner();
    static PrintWriter out = new PrintWriter(System.out);
    
    public static void main(String[] args) throws IOException {
        int n = in.nextInt(), t = 0, l[] = new int[n];
        for(int i = n-1; i > -1; i--)
            l[i] = in.nextInt();
        for(int i = n-1; i > 0; i--) {
            if(l[i] > 0) {
                int a = 1;
                while(a * 2 <= i)
                    a *= 2;
                l[i-a] += l[i];
                t += l[i];
            }
            out.println(t);
        }
        out.close();
    }
    
    static class Scanner {
        BufferedReader br;
        StringTokenizer st;
        
        public Scanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
            st = new StringTokenizer("");
        }
        
        public String next() throws IOException {
            if(!st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
        
        public String nextLine() throws IOException {
            if(!st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            String r = st.nextToken("\n");
            st = new StringTokenizer(br.readLine(), " ");
            return r;
        }
        
        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
        
        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }
}