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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.StringTokenizer;

/**
 * Main
 */
public class Main {

    public static void main(String[] args) {
        InputReader ir = new InputReader();
        OutputWriter ow = new OutputWriter();

        int n = ir.nextInt();

        int[] numbers = new int[n];

        for (int i = 0; i < n; i++) {
            numbers[i] = ir.nextInt();
        }

        int numberOfMoves = 0;

        for (int i = 0; i < n - 1; i++) {
            if (numbers[i] == 0) {
                ow.println(numberOfMoves);
                continue;
            }

            int t = 0;

            while (i + Math.pow(2, t) < n) {
                t++;
            }

            t--;

            numbers[i + (int) Math.pow(2, t)] += numbers[i];
            numberOfMoves += numbers[i];            

            ow.println(numberOfMoves);
        }

        ow.flush();
    }


}

////////////////////////// IO /////////////////////////////////////////////
class InputReader {
    private BufferedReader br;
    private StringTokenizer st;

    InputReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    String nextLine() {
        String s = "";
        try {
            s = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return s;
    }

    String next() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        return st.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }
}

class OutputWriter {
    private BufferedWriter bw;

    OutputWriter() {
        bw = new BufferedWriter(new OutputStreamWriter(System.out));
    }

    void print(String s) {
        try {
            bw.write(s, 0, s.length());
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    void println(String s) {
        print(s);
        try {
            bw.newLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    void print(int x) {
        print(Integer.toString(x));
    }

    void println(int x) {
        println(Integer.toString(x));
    }

    void flush() {
        try {
            bw.flush();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}