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.*;
import java.math.*;
import java.awt.geom.*;

import static java.lang.Math.*;

public class Solution implements Runnable {
	
	static final double EPS = 1e-9;
	
	public void solve () throws Exception {
		int n = nextInt();
		long a [] = new long [n];
		for (int i = 0; i < n; i++) {
			a [i] = nextInt();
		}
		for (int i = 0; i < n - 1; i++) {
			int t = 1;
			while (i + t < n) {
				t *= 2;
			}
			t /= 2;
			a [i + t] += a [i];
		}
		long sum = 0;
		for (int i = 0; i < n - 1; i++) {
			sum = sum + a [i];
			out.println(sum);
		}
	}
	
	static final String fname = "";
	static final int DEBUG = 1;
	static long stime = 0;
	
	BufferedReader in;
	PrintWriter out;
	StringTokenizer st;
	
	private String nextToken () throws Exception {
		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(in.readLine());
		}
		return st.nextToken();
	}
	
	private int nextInt () throws Exception {
		return Integer.parseInt(nextToken());
	}
	
	private long nextLong () throws Exception {
		return Long.parseLong(nextToken());
	}
	
	private double nextDouble () throws Exception {
		return Double.parseDouble(nextToken());
	}
	
	@Override
	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			solve ();
		} catch (Exception e) {
			throw new RuntimeException(e);
		} finally {
			out.close();
		}
	}
	
	public static void main(String[] args) {
		new Thread(null, new Solution(), "", 1<<25).start();
	}

}