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 static java.util.Arrays.deepToString;

import java.io.*;
import java.math.*;
import java.util.*;

public class A {

	static long[] solve(int[] a) {
		long[] res = new long[a.length - 1];
		long cur = 0;
		for (int i = 0; i < a.length - 1; i++) {
			cur += a[i];
			a[nextPos(i, a.length)] += a[i];
			res[i] = cur;
		}
		return res;
	}

	static int nextPos(int i, int n) {
		int t = 1;
		while (i + 2 * t < n)
			t *= 2;
		return i + t;
	}

	public static void main(String[] args) throws Exception {
		reader = new BufferedReader(new InputStreamReader(System.in));
		writer = new PrintWriter(System.out);

		setTime();
		int n = nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = nextInt();
		}
		long[] res = solve(a);
		for (long b : res) {
			writer.println(b);
		}
		printTime();
		printMemory();

		writer.close();
	}

	static BufferedReader reader;
	static PrintWriter writer;
	static StringTokenizer tok = new StringTokenizer("");
	static long systemTime;

	static void debug(Object... o) {
		System.err.println(deepToString(o));
	}

	static void setTime() {
		systemTime = System.currentTimeMillis();
	}

	static void printTime() {
		System.err.println("Time consumed: " + (System.currentTimeMillis() - systemTime));
	}

	static void printMemory() {
		System.err.println("Memory consumed: " + (Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()) / 1000 + "kb");
	}

	static String next() {
		while (!tok.hasMoreTokens()) {
			String w = null;
			try {
				w = reader.readLine();
			} catch (Exception e) {
				e.printStackTrace();
			}
			if (w == null)
				return null;
			tok = new StringTokenizer(w);
		}
		return tok.nextToken();
	}

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

	static long nextLong() {
		return Long.parseLong(next());
	}

	static double nextDouble() {
		return Double.parseDouble(next());
	}

	static BigInteger nextBigInteger() {
		return new BigInteger(next());
	}
}