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A3. Educational Game

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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 *a*_{i} numbered from 1 to *n*. The goal of the game is to make numbers *a*_{1}, *a*_{2}, ..., *a*_{k} (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 *a*_{i} > 0 and an integer *t* (*t* ≥ 0) such that *i* + 2^{t} ≤ *n*. After the values of *i* and *t* have been selected, the value of *a*_{i} is decreased by 1, and the value of *a*_{i + 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 *a*_{i}. 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 *a*_{i} (0 ≤ *a*_{i} ≤ 10^{4}), 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*≤ 10^{5}

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 *a*_{i} 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

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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